JP4369333B2 - Impulse response calculation method, apparatus and program - Google Patents

Description

  The present invention relates to an impulse response calculation method, apparatus, and program, and in particular, converts dynamic stiffness representing the relationship between an external force that vibrates an object and the behavior of the object in the frequency domain into an impulse response representing the relationship in the time domain. The present invention relates to an impulse response calculation method, an impulse response calculation device to which the impulse response calculation method can be applied, and an impulse response calculation program for causing a computer to function as the impulse response calculation device.

  The ground motion (earthquake wave) that propagates from the ground during the earthquake enters the foundation of the building through the surface ground, and part of it is reflected by the foundation and the rest is transmitted to the top of the building, causing the building to vibrate. The building that is vibrated by becomes a new epicenter and releases waves to the ground. In this way, the building and the ground are affected by each other and vibrate during an earthquake, so when analyzing and evaluating the behavior of the building and the seismic safety, etc. during an earthquake by seismic response analysis, Force characteristics) must also be considered. The relationship between seismic motion and ground behavior can be expressed by ground dynamic stiffness (also referred to as ground impedance). The dynamic stiffness of the ground is represented by a complex function in the frequency domain in which the values of the real part and the imaginary part change according to the change in the frequency of vibration, and the Poisson's ratio ν, density ρ, damping rate h, layer thickness H of the ground Or the like based on the calculation.

  Earthquake response analysis is roughly divided into frequency response analysis in which response analysis is performed in the frequency domain and time history response analysis in which response analysis is performed in the time domain. As described above, since the dynamic stiffness of the ground is a complex function in the frequency domain, a frequency response analysis that can use the dynamic stiffness of the ground as it is is often used in the seismic response analysis (see, for example, Patent Document 1). . However, in the event of a large earthquake where a large amount of energy is input to the building, a part of that energy is consumed by causing cracks in the members that make up the building or by partially plasticizing each member. In addition, the behavior of the building has non-linearity because it undergoes a process in which the fracture strength of each member is repeatedly reduced due to the occurrence of cracks, partial plasticization, and the like. For this reason, in order to predict and analyze the behavior of a building at the time of an earthquake with high accuracy, the state of the building at each point in time of the earthquake (what kind of force is applied in the past, It is necessary to analyze the behavior of the building at each time point in consideration of the state). In performing time history response analysis, it is necessary to convert the ground dynamic stiffness, which is a complex function in the frequency domain, into an impulse response represented in the time domain.

As a conversion method that can convert the dynamic stiffness of the ground into an impulse response with high accuracy even when the frequency dependency of the dynamic stiffness of the ground is strong, the inventor of the present application adds to both the displacement-dependent and speed-dependent time delay components. A form having an acceleration-dependent simultaneous component is set as a general solution of the reaction force F (t) using an impulse response, and the general solution of the set reaction force F (t) and the simultaneous component of the impulse response from this general solution And N (= n + 1) ground dynamic stiffness data D (ω) at each frequency of ω _{0 to} ω _n based on the equation of ground dynamic stiffness S (ω) expressed using time delay components. A conversion method is proposed in which simultaneous equations having a coefficient matrix of 2N × 2N are set up using _i ), and components of the impulse response are obtained by solving the simultaneous equations (see Non-Patent Document 1). Further, the inventor of the present application converts the dynamic stiffness of the ground into the time domain and evaluates the characteristics of the impulse response, and performs the seismic response analysis (time history response analysis) of the structure. The effectiveness of the above conversion method has been confirmed.
JP-A-4-27829 Naohiro Nakamura, “Earthquake response analysis of structures embedded in stratified soil by time domain transformation of ground impedance, Part 2 Improvement of transformation method and response analysis based on discrete ground model”, Architectural Institute of Japan, 2003 December, 574, p. 99-106

  If the dynamic stiffness, which is a complex function in the frequency domain, includes a hysteresis damping component, the causality (the temporal order relationship in which the cause is first and the result is later) is broken when this dynamic stiffness is converted to the time domain. Therefore, conventionally, it has been considered difficult to convert dynamic stiffness including a hysteresis damping component into a time domain impulse response. On the other hand, in the technique described in Non-Patent Document 1 described above, even when a non-causal function is approximately replaced with a causal function, the dynamic rigidity to be converted includes a slight history attenuation component. The conversion to the impulse response can be performed with relatively high accuracy. However, as a result of analysis conducted by the inventor of the present application, if a relatively large hysteresis damping component is included in the dynamic stiffness to be converted, a highly accurate impulse even if the technique of Non-Patent Document 1 is applied. It became clear that no response was obtained.

  The present invention has been made in consideration of the above facts, and when the dynamic stiffness representing the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain includes a relatively large hysteresis damping component. Another object of the present invention is to obtain an impulse response calculation method, an impulse response calculation device, and an impulse response calculation program capable of accurately obtaining an impulse response that represents the relationship between the external force and the behavior of an object in the time domain from the dynamic stiffness. It is.

As shown in Fig. 1 (A), the conditions for calculating the dynamic stiffness of the ground are the seismic wave propagation velocity Vs ₂ = 400 (m / s), Poisson's ratio ν = 0.45, and density ρ = 2.0 (t / m ³ ). , _First layer of attenuation h ₁ = 0%, 10% or 20%, layer thickness H = 20 (m), seismic wave propagation velocity Vs ₂ = 800 (m / s), Poisson's ratio ν = 0.45, Assuming the condition that a 50 × 50 (m) square foundation is provided on the ground consisting of the second formation (attenuation rate h ₂ = 0%) of density ρ = 2.0 (t / m ³ ) FIGS. 1B and 1C show an example of the dynamic rigidity of the ground obtained by the thin layer element method in each case of the damping rate h ₁ = 0%, 10%, and 20% according to the calculation conditions. In FIGS. 1B and 1C, “Real” means the real part of the dynamic stiffness, and “Imag” means the imaginary part of the dynamic stiffness. In FIG. The horizontal component of the dynamic stiffness is shown in FIG. 1C, and the rotational component of the dynamic stiffness is shown in FIG.

