JP2017203297A - Base-isolation construction and method of designing base-isolation construction - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a base-isolation construction capable of improving base-insulation performance.SOLUTION: A base-insulation construction 1 is a base-insulation construction 1 applied to a building 100 including an upper structure 3 and a lower structure 2. The base-insulation construction 1 comprises: a viscoelastic device 9 having elastic rubber 8, a spring mechanism 12 and an oil damper 13, and according with a Maxell viscoelastic model; and a rotational mass device 11 which exhibits inertial force based upon acceleration acting horizontally on the upper structure 3. The elastic rubber 8, viscoelastic device 9 and rotational mass device 11 are arranged in parallel with one another, and each coupled to the upper structure 3 and lower structure 2.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a base isolation structure and a method for designing a base isolation structure.

  In recent years, techniques for protecting structures from earthquakes have been studied. One of the technologies is the seismic isolation structure. The base isolation structure attenuates the vibration applied to the structure by the earthquake. The base isolation structure includes a spring element and a damping element. For example, Patent Document 1 discloses a technique for reducing a specific vibration mode. In this technique, a spring element and a damping element are arranged between a foundation structure and a structure to be protected, and an inertial mass for suppressing a specific vibration mode is arranged. As another example of the seismic isolation structure, the natural period of the structure is lengthened to attenuate the vibration based on the primary vibration mode of the structure, and the structure primary by a damping element having a relatively large damping performance. Some suppress deformation based on the vibration mode. However, in such a base-isolated structure, the acceleration response of the structure caused by the earthquake may be amplified. Therefore, in the seismic isolation structure disclosed in Patent Document 2, amplification of acceleration response in the structure is suppressed using a so-called Maxwell damper in which a damping element and a spring element are connected in series.

Japanese Patent Laid-Open No. 2005-213887 JP2015-105554A

  When vibration due to an earthquake or the like is applied to a structure, the primary vibration mode of the structure is often dominant in the influence of vibration such as deformation of the structure. Therefore, in order to suppress the influence of the primary vibration mode, a seismic isolation structure having a relatively large damping performance while increasing the natural period of the structure may be employed. According to this seismic isolation structure, the influence of the primary vibration mode is suppressed to a level with no problem. However, higher order vibration modes than primary vibration modes may be problematic.

  An object of the present invention is to provide a seismic isolation structure capable of improving the seismic isolation performance and a method for designing the seismic isolation structure.

  One aspect of the present invention is a seismic isolation structure applied to a building including an upper structure and a lower structure, and is connected to the upper structure and the lower structure and exhibits a restoring force in the horizontal direction. An elastic part, a viscoelastic part connected to the upper structure and the lower structure and connected in series with each other, and a viscoelastic part according to Maxwell's viscoelastic model, and the upper structure and the lower structure. And an inertial mass part that exerts an inertial force based on acceleration acting in a horizontal direction with respect to the upper structure, and the lower elastic part, the viscoelastic part, and the inertial mass part are arranged in parallel to each other , Each connected to an upper structure and a lower structure.

  In this seismic isolation structure, the increase in deformation caused by the primary vibration mode that can occur when the natural period of the building is lengthened is reduced by the viscoelastic portion. Therefore, the influence caused by the primary vibration mode that can occur when an earthquake is applied to the building is reduced. Furthermore, in the seismic isolation structure, an increase in deformation due to the secondary vibration mode is reduced by the inertial mass portion. Therefore, the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building is reduced. Therefore, according to the seismic isolation structure, the influence caused by the primary vibration mode and the secondary vibration mode can be reduced, so that the seismic isolation performance can be improved.

  The seismic isolation structure may further include a sliding bearing that is mounted on the lower structure and connected to the upper structure, and exerts a horizontal frictional force with the lower structure. According to this sliding support, the upper structure can be favorably supported.

