JP6934669B2 - Rigid seismic isolation structure - Google Patents

Description

The present invention relates to a rigid seismic isolation structure, and more particularly to a rigid seismic isolation structure for buildings.

In the conventional seismic isolation structure, the natural angular frequency ω _eq of the seismic isolation structure is set to an extremely low frequency regardless of the natural angular frequency ω _{1 of the structure.} This is because, as the name of seismic isolation structure indicates, the purpose was to separate the movement of the ground from the movement of the building structure. This is because the response acceleration y can be reduced by creating a vibration system with a long period (low frequency). As a result, the response transformation y was thought to be unavoidable no matter how large it was. Therefore, a large laminated rubber bearing was developed, and the cost of the seismic isolation structure increased.

JP 2006-241918

However, if a structure is created in which almost all of the input seismic energy is absorbed by the seismic isolation layer in which the laminated rubber bearings are arranged, the response displacement y itself can be reduced. As a matter of course, the acceleration y also becomes small, so that a response reduction effect can be expected. First, the response displacement y of the rigid seismic isolation structure is smaller due to the damping effect than the deformation x of the seismic structure. Further, most of the deformation amount y is the deformation z of the laminated rubber, and the horizontal deformation amount yz of the building is extremely small, so that the seismic performance of the structure is dramatically improved. As described above, considering that the purpose of installing the laminated rubber bearing is not to lengthen the period of the building but to block the vibration energy, it is not necessary to make the natural period extremely long.
In the conventional seismic isolation structure, since this point was not noticed, a structure having a longer period (low frequency) than necessary was designed, and a resonance phenomenon with respect to a long period ground motion was unavoidable. The present invention is characterized in that it is clarified in what range the natural frequency of the seismic isolation structure should be set as compared with the original structure to cut off the seismic energy.

The present invention is to provide an invention that solves such a problem.

In order to solve the above problems, the present invention has a seismic isolation structure in which a structure is supported by a laminated rubber bearing, and has a primary natural angular frequency ω ₁ of the structure and a primary natural angular frequency of the seismic isolation structure. ratio of omega _eq is, so as to satisfy _{0.65 <ω eq / ω 1 <} 0.75, and set the horizontal stiffness and damping coefficients of the laminated rubber bearing.

The seismic isolation structure is a structure in which the vibration of the ground is not transmitted to the building by supporting the building structure with laminated rubber bearings. Therefore, it was thought that the smaller the horizontal rigidity of the laminated rubber, the less the transmission of ground vibration to the building. Therefore, the natural period of the seismic isolation structure is as long as 3 seconds or more, and the diameter of the laminated rubber bearing is so large that it is not uncommon for it to be 1 m or more. It is difficult to design in terms of architectural planning, and the price tends to be high.
The present inventor has theoretically clarified that the laminated rubber bearing of the seismic isolation structure has the optimum horizontal rigidity and also has the optimum value of the damping coefficient, and obtained the value. The present invention is a seismic isolation structure to which the above theoretical findings are applied, and the optimum value of its natural period is in the short period region. This fact has not been known at all in the past. The present invention is referred to as a rigid seismic isolation structure. The difference from the conventional seismic isolation structure is that the natural period is short and the shape of the laminated rubber bearing is small. If the optimum value of the natural angular frequency is set within a range of about 70% of the natural angular frequency of the building structure, the response deformation at the time of an earthquake will be the smallest and the damage to the building will be reduced. can.

(1) is a model side view relating to the conventional seismic isolation structure, and (2) is a model side view relating to the rigid seismic isolation structure according to the embodiment of the present invention. It is a dynamic model diagram which concerns on embodiment of this invention. It is a dynamic model diagram which concerns on embodiment of this invention. It is a comparative distribution diagram of _{the function G Y} (η, β) of the rigid seismic isolation structure and the general seismic isolation structure according to the embodiment of the present invention. It is a figure which shows the domain of the natural angular frequency of the rigid seismic isolation structure which concerns on embodiment of this invention.