The inventor of the present application uses the dynamic stiffness of the ground at the damping rate h ₁ = 0%, 10%, and 20% shown in FIGS. 1B and 1C, respectively, and within the frequency range of 0 to 20 (Hz). 0.25 (Hz), 1.0 (Hz), 2.0 (Hz), ... of the total dynamic data of the ground at each of the 21 types of frequencies extracted (total 21), respectively, the extracted 21 complex data In order to verify the accuracy of the obtained impulse response after obtaining each impulse response by converting to the time domain under the condition of Δt = 0.05 seconds by the conversion method described in Non-Patent Document 1 or the like, The dynamic stiffness was reproduced by reconverting the response to the frequency domain, and the reproduced dynamic stiffness was compared with the original dynamic stiffness (dynamic stiffness before conversion). The reproduced dynamic stiffness is divided into a real part and an imaginary part and shown in FIGS. In the re-conversion to the frequency domain, the displacement-dependent time delay component (fifth term in equation (1) below) and the speed-dependent time delay component (see below ( Of the fourth term in equation (1), the computation was performed for each case where the number of data to be computed is not limited (“all terms”) and when it is limited to five (“5 terms”).

2 to 4, the (original) dynamic stiffness (data used for calculation of impulse response) before conversion is shown as “data point”, but it is also apparent with reference to FIGS. 2 to 4. Thus, if the number of displacement-dependent time-delay components and velocity-dependent time-delay components to be calculated is not limited, the motion reproduced by reconverting the impulse response obtained from the dynamic stiffness into the frequency domain The dynamic stiffness is almost identical to the original dynamic stiffness at each data point, but shows a change like a component that oscillates at a relatively high frequency with respect to the original dynamic stiffness. As the damping rate h ₁ increases from 0% → 10% → 20%, the amplitude of the vibration component increases.

On the other hand, when the number of displacement-dependent time-delay components and velocity-dependent time-delay components to be calculated is limited to five, the reproduced dynamic stiffness shows a desirable characteristic that changes smoothly. The above vibration component is not added even under the conditions of the rate h ₁ = 10% and 20%. However, if the number of displacement-dependent time-delay components and speed-dependent time-delay components is limited, the real part of the reproduced dynamic stiffness will change the real part of the original dynamic stiffness in the vertical axis direction. The amount of translation (ie, the deviation between the real part of the reproduced dynamic stiffness and the real part of the original dynamic stiffness) increases as the damping rate h ₁ increases. It is increasing. Thus, it can be understood that when the dynamic stiffness to be converted includes a relatively large hysteresis damping component, an accurate impulse response cannot be obtained even if the technique of Non-Patent Document 1 is applied.

  The inventor of the present application has a relatively desirable characteristic of the reproduced dynamic rigidity when the number of data of the displacement-dependent time delay component and the speed-dependent time delay component to be calculated is limited. Of the data representing the impulse response obtained by converting the dynamic stiffness of the object, the data of the time delay component of the stiffness term that depends on the displacement of the object and the time of the decay term that depends on the velocity of the object Regarding the data of the delay component, the number of data used in the subsequent processing (for example, time history response analysis) is limited, and among the data representing the impulse response, the stiffness term that affects only the real part of the dynamic stiffness is simultaneously used. If the component data and the data of the simultaneous component of the mass term depending on the acceleration of the object are corrected according to the deviation between the dynamic stiffness reproduced from the impulse response and the original dynamic stiffness, for example, Even when a relatively large hysteresis damping component is included in the dynamic stiffness, such as when the decay rate h is relatively large, an accurate impulse response (the dynamic stiffness reproduced by converting to the frequency domain is The present invention has been made in view of the fact that an impulse response that matches the original dynamic rigidity with high accuracy can be obtained.

Based on the above, the impulse response calculation method according to the first aspect of the present invention converts the dynamic stiffness representing the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain to the impulse response representing the relationship in the time domain. In converting, the mathematical expression that defines the impulse response includes a stiffness term consisting of a simultaneous component and a time delay component depending on the displacement of the object, and an attenuation term consisting of a simultaneous component and a time delay component depending on the velocity of the object. , After calculating the impulse response based on the value of the dynamic stiffness when the vibration is at each frequency, using a mathematical formula including a mass term that depends on the acceleration of the object and includes at least a simultaneous component. time t = t ₀ tn in the data representing the impulse response of the period, the same time components of the data corresponding to the time t _0, the time t ₁ tn pieces of time delay 'n corresponds to a period' The calculation is performed to reproduce the dynamic stiffness of the object using the data of minutes (however, n ′ <n, tn ′ <Δt · n ′), and based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, Of the data representing the impulse response, the simultaneous component data of the stiffness term and the simultaneous component data of the mass term are corrected.

According to the first aspect of the present invention, the mathematical expression that defines the impulse response includes a stiffness term that includes a simultaneous component and a time delay component depending on the displacement of the object, and an attenuation term that includes the simultaneous component and the time delay component depending on the velocity of the object. And after obtaining an impulse response using a mathematical formula including a mass term that depends on the acceleration of the object and includes at least a simultaneous component (this mass term may also be composed of a simultaneous component and a time delay component) Of the data representing the impulse response during the period of time t = t _{0 to} t n, the data of the simultaneous component corresponding to time t ₀ and the time delay of n ′ corresponding to the period of time t _{1 to} tn ′ An operation for reproducing the dynamic rigidity of the object is performed using the data of the components (however, n ′ <n, tn ′ <Δt · n ′). As a result, the dynamic stiffness reproduced from the impulse response by this calculation changes smoothly even when the original dynamic stiffness includes a relatively large hysteresis damping component (vibration at a relatively high frequency). The characteristic to which the component to be added is not added).

It should be noted that the period of time t = t _{X to} tmax (according to this period, the data of the time delay component data of the stiffness term and the attenuation term used for the calculation to reproduce the dynamic stiffness (or the time history response analysis of the object described later) For example, the calculation of reproducing the dynamic rigidity is repeated while changing the period (number of the data), and the presence or absence of vibration components and the magnitude of the amplitude in the dynamic rigidity obtained by each calculation Based on the above, it is possible to determine that the reproduced dynamic stiffness does not include a vibration component or the vibration component included in the reproduced dynamic stiffness is very small.

  According to the first aspect of the present invention, based on the reproduced dynamic stiffness and the deviation between the original dynamic stiffness, the data of the simultaneous component of the stiffness term and the data of the simultaneous component of the mass term are included in the data representing the impulse response. Correct it. The data of the simultaneous component of the stiffness term and the data of the simultaneous component of the mass term depending on the acceleration of the object affect only the real part of the dynamic stiffness as described above, and are reproduced from the impulse response when each of the above data is increased or decreased. The real part characteristics of the dynamic stiffness translated in the direction approaching the direction of the real part of the original dynamic stiffness (direction in which the deviation becomes smaller) or in the direction of separation (the direction in which the deviation becomes larger). Based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the data representing the impulse response is corrected by correcting the data of the simultaneous component of the stiffness term and the data of the simultaneous component of the mass term. The impulse response can be modified so that the stiffness (particularly the characteristic of the real part) substantially matches the original dynamic stiffness. Therefore, according to the first aspect of the present invention, even when a relatively large hysteresis damping component is included in the dynamic stiffness that represents the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain, From the dynamic stiffness, an impulse response that represents the relationship between the external force and the behavior of the object in the time domain can be obtained with high accuracy.