Another aspect of the present invention is a method of designing a seismic isolation structure applied to a building, the building comprising a first mass element, a second mass element, and a first mass element with a second mass. An upper structure including an upper elastic element connected to the element, a lower structure spaced apart from the upper structure, a lower elastic element, an inertial mass element, and a connected elastic element and a connected damping element Each of the lower elastic element, the viscoelastic element, and the inertial mass element arranged in parallel with each other is a first mass element. A seismic isolation structure coupled to the lower structure, and an elastic coefficient (k ₁ ) of the lower elastic element, an elastic coefficient (k _c ) of the connected elastic element, and a mass (m ₁ ) of the first mass element using the first function that includes a damping coefficient of the coupling damping element (C ₀₎ And obtaining, by utilizing the elasticity coefficient of the elastic modulus (k ₁₎ and the connecting elastic element of the lower elastic element (k _c), and obtaining a first equivalent elastic modulus (k _a), the first mass element The second function including the mass (m ₁ ), the mass of the second mass element (m ₂ ), the first equivalent elastic modulus (k _a ), and the elastic modulus (k ₂ ) of the upper elastic element. Obtaining the mass (m ₁ ′) of the inertial mass element.

In the seismic isolation structure, an increase in deformation caused by the primary vibration mode that can occur when the natural period of the building is lengthened is reduced by the viscoelastic portion. The characteristic of the viscoelastic part is determined so as to attenuate the primary vibration mode of the building in the step of obtaining the damping coefficient (C ₀ ). According to this method, it is possible to obtain a damping coefficient (C ₀ ) that can suitably reduce the influence caused by the primary vibration mode that can occur when an earthquake is applied to a building. Furthermore, in the seismic isolation structure, an increase in deformation due to the secondary vibration mode is reduced by the inertial mass portion. The characteristic of the inertia mass part is obtained by using the elastic coefficient (k ₁ ) and the elastic coefficient (k _c ) in the step of obtaining the mass (m ₁ ′) of the inertia mass part. According to this method, it is possible to obtain an inertial mass (m ₁ ′) that can suitably reduce the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building. Therefore, according to this method of designing a base isolation structure, it is possible to design a base isolation structure that can improve the base isolation performance by reducing the influence caused by the primary vibration mode and the secondary vibration mode.

A method for designing a base-isolated structure according to another aspect of the present invention is a friction element that is mounted on a lower structure and connected to the upper structure, and exerts a horizontal frictional force with the lower structure. of a equivalent stiffness (k _f) further the step of obtaining a step of obtaining an equivalent stiffness (k _f) is due to the secondary vibration mode of the building, relative horizontal upper structure to the lower structure A step of obtaining a secondary displacement, a step of obtaining a secant stiffness using a displacement friction force characteristic and a secondary displacement indicating a relationship between a displacement of the upper structure in the horizontal direction relative to the lower structure and a friction force; and a secant stiffness Determining the equivalent stiffness (k _f ) of the friction element, and obtaining the first equivalent elastic modulus (k _a ) includes the elastic modulus (k ₁ ) of the lower elastic element, the elasticity of the coupled elastic element coefficient _(k c), and the friction needed Using the equivalent rigidity (k _f), may be obtained first equivalent elastic coefficient (k _a). According to this method, it is possible to obtain the mass (m ₁ ′) of the inertia mass part in consideration of the frictional force of the sliding bearing.

Obtaining a secondary displacement calculates the secondary displacement using Equation (1), in the formula (1), [delta] ₂ is the secondary displacement, [delta] ₁ is due to the primary vibration mode of the building, It is a primary displacement of the upper structure relative to the lower structure in the horizontal direction, β ₁ may be a stimulation coefficient of the primary vibration mode, and β ₂ may be a stimulation coefficient of the secondary vibration mode. According to this formula (1), the horizontal displacement for obtaining the elastic coefficient of the sliding bearing can be suitably obtained.

Obtaining a secondary displacement calculates the secondary displacement by using Equation (2), in the formula (2), [delta] ₂ is the secondary displacement, [delta] ₁ is due to the primary vibration mode of the building, Is the horizontal displacement of the upper structure relative to the lower structure, γ ₁ is the stimulation function of the first mass element in the primary vibration mode, and γ ₂ is the first mass element in the secondary vibration mode. The stimulation function may be According to this formula (2), a horizontal displacement for obtaining the equivalent rigidity of the sliding bearing can be suitably obtained.

