JPH0216463B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a vibration analysis method for analyzing vibration characteristics of a structure. [Prior Art] When developing a new machine or changing a model, it is customary to go through a prototyping process in many cases. That is, after designing a machine based on a new concept, we manufacture parts, assemble them, and conduct various tests. Test content covers a wide range of areas, including performance, functionality, and reliability. If the test results are satisfactory, the prototype will be completed. Conversely, if the test results are not satisfactory,
The parts will be improved and tested again. This operation is repeated until the various test results satisfy their respective target values. Prototyping is rarely achieved in one go; rather, it is often the case that improvements are made and repeated tests are conducted. If a satisfactory test result is obtained, the specifications and specifications in that case are determined to be appropriate values, and then production of the final product begins. In particular, economical design is being strongly promoted in recent machines, and with this, ensuring reliability has become even more important than before. Specific measures for economical design include making the machine more compact or using thinner component parts to save on materials used, but the problem with reliability is that this makes the machine more susceptible to vibration. It is.
Therefore, the reliability of the machine against vibrations, that is, the dynamic reliability, is one of the most important items to be confirmed through prototype production, and thorough vibration measurements and studies are being conducted using prototype production. [Problems to be solved by the invention] Even in the case of prototypes intended to ensure dynamic reliability,
After assembling the parts, conduct a vibration test to determine the vibration amplitude,
Improvement, assembly, and testing of parts are repeated until vibration characteristics such as natural frequency and frequency response characteristics satisfy target values. In particular, if the number of prototypes is large, or if the prototype is small but has a complicated shape, vibration measurement at multiple points is required, which may require a large-scale vibration measurement device or require a large amount of expense and man hours. be forced to spend. The result is inconveniences such as increased product costs and delayed development times. Furthermore, when developing a new machine or changing the model of the machine, vibration analysis is often performed at the design stage to ensure reliability after the machine is manufactured. In recent years, with advances in computers and numerical analysis methods, it has become increasingly common to use calculations to predict machine vibrations and to ensure machine reliability at the design stage. However, when aiming for economical design by increasing the capacity of a single machine, the scale of the machine structure will naturally increase, and even if a computer is used, a huge amount of calculation time will be spent on vibration analysis, or the calculation scale will be too large. I have often experienced situations where it is impossible to analyze because it is too large. The reason for this is that, as in conventional analysis methods such as the finite element method and the transfer matrix method, the machines to be analyzed are handled as a group, resulting in a very large calculation scale. As a result, the smooth progress of design work was significantly impaired, such as increased design costs and uncertainty about ensuring dynamic reliability. An object of the present invention is to provide a vibration analysis method for a structure that can easily and accurately perform vibration analysis of a large-scale or complicated structure. [Means for Solving the Problems] The present invention first calculates or actually measures the basic characteristics of parts or partial structures constituting a machine as a natural vibration mode and a static deformation mode when a static external force is applied. Then, by combining (synthesizing) the basic characteristics of each part (or substructure),
This method realizes a vibration analysis method that calculates the vibration characteristics of the entire structure. [Operation] In other words, in a structure composed of multiple parts or substructures, first, the static deformation mode is when the boundary points of each part or substructure are deformed by a unit amount in terms of displacement and angle. ,