The impulse response calculation method according to the invention of claim 2 is a method for converting the dynamic stiffness representing the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain into an impulse response representing the relationship in the time domain. The simultaneous component of the impulse response that depends on the displacement of the object is k (t ₀ ), the simultaneous component of the impulse response that depends on the velocity of the object is c (t ₀ ), and the simultaneous component of the impulse response that depends on the acceleration of the object is m ( t ₀ ), the time delay component of the impulse response depending on the displacement of the object by k (t _j ), and the time delay component of the impulse response depending on the velocity of the object by the step of Δt c (t _j ) (where j is a natural number, t _j = Δt · j), the displacement of the object in the time domain is u (t), the velocity is u '(t), and the acceleration is u "(t). As a formula that defines the reaction force F (t),

After obtaining the impulse response based on the value of the dynamic stiffness when the vibration is of N types (N = n + 1) using the above equation (1), the obtained time t = t _{0 to} tn Of the data representing the impulse response of the period, it corresponds to the data of the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to the time t ₀ and the period of the times t _{1 to} tn ′. An operation is performed to reproduce the dynamic stiffness of the object using data of n ′ time delay components k (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′), Based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the data representing the impulse response depends on the data of the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and the acceleration of the object. It is characterized by correcting the data of the simultaneous component m (t ₀ ) of the impulse response.

In the invention according to claim 2, in the mathematical expression (equation (1)) for defining the reaction force F (t) using the impulse response, the first term is the mass term in the invention of claim 1 (simultaneous with Component), the second term is the simultaneous component of the attenuation term, the third term is the simultaneous component of the stiffness term, the fourth term is the time delay component of the attenuation term, and the fifth term is the time delay component of the stiffness term. It corresponds. In the invention according to claim 2, among the data representing the determined impulse response, the data of the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to the time t ₀ , and the time t ₁ The dynamic stiffness of the object is reproduced using data of n ′ time delay components k (t _j ), c (t _j ) (n ′ <n, tn ′ <tn) corresponding to the period of tn ′ Based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object (“simultaneous component of the stiffness term” in claim 1) The data of the simultaneous component m (t ₀ ) of the impulse response depending on the data and the acceleration of the object (corresponding to the “simultaneous component of the mass term” in claim 1) is corrected. Similarly, a relatively large hysteresis damping component is included in the dynamic stiffness that expresses the relationship between the external force that vibrates an object and the behavior of the object in the frequency domain. Even if that, from the dynamic stiffness, the impulse response can be obtained accurately representing the relation between the behavior of the external force and the object in the time domain.

  Further, the calculation of the impulse response in the invention according to claim 2 is based on the equation (1) when the angular frequency of the vibration is ω, for example, as described in claim 3. , As a formula defining the dynamic stiffness S (ω) of the object,

Using the above equation (2), N complex data D (ω ₁ ),..., D (ω representing the value of the dynamic stiffness when the vibration has N frequencies from the data of the dynamic stiffness of the object. _N ) and extract the extracted N complex data

  The calculation can be performed by substituting into the above expressions (3) and (4) derived from the expressions (1) and (2).

In the invention according to claim 2, the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object in the data representing the impulse response based on the reproduced dynamic stiffness and the deviation between the original dynamic stiffness. And the data of the impulse response simultaneous component m (t ₀ ) depending on the acceleration of the object, for example, as described in claim 4, the simultaneous component k ( The correction value Δk for the simultaneous component m (t ₀ ) of the impulse response depending on the displacement of the object and the correction value Δk for t ₀ ) is minimized so that the deviation between the reproduced dynamic stiffness and the original dynamic stiffness is minimized. This can be realized by correcting each of the data of the simultaneous components k (t ₀ ) and m (t ₀ ) by using the correction values Δk and Δm obtained by the square method.

In order to confirm the effect of the present invention, the inventor of the present application expresses the dynamic stiffness shown in FIG. 2 to FIG. 4 as “time delay component = 5 term” (time delay component of the impulse response depending on the displacement of the object). (k (t _j )) and the real part of the dynamic stiffness reproduced by limiting the number of data to be calculated in the time delay component (c (t _j )) of the impulse response depending on the velocity of the object to 5 And the correction value Δk for the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and the displacement of the object so that the deviation is minimized based on the deviation of the real part of the original dynamic stiffness The correction value Δm for the simultaneous component m (t ₀ ) of the impulse response is obtained by the least square method, and the data of the simultaneous components k (t ₀ ) and m (t ₀ ) are corrected and corrected using the obtained correction values Δk and Δm. Then, use the corrected impulse response data to limit the number of data to be calculated in the same way as above. It performs an operation of reproducing the dynamic stiffness, compared to the original dynamic stiffness and unmodified dynamic stiffness. The results are shown in FIGS.

As is apparent from FIGS. 5 to 7, the real part of the dynamic stiffness reproduced from the impulse response after correction is the original dynamic stiffness (in the figure, even under the conditions of damping rate h ₁ = 10%, 20%). are shown as data points) are precisely matched, the present invention is applied, among the data representing the impulse response, co-component k (t ₀ corresponding to the time _{t 0), c (t 0} ), m (t ₀ ) and n ′ time delay components k (t _j ) and c (t _j ) corresponding to the period of time t _{1 to} tn ′ (where n ′ <n, tn ′ <Δt · n ′) Is used to calculate the dynamic stiffness of the object, and based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the simultaneous component k (t ₀ ) of the impulse response that depends on the displacement of the object by modifying the data of simultaneous component m (t ₀₎ of the impulse response that depends on the acceleration data and the object, with the understanding that the accurate impulse response is obtained That.

Further, in the invention described in claim 4, the correction value Δk for the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and the correction for the simultaneous component m (t ₀ ) of the impulse response depending on the displacement of the object. The value Δm is, for example, as described in claim 5

(S ′ (ω) is a simultaneous component k (t ₀ ) corresponding to the time t ₀ among the data representing the impulse response in the period from the time t = t _{0 to} t n, respectively. c (t ₀ ), m (t ₀ ) data and n ′ time delay components k (t _j ), c (t _j ) corresponding to the period from time t _{1 to} tn ′ (where n ′ <n , Tn ′ <Δt · n ′) can be used to represent the dynamic stiffness of the reproduced object, and simultaneous components k (t ₀ ), m (t ₀ ) data can be corrected.