請求項の技術的説明を詳細に行う前に、先に結論を述べる。最適な積層ゴムの水平剛性と最適な減衰装置を選定すると、硬質免震構造の固有角振動数は次の値となる。
ω_eq ≒ ０．７ω₁
この値は、地震動のスペクトルがホワイトノイズを仮定して求めたものである。従来は、長周期の地震動成分は少ないと思われていたが、地震の規模や地盤の特性を考えると、いかなるスペクトルを有する地震が発生しても不思議ではない。そこで、全ての振動数成分を含む地震動に対して、最適な積層ゴムの水平剛性や減衰係数を求めるために、地震動のスペクトルを振動数領域で一定（ホワイトノイズ）と仮定した。
実際の地震動のスペクトルは、個々の地震動によって変動する。また、積層ゴムの剛性や減衰係数の最適値からのずれや誤差も存在する。そこで、請求項に示した硬質免震構造の固有角振動数の範囲は、ある程度の幅を持たせて設定した。この範囲であれば、目的とする応答低減効果は、殆ど変動しないことを理論的に証明することができる。
０．６５ω₁＜ω_eq ＜０．７５ω₁
この場合の、積層ゴムの水平剛性の最適値と減衰装置の最適減衰係数は、次式となる。数学的な証明と技術的な説明は、次節以降に示す。

上記の積層ゴム支承の水平剛性の最適値と減衰装置の減衰係数の最適値は、図２及び図３の定義に従う。 通常の建築振動モデル（１質点系）を図２に示す。 また、硬質免震構造を1質点系に置換したモデルを図３に示す。 The angular frequency of the structure itself when it is assumed that the structure supported by the laminated rubber bearing is directly installed on the ground is defined _{as ω 1.} (See Fig. 1 (1) and Fig. 2) The angular frequency of the rigid seismic isolation structure supported by laminated rubber is defined _{as ω eq.} (See FIGS. 1 (2) and 3) At this time, assuming that a damping material or a damping device is installed, the angular frequency when the damping coefficient of the damping device is theoretically close to zero is set to ω ₀ . Define. In addition, the angular frequency when the damping coefficient of the damping device is close to ∞ is equal to _{the angular frequency ω 1 when the building is assumed to be installed directly on the ground.} According to these definitions, the natural angular frequency of the seismic isolation structure lies between _{ω 1} and ω _0.

Before giving a detailed technical description of the claims, the conclusions will be given first. When the optimum horizontal rigidity of the laminated rubber and the optimum damping device are selected, the natural angular frequency of the rigid seismic isolation structure becomes the following values.
ω _eq ≒ 0.7ω ₁
This value was obtained assuming that the spectrum of seismic motion is white noise. In the past, it was thought that there were few long-period ground motion components, but considering the magnitude of the earthquake and the characteristics of the ground, it is no wonder that an earthquake with any spectrum occurs. Therefore, in order to obtain the optimum horizontal rigidity and damping coefficient of the laminated rubber for the seismic motion including all frequency components, the spectrum of the seismic motion was assumed to be constant (white noise) in the frequency region.
The spectrum of actual seismic motion fluctuates depending on the individual seismic motion. In addition, there are deviations and errors from the optimum values of the rigidity and damping coefficient of the laminated rubber. Therefore, the range of the natural angular frequency of the rigid seismic isolation structure shown in the claims is set with a certain range. Within this range, it can be theoretically proved that the desired response reduction effect hardly fluctuates.
0.65ω ₁ <ω _eq <0.75ω ₁
In this case, the optimum value of the horizontal rigidity of the laminated rubber and the optimum damping coefficient of the damping device are given by the following equations. Mathematical proofs and technical explanations are given in the following sections.

The optimum value of the horizontal rigidity of the laminated rubber bearing and the optimum value of the damping coefficient of the damping device follow the definitions of FIGS. 2 and 3. A normal building vibration model (one mass system) is shown in FIG. FIG. 3 shows a model in which the rigid seismic isolation structure is replaced with a one-mass system.