Find the natural vibration mode when a fixed condition is given to the mode. Next, based on the static deformation mode and the natural vibration mode, the natural vibration mode of the entire structure constituted by the parts or partial structures is determined. The natural vibration mode of the structure is then used to calculate the frequency response and transient response of the structure to perform vibration analysis of the structure, making it easy and highly accurate to perform vibration analysis of large-scale or complex structures. can be done. [Example] An example of the vibration analysis method according to the present invention is shown in Figures 1-
This will be explained using FIG. FIG. 1 shows the procedure for performing vibration analysis of a machine according to the present invention. 2 to 6 are diagrams illustrating each content of the present invention in principle, using a beam fixed at both ends as an example of the object of analysis instead of a complicated machine for the purpose of simplifying the explanation. As shown in FIGS. 2 and 3, it is assumed that a beam 1 with fixed ends to be analyzed consists of partial structures 2 and 3 as cantilever beams. Cantilever beams 2 and 3
are rigidly connected by welding or the like at both end points (boundary points) 4 and 5, thereby forming a beam 1 fixed at both ends. An embodiment of this vibration analysis method will be described along the work procedure shown in FIG. 1 using FIGS. 2 to 6. (A) First, Figure 4 shows the principle of finding two types of static deformation modes for the partial structure in the state before assembly. As shown in the figure, this is the deformation mode when a static force is applied to the boundary points to generate unit displacement x=1 at boundary points 4 and 5. (B) Another static deformation mode is when a static moment is applied to the boundary points to generate unit local displacement q = 1 at boundary points 4 and 5, as shown in the lower part of Figure 4. This is the transformation mode. This static deformation mode is determined for all parts or all partial structures that make up the machine. (C) Next, for the parts or substructures that are still in their pre-assembly state, fixed conditions are applied to each boundary point, and the natural vibration modes at that time are determined. This natural vibration mode is determined for all parts or partial structures that make up the machine. (D) Combining (synthesizing) the basic properties (static deformation mode and natural vibration mode) of all substructures obtained under the conditions described in (A) to (C),
Perform calculations to find the natural vibration mode assuming that the machine is assembled. The principle of this calculation will be described later, but in the present invention, this method is referred to as a mode synthesis method or a mode synthesis calculation. When calculating this mode synthesis, coordinate transformation is performed to match the engagement relationship between each part or substructure, and the basic characteristics of each part or substructure are combined (synthesized). (E) Perform calculations to determine the frequency response of the machine based on the natural vibration mode of the vibrating machine obtained as a result of the mode synthesis calculation in section (D). The calculation principle for determining the frequency response from the natural vibration modes is clear from the references and can be easily achieved. (F) Together with the calculation results of the natural vibration mode of (D),
Perform calculations to determine the transient response of the machine. The calculation principle for determining the transient response from the natural vibration mode is also clear from the reference literature. References KJ Bathe, EL Wilson, Translated by Kikuchi: Numerical Calculation of the Finite Element Method, P345-4389 (Science and Technology Publishing,
(Published September 1979) Next, we will explain the calculation principles for deriving the natural vibration mode of a machine from the basic characteristics (static deformation mode and natural vibration mode) of a component (or partial structure). In the present invention, this method is abbreviated as mode synthesis method. It is assumed that a machine is made up of a finite number of parts or substructures. Parts in pre-assembled state (or substructures in divided state)
Let r be the representative number of , and write the static stiffness equation for the part as follows. In equation (1), B is the boundary displacement (displacement at the point where it connects with other parts), and I is the symbol representing the internal displacement [k](r), {u}(r), {f}(r ) are the stiffness matrix, displacement vector, and external force vector of the part (or partial structure) r, respectively. By setting {f}(r)={0} in equation (1), the static deformation mode [φ ^C ](r) of the above-mentioned part (or substructure) r can be calculated as [φ ^C ](r). It is obtained as =−[k ^II ] ^-1 (r)[k ^IB ](r) …(2). This static deformation mode〔φ ^C 〕(r)