Further, in the invention according to any one of claims 2 to 4, in the time history response analysis of the object, for example, as described in claim 6, impulses obtained during a period of time t = t _{0 to} tn are obtained. Of the data representing the response, data of simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ and n ′ pieces corresponding to the period of time t _{1 to} tn ′ Data of time delay components k (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′), and the difference between the reproduced dynamic stiffness and the original dynamic stiffness On the basis of the above, it is preferable to use data obtained by correcting the data of the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and the data of the simultaneous component m (t ₀ ) of the impulse response depending on the acceleration of the object. . The data of the impulse response is data that accurately matches the original dynamic rigidity by applying the present invention. Therefore, the time history response analysis can be performed with high accuracy by using this data. .

  Further, in the invention according to any one of claims 1 to 6, for example, as described in claim 7, the ground can be applied as the object, and seismic motion can be applied as the external force. The obtained ground impulse response can be used, for example, for a time history earthquake response analysis of a building.

The impulse response calculation device according to the ninth aspect of the present invention is an impulse that converts a dynamic stiffness that represents a relationship between an external force that vibrates an object and a behavior of the object in a frequency domain into an impulse response that represents the relationship in a time domain. A response arithmetic unit comprising N complex data D (ω ₁ ),... Representing dynamic stiffness values when the vibration has N types of frequencies (N = n + 1) from the dynamic stiffness data. The extraction means for extracting D (ω _N ), the simultaneous component of the impulse response depending on the displacement of the object k (t ₀ ), the simultaneous component of the impulse response depending on the velocity of the object c (t ₀ ), The simultaneous component of the impulse response that depends on the acceleration is m (t ₀ ), the time delay component of the impulse response that depends on the displacement of the object is k (t _j ), and the impulse response that depends on the velocity of the object The time delay component is c (t _j ) (where j is a natural number and t _j = Δ t · j), the N complex data extracted by the extracting means

By calculating by substituting into the above equations (3) and (4), the calculation means for obtaining the impulse response, and the data representing the impulse response during the time t = t _{0 to} tn obtained by the calculation means Among them, data of simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ and n ′ time delay components corresponding to the period of time t _{1 to} tn ′ dynamic stiffness reproduction means for performing computation to reproduce the dynamic stiffness of an object using data of k (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′); Based on the deviation between the dynamic stiffness reproduced by the dynamic stiffness reproducing means and the original dynamic stiffness, the data of the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object among the data representing the impulse response. And correction means for correcting the data of the simultaneous component m (t ₀ ) of the impulse response depending on the acceleration of the object, Therefore, as in the invention described in claim 2, when a relatively large hysteresis damping component is included in the dynamic stiffness representing the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain. However, an impulse response that represents the relationship between the external force and the behavior of the object in the time domain can be obtained with high accuracy from the dynamic stiffness.

According to an ninth aspect of the present invention, there is provided an impulse response calculation program for converting a computer to an impulse response that represents a dynamic stiffness representing a relationship between an external force that vibrates an object and a behavior of the object in a frequency domain, and representing the relationship in a time domain. An impulse response calculation program for functioning as an impulse response calculation device for conversion, wherein the computer calculates a value of dynamic stiffness when the vibration has N frequencies (N = n + 1) from the dynamic stiffness data. Extracting means for extracting _N complex data D (ω ₁ ),..., D (ω _N ), k (t ₀ ), an impulse response that depends on the displacement of the object, and an impulse that depends on the speed of the object The simultaneous component of the response is c (t ₀ ), the simultaneous component of the impulse response that depends on the acceleration of the object is m (t ₀ ), and the time delay component in Δt increments of the impulse response that depends on the displacement of the object is k (t _j ). The object N complex data extracted by the extraction means when the time delay component of the impulse response depending on the speed is c (t _j ) (where j is a natural number, t _j = Δt · j). The

By calculating by substituting into the above equations (3) and (4), the calculation means for obtaining the impulse response, the data representing the impulse response during the period of time t = t _{0 to} tn obtained by the calculation means Among them, data of simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ and n ′ time delay components k corresponding to the period of time t _{1 to} tn ′. (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′) using dynamic rigidity reproducing means for performing an operation for reproducing the dynamic rigidity of the object, Based on the deviation between the dynamic stiffness reproduced by the dynamic stiffness reproducing means and the original dynamic stiffness, the data of the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object among the data representing the impulse response. And the function of correcting the data of the simultaneous component m (t ₀ ) of the impulse response depending on the acceleration of the object. It is a feature.

  The impulse response calculation program according to the invention described in claim 9 is a program for causing a computer to function as the extraction means, the calculation means, the dynamic rigidity reproduction means, and the correction means. By executing the impulse response calculation program according to the invention, the computer functions as the impulse response calculation device according to claim 8, and similarly to the invention according to claim 8, the external force that vibrates the object and the object Even when a relatively large hysteresis damping component is included in the dynamic stiffness representing the relationship with the behavior in the frequency domain, the impulse representing the relationship between the external force and the behavior of the object in the time domain from the dynamic stiffness. A response can be obtained with high accuracy.

As described above, according to the present invention, as a mathematical expression for defining the impulse response, a stiffness term composed of a simultaneous component and a time delay component, an attenuation term composed of the simultaneous component and a time delay component, and a mass term including at least the simultaneous component. Among the data representing the impulse response during the period of time t = t _{0 to} tn, after obtaining the impulse response based on the value of the dynamic stiffness when the vibration of the object is at each frequency, Data of simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ and n ′ time delay components k (t corresponding to the period from time t _{1 to} tn ′ _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′) is used to calculate the dynamic stiffness of the object, and the reproduced dynamic stiffness and the original dynamic Based on the deviation of stiffness, among the data representing the impulse response, the data of the simultaneous component of the stiffness term and the simultaneous component of the mass term Since the data was corrected, the dynamic stiffness that expresses the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain includes a relatively large hysteresis damping component. Therefore, it has an excellent effect that an impulse response representing the relationship between the external force and the behavior of the object in the time domain can be obtained with high accuracy.

  Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 8 shows a personal computer (PC) 10 to which the present invention can be applied. The PC 10 is configured by connecting a CPU 10A, a ROM 10B, a RAM 10C, and an input / output port 10D to each other via a bus 10E including a data bus, a control bus, an address bus, and the like. The input / output port 10D is a CD 12 for reading out information from a display 12, a keyboard 14, a mouse 16, a printer 18, a hard disk drive (HDD) 20, and a CD-ROM 22 as various input / output devices. -ROM drives 24 are connected to each other.