ここで、（３）式の置換を行う。
このとき、積層ゴムの水平剛性ｋ_dと建物の水平剛性ｋ（建物の固有角振動数をω₁とする）の比率βと、減衰装置の減衰係数C_dに対応した減衰率ηは、（４）式で定義される。
式（３）と（４）を運動方程式（１）,（２）に代入すると、式（５）、（６）を得る。
ラプラス変換を行うと、（７）式を得る。

左辺から逆行列を掛けると（８）式を得る。
従って、全体応答変位ｙの伝達関数は（９）、（１０）式で与えられる。
また、免震用積層ゴムの応答変位ｚの伝達関数は（１１）式で与えられる。
一方、建物応答変位ｙ−ｚをｘとすれば、その伝達関数は（１２）式で与えられる。
硬質免震構造では、まず、全体応答変位ｙ＝ｘ＋ｚを最小にするパラメータβを特定する。次に積層ゴムの応答変位ｚに比較して建物応答変形ｘを最小とするパラメータηを特定する。このパラメータが最適値であり、次のようにして求めることができる。
前提条件として、地震動のスペクトルが一定値S₀のホワイトノイズと仮定する。このとき、定常不規則外乱としての全体応答変形Ｙ(s)は（１３）式で与えられる。

（１０）式を（１３）式に代入し、留数積分を行うと（１４）式を得る。
Ｙ(s)のパワースペクトルは、剛性の比率βと減衰率ηの2変数関数G_Y(η,β)に比例し、かつ最小値が存在する。（１４）式の関数G_Y(η,β)を、（１５）式で定義する。
関数G_Y(η,β)を最小とするβは、（１６）式より求まる。
（１６）式を満足するβは、関数G_Y(η,β)の最小値を与える。（１６）式を解くとβは（１７）式となる。この結果から、免震構造の全体変位応答を最も小さくする剛性の比率β_optの存在が明らかとなった。この値が、最適な免震構造の固有角振動数（あるいは、固有周期）を与えることとなる。
全体の応答変位ｙを最小値に抑えたまま、積層ゴムの応答変位ｚと建物応答変位ｘの比率を変えて、ｘを小さくすれば建物の地震被害を削減することができる。そのためには、建物応答変位を最小とする減衰率ηを求めればよい。地震動のスペクトルが一定値S₀のホワイトノイズと仮定すれば、定常不規則外乱としての建物応答変形ｘ(s)は（１８）式で与えられる。

（１２）式を（１８)式に代入し、留数積分を行うと（１９）式を得る。
Ｘ(s)のパワースペクトルは、剛性の比率βと減衰率ηの2変数関数G_Ｘ(η,β)に比例する。（１９）式の関数G_X(η,β)は、（２０）式で定義される。
関数G_X(η,β)を最小とするηは、（２１）式より求まる。
よって、最適η_optは（２２）式で与えられる。
（２２）式に（１７）式を代入するとη_opt値は（２３）式の値となる。
また、これらの値が与えられたときの関数G_Y(η,β)は（２４）式で与えられる。
このように、Y(s)のパワースペクトルを最小とする最適な積層ゴムの水平剛性とX(s)のパワースペクトルを最小とする最適な減衰係数が存在する。従来、免震構造では積層ゴム支承の剛性を低くすればするほど長周期化できるので優れた性能があると信じられてきた。しかし、応答変位を下げるという目的からは、積層ゴムを極端に低剛性とすると、応答変位が増大し逆効果となることが判明したのである。しかし、最適な積層ゴム支承の性能が理論的に判明しても、実際にその値に調整することは難しく、また、地震動のスペクトルは必ずしもホワイトノイズと等しくはない。そこで、現実的に設定できる積層ゴム支承の剛性の範囲を最適値の±20％が現実的な範囲と考えると、βは次式の範囲に設定できる。これを硬質免震構造の定義とする。 Mathematical proof The equations of motion of the rigid seismic isolation structure shown in FIG. 3 are given by Eqs. (1) and (2). Here, z represents the deformation of the laminated rubber bearing, and y represents the deformation of the entire building including the deformation of the laminated rubber. The deformation of the building is represented by yz. Also, let the acceleration of the seismic motion be the X _G double dot.

Here, the substitution of Eq. (3) is performed.
_{At this time, the ratio β of the horizontal rigidity k d} of the laminated rubber and the horizontal rigidity k of the building (the natural angular frequency of the building is ω ₁ ) and the damping factor η corresponding to the damping coefficient C _{d of the damping device are (.} 4) Defined by equation.
Substituting equations (3) and (4) into the equations of motion (1) and (2) gives equations (5) and (6).
When the Laplace transform is performed, the equation (7) is obtained.