is a matrix. Each column of [φ ^C ](r) is the amount of change in internal displacement when the displacement of each corresponding boundary point is changed by a unit amount. Now, regarding the above-mentioned natural vibration mode, boundary displacement is defined as the natural vibration mode of free vibration for any boundary condition (completely fixed or free condition). In general, parts (or substructures)
When is a continuous elastic body, there are theoretically an infinite number of natural vibration modes, but in this solution, a finite number of natural vibration modes up to the P order are considered. A matrix in which the P natural vibration modes are arranged in a row is represented by [φ](r), and here, [φ](r) will be called the natural vibration mode. In the mode synthesis method ^, the generalized coordinate vector {p ^B }(r) and [q ^N }(r), the displacement vector {u}(r) of the part (or partial structure) is divided into boundary point displacement and internal displacement and expressed as follows. [I ^B ] in equation (3) is a unit matrix corresponding to the boundary displacement. From equation (3), {u ^B }(r)={p ^B }(r)+[φ ^B }(r){q ^N }(r) …(4) is derived, but in general, [φ ^B }( r)＝

[0], so {u ^B }(r)={p ^B }(r). This relationship is a very useful property when creating calculation programs. If equation (4) is transformed, {p ^B }(r)={u ^B }(r)−[φ ^B ](r){q ^N }(r) (5). From equation (3), the following equation is further derived. {u ^I }(r)＝[φ ^C }(r){p ^B }(r)＋[φ ^I ](r){q ^N }(r
)
...(6) Substituting the relationship in (5) for {p ^B }(r) on the right side of equation (6), the following equation is obtained. {u ^I }(r)＝[φ ^C }(r){u ^B }(r)＋[φ ^N ](r){q ^N }(r
)
…(7) Here, [φ ^N ](r)=[φ ^I ](r)−[φ ^C ](r)[φ ^B ](r) …(8). From equation (7), the internal displacement vector {u ^I }(r) is the generalized coordinate vector {q ^N } corresponding to the boundary point displacement vector {u ^B }(r) and the above-mentioned natural vibration mode [φ](r). It can be seen that it is expressed as (r). Therefore, equation (3) can be rewritten as follows. Equation (9) is the final equation expressing the basic characteristics of the part (or partial structure), and is the basic equation of the mode synthesis method. The relationship obtained from equation (9) is a very important property in creating the calculation {q ^B }(r)={u ^B }(r) program. In other words, only {u ^B }(r) appears at the boundary points (connection points) of parts (or substructures), and {q ^N }(r) is not involved. It becomes easy to determine the vibration characteristics of the entire machine system by combining the basic characteristics of the structures (structures). This combination method is exactly the same as the conventional superposition method of the finite element method. When finding the equation of motion of each part (or substructure) r in the mode synthesis method using equation (9),
It will look like this: [M] (r) {q¨} (r) + [K] (r) {q] (r) = {F} (r
)
…(10) Here, dot represents the time differential, and [M](r)=[N] ^T (r)[m](r)[N](r) [K](r)=[ N] ^T (r) [k] (r) [N] (r) [F] (r) = [N] ^T (r) {f} (r) ...(11). T is a symbol indicating matrix transposition. [m](r), [k](r), and {f}(r) are the discretized mass matrix, stiffness matrix, and external force vector of the part (or substructure) r.
[N](r) and {q}(r) are symbols defined as follows in formula (9). When the operating equations for the parts (or substructures) in the mode synthesis method expressed by equation (10) are combined (superimposed) for the entire machine system, the following is obtained. [M] {q¨} + [K] {q} = {F} ...(14) Here, {q}, [M], [K], and {F} are the entire machine system that has been modally synthesized, respectively. These are the generalized coordinate vector, mass matrix, stiffness matrix, and external force vector. The eigenvalue problem for finding the natural frequency and natural vibration mode of the machine is as follows in equation (14): {F}={0} {q}={φ}e ^j 〓 ^t ω: Frequency t: Time j=√ -1, it becomes as follows. [K] {φ}=ω ² [M] {φ} (15) ω and {φ} that satisfy equation (15) can be calculated as the natural frequency and natural vibration mode of the machine, respectively. The above are the equations related to the mode synthesis method. In Fig. 5, when determining the natural vibration mode as a basic characteristic of a part or substructure, a fixed condition is given to the boundary points. The solution shown in Figure 1 holds true even in mode. The effects of adopting the embodiment shown in FIG. 1 are as follows. (b) Machine vibration analysis can be roughly divided into two stages: first determining the basic characteristics of the parts or substructures, and then combining them to determine the vibration characteristics of the entire machine. measurement·