  An earthquake response analysis program for performing an earthquake response analysis process, which will be described later, is installed in the HDD 20 of the PC 10. This earthquake response analysis program is configured to include an impulse response calculation program according to the invention of claim 9. There are several methods for installing (transferring) the earthquake response analysis program to the PC 10. For example, the earthquake response analysis program is recorded on the CD-ROM 22 together with the setup program, and the CD-ROM 22 is stored in the CD-ROM drive 24. If the CPU 10A is instructed to execute the setup program, the earthquake response analysis program is sequentially read from the CD-ROM 22, and the read earthquake response analysis program is sequentially written to the HDD 20, thereby providing an impulse. Installation of earthquake response analysis program including response calculation program. The PC 10 functions as an impulse response calculation device according to the invention of claim 8 when the CPU 10A executes an earthquake response analysis program (impulse response calculation program).

  The computer according to claim 7 is not limited to the PC 10, and may be, for example, a workstation or a general-purpose large computer.

  Next, as an operation of the present embodiment, the execution of the earthquake response analysis program is instructed via the keyboard 14 or the mouse 16 by the operator who desires to execute the earthquake response analysis of the building to be analyzed, whereby the CPU 10A of the PC 10 The earthquake response analysis process executed in step 1 will be described with reference to the flowchart of FIG.

  In step 100, calculation condition data for calculating the dynamic stiffness of the ground (the ground to be calculated) in the planned construction site of the building to be analyzed is acquired. As the calculation condition data, for example, as shown in FIG. 1 (A), the formation structure of the ground to be calculated, the layer thickness H of each layer, the propagation velocity Vs of the seismic wave, the Poisson's ratio ν, the density ρ, the attenuation rate h, Data such as the shape and size of the foundation of the building to be analyzed can be listed. Among these data, various data related to the ground to be calculated can be obtained by, for example, performing drilling at the planned construction site of the building to be analyzed, and performing a predetermined test on the sample obtained by this boring. . The calculation condition data is not limited to using the data obtained by performing a predetermined test on the sample as it is. For example, the calculation condition data of the building to be analyzed for aftershocks after a relatively strong earthquake has occurred. If you want to analyze the behavior, assume that the characteristics of the ground subject to calculation will change due to a relatively strong earthquake, and change the value corresponding to the characteristic change to the data obtained by the predetermined test. The obtained data may be used as calculation condition data. In step 100, the calculation condition data is acquired by allowing the operator to input the calculation condition data through the keyboard 14 or by reading the calculation condition data from a recording medium (for example, a CD-ROM) in which the calculation condition data is recorded in advance. Is temporarily stored in the memory (RAM 10C) or HDD 20.

  In the next step 102, the calculation condition data acquired in step 100 is read from the memory or the HDD 20, and based on the read calculation condition data, the dynamic rigidity of the ground to be calculated is calculated using a calculation method such as a thin layer element method. Applying and calculating, the dynamic rigidity data obtained by the calculation is temporarily stored in the memory or the HDD 20. Thereby, as shown in FIGS. 1B and 1C as an example, dynamic stiffness data representing the relationship between the external force (earthquake motion) that vibrates the ground and the ground behavior can be obtained in the frequency domain. The dynamic stiffness data is not limited to being obtained by calculation, but can be obtained by performing an experiment.

In Step 104, the dynamic stiffness data of the calculation target ground obtained by the calculation in Step 102 is read from the memory or the HDD 20, and the read dynamic stiffness data is read from within the preset frequency range of the calculation target. N species frequency (N kinds of angular frequency omega _1, ..., omega _N) N pieces of complex data D (omega ₁₎ representing the value of the dynamic stiffness at, ..., extracting respectively D (omega _N), The extracted complex data is stored in the memory or the HDD 20. This step 104 corresponds to the extracting means according to the present invention. In addition, as a frequency range of calculation object, the range of 0-20 (Hz) is applicable, for example. The N types of frequencies for extracting the complex data are, for example, frequencies corresponding to the upper limit of the frequency range to be calculated (for example, if the frequency range to be calculated is 0 to 20 (Hz), the upper limit frequency is 20 ( Hz)). Further, the complex data extracted from the dynamic stiffness data of the ground is used for impulse response calculation. By this calculation, each of time t = 0 and time t = Δt · j (j = 1, 2,..., N) is obtained. Impulse response data representing the impulse response of the ground at the time is obtained. The number of impulse response data obtained is determined according to the number of complex data used in the calculation (that is, the maximum value n of j is the number of complex data minus 1 ( = N-1)), the time range of the impulse response of the ground represented by the obtained impulse response data is also determined according to the number of complex data used in the calculation (for example, the number of complex data is 21 and Δt = 0.05 seconds). Then, tn = Δt · jmax = 0.05 × 20 = 1 second, and 21 impulse response data representing the impulse response of the ground in the time range of time t = 0 to 1 second are obtained. Dynamic stiffness The number of complex data to be al extracted (the number of types of frequencies to extract the complex data) can be predetermined by taking into consideration the length of the time range to be calculated the impulse response of the soil.

In the next step 106, the simultaneous equations according to the present invention for converting the dynamic stiffness representing the relationship between the ground motion and the ground behavior in the frequency domain into the impulse response representing the relationship between the ground motion and the ground behavior in the time domain. (Formulas (3) and (4) having a 2N × 2N coefficient matrix) are read from the HDD 20, and the N complex data D (ω ₁ ),. , D (ω _N ) and obtaining a solution of the simultaneous equations, the impulse response data representing the impulse response of the ground is calculated in increments of Δt set in advance. This step 106 corresponds to the computing means according to the present invention. As a result of this calculation, as impulse response data representing the impulse response of the ground, a simultaneous component k (t ₀ ) of the impulse response that depends on the displacement of the ground, a simultaneous component c (t ₀ ) of the impulse response that depends on the speed of the ground, The data of the impulse response simultaneous component m (t ₀ ) depending on the acceleration is obtained, and the time delay component k (t _j ) data of the impulse response depending on the ground displacement is n in increments of Δt (n = N-1) is obtained, and n-1 pieces of data of the time delay component c (t _j ) of the impulse response depending on the ground speed are obtained in increments of Δt. The obtained impulse response data is temporarily stored in the memory or the HDD 20.