Multiplying the inverse matrix from the left side gives Eq. (8).
Therefore, the transfer function of the total response displacement y is given by Eqs. (9) and (10).
Further, the transfer function of the response displacement z of the seismic isolation laminated rubber is given by Eq. (11).
On the other hand, if the building response displacement yz is x, the transfer function is given by Eq. (12).
In the rigid seismic isolation structure, first, the parameter β that minimizes the overall response displacement y = x + z is specified. Next, the parameter η that minimizes the building response deformation x with respect to the response displacement z of the laminated rubber is specified. This parameter is the optimum value and can be obtained as follows.
As a precondition, it is assumed that the spectrum of seismic motion is _{white noise with a constant value S 0.} At this time, the overall response deformation Y (s) as a steady irregular disturbance is given by Eq. (13).

Substituting Eq. (10) into Eq. (13) and performing residue integration gives Eq. (14).
The power spectrum of Y (s) is proportional to the two-variable function G _Y (η, β) of the stiffness ratio β and the attenuation factor η, and there is a minimum value. _{The function G Y} (η, β) of Eq. (14) is defined by Eq. (15).
Β that minimizes the function G _Y (η, β) can be obtained from Eq. (16).
Β that satisfies equation (16) _{gives the minimum value of the function G Y} (η, β). When equation (16) is solved, β becomes equation (17). From this result, it was clarified that there is _{a rigidity ratio β opt} that minimizes the overall displacement response of the seismic isolation structure. This value gives the natural angular frequency (or natural period) of the optimum seismic isolation structure.
Seismic damage to buildings can be reduced by reducing the ratio of the response displacement z of the laminated rubber and the building response displacement x while keeping the overall response displacement y to the minimum value. For that purpose, the damping factor η that minimizes the building response displacement may be obtained. Assuming that the spectrum of seismic motion is _{white noise with a constant value S 0} , the building response deformation x (s) as a stationary irregular disturbance is given by Eq. (18).

Substituting Eq. (12) into Eq. (18) and performing residue integration gives Eq. (19).
Power spectrum X (s) is proportional to the variable function G _X ratio beta and the attenuation ratio eta stiffness _(eta, beta). _{The function G X} (η, β) of Eq. (19) is defined by Eq. (20).
Η that minimizes the function G _X (η, β) can be obtained from Eq. (21).
Therefore, the optimum η _opt is given by Eq. (22).
Substituting equation (17) into equation (22), the η _opt value becomes the value of equation (23).
_{Further, the function G Y} (η, β) when these values are given is given by Eq. (24).
As described above, there is an optimum horizontal rigidity of the laminated rubber that minimizes the power spectrum of Y (s) and an optimum damping coefficient that minimizes the power spectrum of X (s). Conventionally, it has been believed that the seismic isolation structure has excellent performance because the longer the period can be, the lower the rigidity of the laminated rubber bearing is. However, for the purpose of lowering the response displacement, it was found that if the laminated rubber has extremely low rigidity, the response displacement increases and has an adverse effect. However, even if the optimum laminated rubber bearing performance is theoretically found, it is difficult to actually adjust it to that value, and the spectrum of seismic motion is not always equal to white noise. Therefore, considering that the range of rigidity of the laminated rubber bearing that can be realistically set is ± 20% of the optimum value, β can be set in the range of the following equation. This is the definition of a rigid seismic isolation structure.

そこで、ηの範囲は最適値を含む次の範囲として（２７）式で定義した。
事実、硬質免震構造の（１５）式で定義された全体応答変位のパワースペクトルを代表する関数G_Y(η,β)の値は、次の範囲に存在する。ηとβとが（２５）式と（２７）式の範囲を変動するとき、関数G_Y(η,β)の変動は（２８）式の範囲になる。
これらの値は硬質免震構造の性能を示しており、硬質免震構造の剛性と減衰装置の減衰率の定義域を与えるものであるが、発明の定義としては不明確である。そこで、硬質免震構造の定義を明確にするため、硬質免震構造の固有角振動数を算定し、請求項に記載した。
以下の計算は、βとηが（２５）式と（２７）式との範囲で変動するとき、硬質免震構造の固有角振動数ω_eqの変動範囲を算定したものでる。固有角振動数ω_eqと等価な減衰率h_eqは、固有方程式から推定できる。（１０）式の分母が固有方程式であるから、固有方程式は（２９）式となる。最適なパラメータを設定した場合、最適値（１７）式と（２３）式とを（２９）式に代入すると（３０）式を得る。