This method has the advantage of reducing the scale of calculations and making it easier to perform vibration analysis of large-scale machines. (b) For vibration analysis of machines in which multiple identical parts or substructures are arranged periodically, it is only necessary to obtain the basic characteristics of one part or substructure. It is possible to streamline the vibration analysis of various types of machines. (c) By comparing the basic characteristics of parts or substructures (static deformation mode and natural vibration mode) with the machine's natural vibration mode, it is possible to quickly catch vibrational problems with the machine. It also makes it easier to find countermeasures. FIG. 7 shows another embodiment of the present invention in which the starting point of vibration analysis is to obtain all the basic characteristics (static deformation mode and natural vibration mode) of the parts or substructures constituting the machine through actual measurements. . If the basic characteristics of a part or substructure are measured many times and there are variations or there are few measurement points, use the least squares method to express the static deformation mode or natural vibration mode of the part or substructure. It is also possible to obtain an approximate function and use the result for synthetic calculations. According to the embodiment shown in FIG. 7, the following effects can be expected. (b) Since the starting point of analysis is to obtain the basic characteristics (static deformation mode and natural vibration mode) of a part or partial structure through actual measurement, if the measurement accuracy of the basic characteristics of the part or partial structure is improved, It is possible to improve the accuracy of the final machine vibration prediction. (b) The vibration characteristics of assembled machines can be predicted based on the basic characteristics (static deformation mode and natural vibration mode) of parts or substructures, so it is possible to measure vibrations after assembling machines. can be omitted. Particularly in the case of large-scale machines, the work of assembling the machine and measuring the vibration of the machine after assembly requires a huge amount of man-hours, so being able to omit these tasks is a great advantage during the prototyping stage. This has the effect of significantly reducing the development costs for machines currently in use, and the costs required for inspection for machines in the production stage. (c) The effect of being able to omit the vibration test of the machine is as follows:
It's not just about saving man hours. That is, according to the present invention, since the measurement work is limited to structurally small components or substructures, a small-scale measuring device is sufficient, which also has the effect of preventing the introduction of expensive large-scale measuring devices. . (iv) If, as a result of vibration testing of the machine, satisfactory vibration characteristics are not obtained, improvement measures must be taken. In such cases, if you manufacture a modified part (or partial structure) and measure its basic characteristics, you can use the data that has already been measured for the basic characteristics of other parts (or partial structures). Therefore, actual vibration measurements of a machine assuming that modified parts have been installed can be easily carried out. In other words, it is possible to limit the work related to improving the mechanical characteristics of the machine to a minimum of creating a parts list and actual measurements, and it is possible to streamline the work related to vibration tests. Next, still another embodiment of the present invention is shown in FIG. The example shown in Figure 8 calculates the basic characteristics (static deformation mode and natural vibration mode) of all the parts that make up the machine, and then combines the basic characteristics of each part obtained by calculation. , a method for calculating the vibration characteristics of the entire machine. The finite element method or transfer matrix method, which is well known in the field of vibration analysis, is used to calculate the basic characteristics of the parts in the embodiment shown in FIG.
Since this method processes all work by calculation, it is possible to predict the vibration of the machine assuming that the machine will be manufactured at the design stage before it is manufactured. The fact that vibration prediction is valid even if the actual machine does not exist means that
This means that it is possible to design effectively to ensure reliability. In other words, as a result of being able to easily perform so-called parameter surveys to investigate how the machine will vibrate when the dimensions of the parts are changed in various ways, design defects can be prevented.