In step 108, among the impulse response data obtained by the calculation in step 106, the data of the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to the time t ₀ , and the time t ₁ Data of n ′ time delay components k (t _j ), c (t _j ) (n ′ <n, tn ′ <Δt · n ′) corresponding to the period of tn ′ are calculated. Select as each. In step 108, the selected time delay component data and the impulse response simultaneous component data k (t ₀ ), c (t ₀ ), m (t ₀ ) are read from the memory or HDD 20 and the ground represented by the read data is displayed. The data representing the dynamic stiffness of the ground corresponding to the impulse response of the ground represented by these data is obtained by reconverting the impulse response of the above to the frequency domain, and the obtained data is temporarily stored in the memory or the HDD 20. Step 108 corresponds to the dynamic rigidity reproducing means according to the present invention.

  In the next step 110, the ground dynamic stiffness data (reproduced dynamic stiffness) obtained by the calculation in step 108 is read out from the memory or the HDD 20, and the dynamic stiffness obtained in the previous step 102 is obtained. Data (hereinafter referred to as “original dynamic stiffness”) is read from the memory or the HDD 20, and correction values Δk and Δm that minimize the error of the real part of the reproduced dynamic stiffness are calculated.

Here, the impulse response data used for reproducing the dynamic stiffness is corrected by the correction value Δk obtained by calculating the simultaneous component k (t ₀ ) of the stiffness term (k ′ (t ₀ ) = k (t ₀ )). + Δk) and the same component m (t ₀ ) of the mass term is corrected by the corrected value Δm (m ′ (t ₀ ) = m (t ₀ ) + Δm), and then obtained by performing the above reproduction calculation. The dynamic stiffness reproduction value S ′ _mod (ω) is expressed by the following equation (6).
S ′ _mod (ω) = S ′ (ω) −ω ² · Δm + Δk (6)
However, the dynamic stiffness S ′ (ω) is the time delay component data k (t _j ) of the stiffness term and the data c (t of the time delay component of the damping term among the impulse response data obtained by the calculation of step 106. _j ) with the dynamic stiffness reproduced from the data of n ′ data starting from the time t ₁ selected from the time t ₁ and the data of the impulse response simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) Yes, it is expressed by the following equation (7).

The square sum Sum of errors between N complex data D (ω _i ) (i = 1 to N) extracted from the dynamic stiffness data and the dynamic stiffness reproduction value S ′ _mod (ω) is It is expressed by equation (8). Then, an arithmetic expression for obtaining correction values Δk and Δm that minimize the error of the real part of the dynamic stiffness reproduced with respect to the real part of the original dynamic stiffness by the least square method from the stopping condition of the following equation (9) The above equation (5) is derived.

In step 110, N complex data D (ω _i ) extracted from the dynamic stiffness data and N complex data S ′ (ω _i ) extracted from the reproduced dynamic stiffness S ′ (ω) data. ) Are substituted into the above equation (5) to calculate the correction values Δk and Δm.

In the next step 112, the simultaneous component k (t ₀ ) of the stiffness term in the impulse response data is corrected with the corrected value Δk using the corrected values Δk, Δm calculated in step 110, and the simultaneous component m of the mass term is corrected. (t ₀ ) is corrected with the correction value Δm (see the following equation (10)).
k ′ (t ₀ ) = k (t ₀ ) + Δk m ′ (t ₀ ) = m (t ₀ ) + Δm (10)
Note that steps 110 and 112 described above correspond to the correcting means according to the present invention.

In step 114, among the impulse response data stored in the memory or HDD 20, a predetermined number n ′ of time delay component data and the simultaneous component k ′ (t _{0 of} the stiffness term corrected in step 112 are stored. ) And mass term simultaneous component m ′ (t ₀ ) data and attenuation term simultaneous component data c (t ₀ ) are read from the memory or HDD 20, and the time history of the building to be analyzed using the read impulse response data Perform earthquake response analysis. Since the impulse response data used for this time history earthquake response analysis is data that has been calculated and corrected by applying the present invention, the dynamic stiffness of the ground subject to calculation includes a relatively large history attenuation component. Is data that accurately expresses the relationship between the earthquake motion and the ground behavior in the time domain, and the time history earthquake response analysis of the analysis target building can be performed with high accuracy.

  In the above description, a mode has been described in which data of a predetermined number n ′ is selected from the data of the time delay component of the impulse response data and used for dynamic rigidity reproduction calculation and time history response analysis. Is not limited to this, for example, while repeating the calculation of the dynamic stiffness and the degree of coincidence with the original dynamic stiffness while sequentially increasing the selected number of time delay component data from the minimum value, The selected number when the degree of coincidence becomes a predetermined value or more may be set as the final selected number of data of the time delay component. In addition, by selecting the time delay component data from the maximum value to the minimum value or changing from the minimum value to the maximum value, the dynamic stiffness calculation and the coincidence calculation are repeated to select the time delay component data. The relationship between the number and the degree of coincidence may be obtained, and the minimum selection number that makes the degree of coincidence equal to or greater than a predetermined value in the obtained relationship may be set as the final selection number of the time delay component data.

  In the above description, an example in which a predetermined number N of complex data is extracted from dynamic rigidity data to be calculated has been described. However, the present invention is not limited to this. For example, if the dynamic stiffness of the calculation target has a characteristic that changes in a complex manner with changes in frequency, the reproduced dynamic stiffness and original Since the degree of coincidence with the dynamic stiffness of the motor does not exceed a predetermined value (that is, the accuracy of the impulse response data obtained by applying the present invention is insufficient), such a condition is satisfied. In this case, the impulse response (data) may be calculated again after increasing the number of complex data extracted from the dynamic rigidity data to be calculated.

  In the above, N = n + 1 in the equation (1) that defines the reaction force F (t) using the impulse response of the object. However, the present invention is not limited to this. It is also possible to obtain an impulse response by establishing simultaneous equations having more equations than the number of and solving by applying a least square method or the like.

  Further, in the above description, the time delay component (fourth term) of the attenuation term is integrated over a period of j = 1 to (n−1) and the time delay component of the stiffness term as a mathematical expression that defines the impulse response of the object. (5) is integrated using the equation (1) over a period of j = 1 to n. However, the present invention is not limited to this, and the following ( As shown in Equation (10), this equation and the motion of the object derived from Equation (10) are obtained by reversing the integration period of the time delay component of the attenuation term and the time delay component of the stiffness term. The impulse response of the object may be obtained based on the following equation (11) that defines the mechanical rigidity.