（２９）式と（３０）式を比較すると、最適値を設定した時の固有角振動数ω_eqと等価な減衰率h_eqは、それぞれ（３１）式で与えられる。
もしも、積層ゴム支承の剛性と減衰装置の減衰係数が双方とも最適値よりも小さい場合は、硬質免震構造の角振動数は（３１）式よりも低振動数となる。例えば、両者が（３２）式の場合は、これらの値を（２９）式に代入すると、固有方程式は（３３）式となる。
再び、（３３）式と（２９）式を比較すると、硬質免震構造の固有角振動数が最も低くなった時の固有角振動数ω_eqと等価な減衰率h_eqは、それぞれ（３４）式で与えられる。
硬質免震構造の固有角振動数が最も高くなる場合として、次の条件を設定すれば、同様の計算を行うことにより、次の結果を得る。
（３６）式と（２９）式を比較すると、最適値を設定した時の固有角振動数ω_eqと等価な減衰率h_eqは、それぞれ（３７）式で与えられる。
以上の結果を図示したものが図４及び図５である。硬質免震構造は固有角振動数が次の範囲を満足することがわかる。そこで、硬質免震構造の定義として固有角振動数が（３８）式を満足する範囲と定義する。 On the other hand, when β changes in the range of Eq. (25), the possible range of the optimum attenuation factor η _opt can be calculated from Eq. (22) and is in the range of Eq. (26).

Therefore, the range of η is defined by Eq. (27) as the next range including the optimum value.
_{In fact, the value of the function G Y} (η, β), which represents the power spectrum of the overall response displacement defined by Eq. (15) of the rigid seismic isolation structure, exists in the following range. When η and β fluctuate in the range of Eqs. (25) and (27), the fluctuation of the function G _Y (η, β) falls in the range of Eq. (28).
These values indicate the performance of the rigid seismic isolation structure and give the domain of the rigidity of the rigid seismic isolation structure and the damping factor of the damping device, but the definition of the invention is unclear. Therefore, in order to clarify the definition of the rigid seismic isolation structure, the natural angular frequency of the rigid seismic isolation structure was calculated and described in the claims.
The following calculation calculates the fluctuation range of _{the natural angular frequency ω eq} of the rigid seismic isolation structure when β and η fluctuate in the range of equations (25) and (27). The damping factor h _eq equivalent to the natural angular frequency ω _eq can be estimated from the eigen equation. Since the denominator of equation (10) is an eigen equation, the eigen equation is equation (29). When the optimum parameters are set, the optimum values (17) and (23) are substituted into the equation (29) to obtain the equation (30).

Comparing Eqs. (29) and (30), the attenuation rate h _{eq equivalent to the natural angular frequency ω eq} when the optimum value is set is given by Eq. (31), respectively.
If both the rigidity of the laminated rubber bearing and the damping coefficient of the damping device are smaller than the optimum values, the angular frequency of the rigid seismic isolation structure is lower than that of Eq. (31). For example, when both are equations (32), substituting these values into equation (29), the eigen equation becomes equation (33).
Comparing Eqs. (33) and (29) again, the damping factor h _{eq equivalent to the natural angular frequency ω eq} when the natural angular frequency of the rigid seismic isolation structure is the lowest is (34). Given in the formula.
Assuming that the natural angular frequency of the rigid seismic isolation structure is the highest, if the following conditions are set, the following results can be obtained by performing the same calculation.
Comparing Eqs. (36) and (29), the attenuation rate h _{eq equivalent to the natural angular frequency ω eq} when the optimum value is set is given by Eq. (37), respectively.
The above results are illustrated in FIGS. 4 and 5. It can be seen that the rigid seismic isolation structure satisfies the following range in the natural angular frequency. Therefore, as the definition of the rigid seismic isolation structure, the natural angular frequency is defined as the range that satisfies the equation (38).

The rigid seismic isolation structure according to the present invention can be widely used as a seismic isolation structure for buildings in particular.

Claims (1)

In a seismic isolation structure in which the structure is supported by laminated rubber bearings,
The ratio of the primary intrinsic angular frequency ω ₁ of the structure to the primary intrinsic angular frequency ω _{eq of the seismic isolation structure is}
0.65 <ω _eq / ω ₁ <0.75
A rigid seismic isolation structure characterized by setting the horizontal rigidity and damping coefficient of the laminated rubber bearings to satisfy.

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