It is effective in preventing the manufacture of defective products. Furthermore, the advantage of the embodiment shown in FIG. 8 is added. When performing vibration analysis of a machine using the finite element method or transfer matrix method, the conventional method seems convenient at first glance because it treats the machines to be analyzed as one unit in the calculation, but in reality the scale of the calculation is large. becomes large, and even if a computer is used, an enormous amount of calculation time is required, or calculation becomes impossible on a small-scale computer. According to the embodiment shown in FIG. 8, in order to pre-calculate the basic characteristics of each component with a small calculation scale,
When calculating the vibration characteristics of the entire machine, the amount of information used for the calculation can be compressed, so the calculation time can be reduced compared to conventional methods, and it can also be used to calculate It becomes possible to analyze large-scale machines. Further, the implementation shown in FIG. 8 is effective for vibration analysis of mechanical structures that are integrated and cannot be actually divided. Examples of such mechanical structures include towers, tanks, casings, etc. For vibration control of this type of mechanical structure, the object to be analyzed is virtually divided into a finite number of substructures based on the design drawing, and the basic characteristics of each of the structures in the virtually divided parts are calculated. However, if a combination of these calculations is performed, the vibration analysis of the original mechanical structure can be achieved. Furthermore, another embodiment of the present invention will be described based on FIG. The embodiment shown in FIG. 7 shows a method in which the basic characteristics (static deformation mode and natural vibration mode) of all parts or partial structures are obtained by actual measurement. Further, the embodiment shown in FIG. 8 is a method in which the basic characteristics of all parts or partial structures are determined by calculation. On the other hand, the method shown in FIG. 9 is a vibration analysis method that starts by actually measuring the basic characteristics of a certain part and calculating the basic characteristics of other parts. For convenience of explanation, the following numbers are assigned as part numbers z to the Z parts that make up the machine: z=1, 2, ..., L, L+1, ..., Z. In this example, for parts with z=1, 2, ..., L, basic characteristics obtained by actual measurements, z=L+
This is a method of calculating the vibration characteristics of the machine by using the calculated basic characteristics for the parts 1, L+2, . . . , Z, and combining two types of basic characteristics. The arithmetic processing after determining the basic characteristics of each component by actual measurement and calculation is the same as the method explained in the embodiment of FIG. Depending on the shape and configuration of the parts that make up the machine, and the scale and performance of the measuring equipment, there are some parts where it is easier to actually measure the basic characteristics, and others where it is more convenient to rely on calculations. There is something. According to the principles of the present invention, machine vibration analysis can be achieved regardless of the means used to determine the basic characteristics of the parts. All you have to do is find the basic characteristics of. The flexibility of being able to analyze vibrations of machines regardless of the means for determining the basic characteristics of parts means that the present invention can be widely applied. As a method for calculating the basic characteristics of a part, a method suitable for the vibration analysis of each part may be selected from among the methods often used in conventional vibration analysis, such as the finite element method or the transfer matrix method. Further, the embodiment shown in FIG. 9 is effective in improving the vibration characteristics of a machine. That is,
If the vibration characteristics of the machine determined by the method in the example shown in Figure 7 are unacceptable, the specifications of the part will be modified, but before the modified part is manufactured, Since the effects of modifications can be predicted at the design stage, improvement work can be streamlined. For modified parts, basic characteristics may be calculated based on the design drawings, and for other parts, basic characteristics already obtained through actual measurements may be used. If the vibration characteristics of the machine predicted in this manner are not acceptable, it means that the modifications to the part in question were not appropriate, and the design may be changed again. In other words, according to the embodiment shown in FIG. 9, it is easy to find appropriate specifications or specifications at the design stage for modifying parts without producing modified parts for design changes, and there is no improvement effect. It is possible to prevent the production of incorrect parts. The embodiment shown in FIG. 7 shows a case in which the basic characteristics of a component are determined by actual measurement, and the embodiment shown in FIG. 8 shows a case in which the basic characteristics of a component are determined by calculation. In contrast to these methods, FIG. 10 shows a method according to another embodiment of the present invention in which the static deformation mode is calculated and the natural vibration mode is actually measured as a means for