Further, in the above, the equation (1) including the mass term consisting only of the simultaneous component (first term) is used as the equation defining the impulse response of the object. However, the present invention is not limited to this. As a formula that defines the response, as shown in the following formula (12), a formula including a mass term consisting of a simultaneous component (first term) and a time delay component (fourth term) is used (note that formula (12) 2N = n ₁ + n ₂ + n ₃ +3), the impulse response of the object on the basis of the equation (12) and the following equation (13) that defines the dynamic stiffness of the object derived from the equation (12) May be requested.

  In the above description, the present invention is applied from the dynamic rigidity of the ground to determine the impulse response of the ground, and the example of using the determined impulse response for the time history earthquake response analysis of the building to be analyzed has been described. Needless to say, the present invention can also be applied when converting the dynamic stiffness of another object such as a viscous damper used as a vibration damping device of a building into an impulse response.

  Next, the results of an analysis study conducted by the present inventor in order to confirm the effect of the present invention will be described. In this analysis study, as the seismic response analysis for the building model, the frequency response analysis using the dynamic stiffness of the ground as it is and the impulse obtained by applying the technique described in Non-Patent Document 1 to the above dynamic stiffness Time history response analysis used without correcting the response (time history response analysis without correction and time history response analysis using the corrected impulse response obtained by applying the present invention to the above impulse response ( A time history response analysis with correction) was performed, and the analysis results were compared.

In this analysis study, the building model was a structure with a bottom of 50 x 50 m and a mass of 67,000 t. The constants of the building model are shown in FIG. Also, the ground is defined as the two-layer ground shown in Fig. 1 (A) (attenuation rate h ₁ = 20%), and the input ground motion is defined as the maximum acceleration 300Gal of El Centro1940NS (time increment 0.0025 seconds, duration 10.24 seconds) did. In addition, in order to enable comparison of each response analysis result, the building was assumed to be unattenuated (the behavior of the building with respect to ground motion was linear). Further, the frequency response analysis was performed according to the above equation (7), the analysis range was 0 to 20 Hz, and the analysis frequency step (Δf) was 0.0977 Hz. The dynamic stiffness of the ground is a 2 × 2 diagonal matrix with uncoupled horizontal and rotational degrees of freedom.

  In this analysis study, the building is not damped, so the accuracy of analysis by each response analysis is the highest in frequency response analysis using the dynamic stiffness of the ground as it is, and by the individual time history response analysis for the analysis result by frequency response analysis The deviation of the analysis result can be regarded as being caused by the accuracy of the impulse response used for the response analysis. As analysis results by each response analysis, FIG. 11 shows the maximum response value (maximum acceleration and maximum shear force) of the building, and FIG. 12 shows the acceleration transfer function of the building top. As is clear from FIGS. 11 and 12, the modified time history response analysis to which the present invention is applied provides a better analysis result closer to the analysis result by the frequency response analysis than the conventional uncorrected time history response analysis. It can be understood that the accuracy of the impulse response is improved by applying the present invention to correct the impulse response.

(A) is an image figure which shows an example of the calculation conditions of the dynamic rigidity of a ground, (B) and (C) are diagrams which show an example of the dynamic rigidity of the ground calculated | required by calculation according to the calculation conditions of (A). . FIG. 4 is a diagram showing dynamic stiffness characteristics reproduced by obtaining an impulse response from the ground dynamic stiffness calculated under the condition of a damping rate h ₁ = 0% and reconverting the obtained impulse response into the frequency domain. . Attenuation factor h ₁ = calculated impulse responses from the dynamic stiffness of the calculated ground with 10% for is the diagram characteristics respectively show the dynamic stiffness that reproduces by reconversion into the frequency domain impulse response obtained . FIG. 5 is a diagram showing dynamic stiffness characteristics reproduced by obtaining an impulse response from the ground dynamic stiffness calculated under the condition of a damping rate h ₁ = 20% and reconverting the obtained impulse response into the frequency domain. . In attenuation factor h ₁ = 0% of the conditions is a graph showing the dynamic stiffness which reproduces the impulse response fixes according to the present invention. In attenuation factor h ₁ = 10% conditions, a graph showing the dynamic stiffness which reproduces the impulse response fixes according to the present invention. In attenuation factor h ₁ = 20% conditions, a graph showing the dynamic stiffness which reproduces the impulse response fixes according to the present invention. It is a block diagram which shows schematic structure of PC concerning this embodiment. It is a flowchart which shows the content of an earthquake response analysis process. It is a conceptual diagram which shows the various constants of the building model in the analysis examination which this inventor implemented. It is a diagram which shows the result (maximum response value of a building) of the analysis examination which this inventor implemented. It is a diagram which shows the result (acceleration transfer function of the top part of a building) of the analysis examination which this inventor implemented.

Explanation of symbols

10 PC
12 Display 14 Keyboard 16 Mouse 20 HDD

Claims (9)

In converting the dynamic stiffness that expresses the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain into an impulse response that expresses the relationship in the time domain,
Formulas defining the impulse response include a stiffness term consisting of a simultaneous component and a time delay component depending on the displacement of the object, an attenuation term consisting of a simultaneous component and a time delay component depending on the velocity of the object, After determining the impulse response based on the value of the dynamic stiffness when the vibration is at each frequency, using a mathematical formula that includes a mass term that depends on acceleration and includes at least a simultaneous component,
Of the data representing the impulse response during the period of time t = t _{0 to} t n, data of the simultaneous component corresponding to time t ₀ and n ′ time delay components corresponding to the period of time t _{1 to} t n ′ (Where n ′ <n, tn ′ <Δt · n ′) is used to calculate the dynamic rigidity of the object,
Based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the simultaneous component data of the stiffness term and the simultaneous component data of the mass term in the data representing the impulse response are corrected. Impulse response calculation method. In converting the dynamic stiffness that expresses the relationship between the external force that vibrates the object and the behavior of the object in the frequency domain, to the impulse response that expresses the relationship in the time domain,
The simultaneous component of the impulse response that depends on the displacement of the object is k (t ₀ ), the simultaneous component of the impulse response that depends on the velocity of the object is c (t ₀ ), and the simultaneous component of the impulse response that depends on the acceleration of the object is m ( t ₀ ), the time delay component of the impulse response depending on the displacement of the object by k (t _j ), and the time delay component of the impulse response depending on the velocity of the object by the step of Δt c (t _j ) (where j is a natural number, t _j = Δt · j), the displacement of the object in the time domain is u (t), the velocity is u '(t), and the acceleration is u "(t). As a formula that defines the reaction force F (t),