determining the basic characteristics of the component. Further, FIG. 11 shows a method of yet another embodiment in which the static deformation mode is determined by actual measurement and the natural vibration mode is determined by calculation, contrary to the method shown in FIG. 10. This method is useful when you want to perform vibration analysis on a machine based on actual measurement data for each part as much as possible, but you can only actually measure one of the basic characteristics of the part due to the equipment you have. It is effective as a means of coping. The vibration analysis method of the present invention includes all methods of determining the basic characteristics of parts, regardless of the means used to determine them. When looking at the main parts of a machine, it is often the case that the machine itself is made up of multiple parts. An example of a main component made by assembling a plurality of components is a casing for a rotating machine, which is made up of an upper lid and a lower lid. The present invention can be applied to such a seismic object, and the analysis object of the present invention includes not only a complete machine but also a partial structure of a machine consisting of a plurality of parts. FIG. 12 shows a vibration analysis device that is based on the vibration analysis method of the present invention and is capable of consistently performing various tasks using a computer. 11 is a computer, 12 to 17 are peripheral devices connected to the computer 11, 12 is an input device, 13 and 14 are disks as storage devices,
15 is a CRT as a display device, and 16 and 17 are plotters and line printers as recording devices. The disk 13 stores specifications such as dimensions and materials of parts (or partial structures) that constitute the machine. The disk 14 is a program for calculating the basic characteristics of each part (static deformation mode and natural vibration mode) using the specifications of each part stored in the disk 13, and a program that synthesizes the basic characteristics of each part and calculates the machine. Contains a program to calculate the overall vibration characteristics and a program to display and record the calculation results. If the vibration analysis device shown in FIG. 12 is used, the vibration characteristics of the machine can be calculated based on the specifications of the parts. In particular, it has the advantage of being able to efficiently and consistently determine the basic characteristics of a component and the vibration characteristics of a machine based on the component specifications on the drawings using a single computer. Figure 13 shows a vibration analysis device also according to the present invention, which includes a measuring device that detects the basic characteristics of parts (static deformation mode and natural vibration mode) and also measures the vibration characteristics of the machine based on the detected data. Consistently calculate and
It has become a processing system. 18 is a displacement pick-up for detecting the static deformation mode of the part; 19 is a vibration pick-up for detecting the natural vibration mode of the member; 20 and 2
1 are amplifiers of pickups 18 and 19, respectively. 22 is a data input device whose main element is an A-D converter, and displacement signals and vibration signals detected with respect to the parts are taken into a disk 24 as a data file storage device via the data input device and computer 23. It will be done. 25 is also a disk serving as a storage device, and is used to store various data processing, calculation, and display programs to be described later. 26, 27, and 28 are the CRT, printer, and printer attached to the computer 23, respectively.
It is a line printer. There are three main programs stored on the disk 25 as shown below. A data processing program that calculates the static deformation mode and natural vibration mode of each part based on multi-point measurement data about the part. A synthetic calculation program that calculates the vibration characteristics of the entire part by combining the static deformation mode and natural vibration mode of each part. A program to display and record the basic characteristics of each part and the vibration characteristics of the entire machine. In the device shown in Figure 13, the displacement pick-up and vibration pick-up for measuring the basic characteristics of parts are represented by one each, but it is easy to arrange multiple pick-ups to increase the efficiency of actual measurements. Therefore, the present invention does not depend on the scale of the measurement system. According to the embodiment shown in FIG. 13, a great advantage is that one set of systems can perform the entire process from measuring parts to predicting vibration characteristics of the machine. [Effects of the Invention] As described above, according to the present invention, it is possible to provide a vibration analysis method for a structure that easily and accurately achieves vibration analysis of a large-scale or complicated structure.

[Brief explanation of drawings]

FIG. 1 is a flowchart showing a vibration analysis method for a structure which is an embodiment of the present invention, and FIGS. 2 to 6 are explanatory diagrams each illustrating the principle of the present invention by exemplifying a beam as an analysis target. 7 to 11 are flowcharts showing a vibration analysis method for a structure according to another embodiment of the present invention, and FIGS. 12 and 13 show a vibration analysis apparatus for a structure to which the present invention is applied. FIG.

Claims (1)

[Scope of Claims] 1. A vibration analysis method for a structure composed of a plurality of parts or partial structures, including the following: for each of the parts or partial structures, displacement and angle are determined at the boundary points of the parts or partial structures. Find the static deformation mode when a unit amount of deformation is applied to each of them, find the natural vibration mode when the condition of fixing the boundary points of the part or partial structure is given, and further, The natural vibration mode of the structure as a whole constituted by is determined by combining the static deformation mode and the natural vibration mode of the already determined parts or partial structures, and the natural vibration mode of the structure as a whole is determined. A vibration analysis method for a structure, characterized in that vibration characteristics such as a frequency response and a transient response of the structure are calculated using the above method. 2 In claim 1, when determining the natural vibration mode of a certain part (or partial structure), it is assumed that the part (or partial structure) engages with or couples with another part (or partial structure). A vibration analysis method for a structure, characterized in that the boundary points of the structure are determined under fixed conditions, and the vibration characteristics of the structure are calculated based on the natural vibration mode thus obtained. 3 In claim 1, when determining the natural vibration mode of a certain part (or partial structure), it is assumed that the part (or partial structure) engages or couples with another part (or partial structure). A vibration analysis method for a structure, which is characterized by determining the boundary point under conditions of mechanical freedom, and calculating the vibration characteristics of the structure based on the natural vibration mode obtained under such conditions. 4. In the vibration analysis method set forth in claim 1, as a static deformation mode of a component (or partial structure), a unit displacement is applied to a boundary point where the component engages or connects with another component. The static deformation mode when a unit of angular displacement is given to the same boundary point and the static deformation mode when a unit angular displacement is given to the same boundary point are determined, and the vibration characteristics of the structure are calculated using both static deformation modes. vibration analysis method for structures. 5 In the vibration analysis method set forth in claim 1 or 2 or 3 or 4, the basic characteristics (static deformation mode and natural vibration mode) of all parts (or partial structures) are actually measured. A vibration analysis method for a structure, which is characterized in that the vibration characteristics of the entire structural structure are predicted by calculation by combining the basic characteristics of all parts (or partial structures) found and actually measured. 6 In the vibration analysis method set forth in claim 5, after actually measuring the static deformation mode and natural vibration mode of a component or component structure, the static deformation mode and natural vibration mode are determined by the least squares method based on the measured data. A vibration analysis method for a structure, which comprises calculating the vibration characteristics of the structure by calculating an approximation function of the natural vibration mode and finally combining all the approximation functions representing the basic characteristics of each part or substructure. 7 In the vibration analysis method set forth in claim 1, the basic characteristics (static deformation mode and natural vibration mode) of all parts or partial structures constituting a structure are calculated, and all calculated parts are calculated. Alternatively, a vibration analysis method for a structure is characterized in that the vibration characteristics of the entire structure are predicted by calculation by combining the basic characteristics of the partial structures. 8 In the vibration analysis method set forth in claim 1, the basic characteristics (static deformation mode and natural vibration mode) of a certain part (or partial structure) are determined by actual measurement, and the fundamental characteristics (static deformation mode and natural vibration mode) of a certain part (or partial structure) are determined by actual measurement, and A vibration analysis method for a structure, which is characterized in that basic characteristics are determined by calculation, and the vibration characteristics of the entire structure are predicted by calculation by combining the basic characteristics of all parts obtained through actual measurements or calculations. 9. A vibration analysis method for a structure according to claim 1, characterized in that the static deformation mode of the component or partial structure is determined by actual measurement, and the natural vibration mode is determined by calculation. 10. A vibration analysis method for a structure according to claim 1, characterized in that the static deformation mode of the component or partial structure is determined by calculation, and the natural vibration mode is determined by actual measurement.