After obtaining the impulse response based on the value of the dynamic stiffness when the vibration has N kinds of frequencies (N = n + 1) using the equation (1),
Of the data representing the impulse response during the obtained time t = t _{0 to} t n, the data of the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to the time t ₀ , and the time Using the data of n ′ time delay components k (t _j ) and c (t _j ) (n ′ <n, tn ′ <Δt · n ′) corresponding to the period from t _{1 to} tn ′, Perform calculations to reproduce the dynamic stiffness,
Based on the deviation between the reproduced dynamic stiffness and the original dynamic stiffness, the data representing the impulse response depends on the data of the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and the acceleration of the object. An impulse response calculation method comprising correcting data of a simultaneous component m (t ₀ ) of an impulse response. Assuming that the angular frequency of the vibration is ω, on the basis of the equation (1), the mathematical formula defining the dynamic stiffness S (ω) of the object is as follows:

Using the above equation (2), N complex data D (ω ₁ ),..., D (ω representing the value of the dynamic stiffness when the vibration has N frequencies from the data of the dynamic stiffness of the object. _N ) and extract the extracted N complex data

3. The impulse response according to claim 2, wherein the impulse response is obtained by substituting the calculation into the equations (3) and (4) derived from the equations (1) and (2). Calculation method. A modified value Δk for the simultaneous component k (t ₀ ) of the impulse response dependent on the displacement of the object and a modified value Δm for the simultaneous component m (t ₀ ) of the impulse response dependent on the displacement of the object are reproduced as described above. Each is obtained by the least square method so that the deviation between the stiffness and the original dynamic stiffness is minimized, and the data of the simultaneous components k (t ₀ ) and m (t ₀ ) are corrected using the obtained correction values Δk and Δm. The impulse response calculation method according to claim 2. A correction value Δk for the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object and a correction value Δm for the simultaneous component m (t ₀ ) of the impulse response depending on the displacement of the object,

(S ′ (ω) is a simultaneous component k (t ₀ ) corresponding to the time t ₀ among the data representing the impulse response in the period from the time t = t _{0 to} t n, respectively. c (t ₀ ), m (t ₀ ) data and n ′ time delay components k (t _j ), c (t _j ) corresponding to the period from time t _{1 to} tn ′ (where n ′ <n , Tn ′ <Δt · n ′) representing the dynamic rigidity of the object reproduced), and using the obtained correction values Δk and Δm, the simultaneous components k (t ₀ ) and m (t ₀ ) 5. The impulse response calculation method according to claim 4, wherein the data is corrected. Of the data representing the impulse response during the period of time t = t _{0 to} t n, data of simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ , Data of n ′ time delay components k (t _j ) and c (t _j ) (where n ′ <n, tn ′ <Δt · n ′) corresponding to the period of time t _{1 to} tn ′, Based on the reproduced dynamic stiffness and the deviation of the original dynamic stiffness, the data of the impulse response simultaneous component k (t ₀ ) depending on the displacement of the object and the impulse response simultaneous component m (( The impulse response calculation method according to any one of claims 2 to 4, wherein data obtained by correcting the data of t ₀ ) is used for time history response analysis of the object.   The impulse response according to any one of claims 1 to 6, wherein the object is ground, and the external force is seismic motion, and the obtained impulse response of the ground is used for a time history earthquake response analysis of a building. Calculation method. An impulse response computing device that converts dynamic stiffness representing a relationship between an external force that vibrates an object and a behavior of the object in a frequency domain into an impulse response representing the relationship in a time domain,
From the dynamic stiffness data, N complex data D (ω ₁ ),..., D (ω _N ) representing dynamic stiffness values when the vibration has N types of frequencies (N = n + 1) are extracted. Extraction means to
The simultaneous component of the impulse response that depends on the displacement of the object is k (t ₀ ), the simultaneous component of the impulse response that depends on the velocity of the object is c (t ₀ ), and the simultaneous component of the impulse response that depends on the acceleration of the object is m ( t ₀ ), the time delay component of the impulse response depending on the displacement of the object by k (t _j ), and the time delay component of the impulse response depending on the velocity of the object by the step of Δt c (t _j ) (where j is a natural number and t _j = Δt · j), N complex data extracted by the extracting means are

An arithmetic means for obtaining the impulse response by substituting into the above formulas (3) and (4) and calculating,
Of the data representing the impulse response during the period from time t = t _{0 to} t n obtained by the computing means, the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ And n ′ time delay components k (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′) corresponding to the period from time t _{1 to} tn ′. Dynamic rigidity reproduction means for performing computation to reproduce the dynamic rigidity of an object using
Based on the deviation between the dynamic stiffness reproduced by the dynamic stiffness reproducing means and the original dynamic stiffness, the simultaneous component k (t ₀ ) of the impulse response depending on the displacement of the object among the data representing the impulse response. Correction means for correcting the data of the simultaneous component m (t ₀ ) of the impulse response depending on the data and the acceleration of the object;
An impulse response calculation device comprising: An impulse response calculation program that causes a computer to function as an impulse response calculation device that converts a dynamic stiffness that represents the relationship between an external force that vibrates an object and the behavior of the object in the frequency domain into an impulse response that represents the relationship in the time domain. There,
The computer,
From the dynamic stiffness data, N complex data D (ω ₁ ),..., D (ω _N ) representing dynamic stiffness values when the vibration has N types of frequencies (N = n + 1) are extracted. Extraction means to
The simultaneous component of the impulse response that depends on the displacement of the object is k (t ₀ ), the simultaneous component of the impulse response that depends on the velocity of the object is c (t ₀ ), and the simultaneous component of the impulse response that depends on the acceleration of the object is m ( t ₀ ), the time delay component of the impulse response depending on the displacement of the object by k (t _j ), and the time delay component of the impulse response depending on the velocity of the object by the step of Δt c (t _j ) (where j is a natural number and t _j = Δt · j), N complex data extracted by the extracting means are

Calculation means for obtaining the impulse response by substituting into the above equations (3) and (4),
Of the data representing the impulse response during the period from time t = t _{0 to} t n obtained by the computing means, the simultaneous components k (t ₀ ), c (t ₀ ), m (t ₀ ) corresponding to time t ₀ And n ′ time delay components k (t _j ), c (t _j ) (where n ′ <n, tn ′ <Δt · n ′) corresponding to the period from time t _{1 to} tn ′. Dynamic stiffness reproduction means for performing computation to reproduce the dynamic stiffness of an object using
Based on the deviation between the dynamic stiffness reproduced by the dynamic stiffness reproducing means and the original dynamic stiffness, the simultaneous component k (t _{0 of} the impulse response depending on the displacement of the object in the data representing the impulse response. ) And the data of the simultaneous component m (t ₀ ) of the impulse response depending on the acceleration of the object.

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