The first function is Equation (3), where C ₀ is the damping coefficient of the coupled damping element, k ₁ is the modulus of elasticity of the lower elastic element, and k _c is the elasticity of the coupled elastic element. Ω is the circular frequency shown in Equation (4), and N is the stiffness ratio (k) as the ratio of the elastic coefficient (k _c ) of the coupled elastic element to the elastic coefficient (k ₁ ) of the lower elastic element _c / k ₁ ), and m ₁ may be the mass of the first mass element. According to these equations (3) and (4), it is possible to obtain a damping coefficient (C ₀ ) that can suitably reduce the displacement caused by the primary vibration mode.

The second function is the equation (5), in equation (5), m 1 _'is the mass of the inertia mass elements, k _a is the first equivalent elastic modulus, m ₁ is the first mass element M ₂ may be the mass of the second mass element, and k ₂ may be the elastic modulus of the upper elastic element. According to this formula (5), it is possible to obtain an inertial mass (m ₁ ′) that can suitably reduce the displacement caused by the secondary vibration mode.

  Still another embodiment of the present invention is a seismic isolation structure applied to a building including an upper structure and a lower structure, which is connected to the upper structure and the lower structure, and has horizontal restoring force and damping. A laminated rubber bearing with a lead plug that exerts a force, and an inertial mass part that is coupled to the upper structure and the lower structure and that exerts an inertial force based on acceleration acting in a horizontal direction on the upper structure, The laminated rubber bearing with lead plug and the inertial mass portion are arranged in parallel to each other and are connected to the upper structure and the lower structure, respectively.

  In this seismic isolation structure, the increase in deformation caused by the primary vibration mode that can occur when the natural period of the building is lengthened is reduced by the laminated rubber bearing with the lead plug. Therefore, the influence caused by the primary vibration mode that can occur when an earthquake is applied to the building is reduced. Furthermore, in the seismic isolation structure, an increase in deformation due to the secondary vibration mode is reduced by the inertial mass portion. Therefore, the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building is reduced. Therefore, according to the seismic isolation structure, since the influence caused by the primary vibration mode and the secondary vibration mode can be reduced, the seismic isolation performance can be improved.

Yet another aspect of the present invention is a method of designing a seismic isolation structure applied to a building, the building comprising a first mass element, a second mass element, and a first mass element in a second An upper structure including an upper elastic element connected to the mass element; a lower structure spaced apart from the upper structure; an inertial mass element; and a laminated rubber bearing with a lead plug, Each of an inertial mass element and a lead-plug laminated rubber bearing arranged in parallel with each other, and a seismic isolation structure connected to the first mass element and the lower structure, and a deformation of the lead-plug laminated rubber bearing; The step of obtaining the second equivalent elastic modulus (k _r ) of the laminated rubber bearing with the lead plug using the deformation load characteristic indicating the relationship with the load, the second equivalent elastic modulus (k _r ), the first mass of the mass element _(m 1), the mass of the second mass element _{(m 2} And using the third function comprising the elastic modulus of the upper elastic element (k _2), comprising the steps of obtaining the inertial mass mass (m ₁ '), a second equivalent elastic modulus (k _r Is obtained due to the secondary vibration mode of the building, and the step of obtaining the horizontal displacement of the upper structure relative to the lower structure, the deformation load characteristic and the secondary displacement are used. Obtaining a secant stiffness and determining the secant stiffness as a second equivalent elastic modulus (k _r ) of the laminated rubber bearing with lead plug.

  According to the method of designing this seismic isolation structure, it is possible to obtain an inertial mass capable of reducing the influence caused by the primary vibration mode and the secondary vibration mode using the deformation load characteristics of the laminated rubber bearing with lead plug. . Therefore, it is possible to design a base isolation structure that can improve base isolation performance.

Obtaining a secondary displacement calculates the secondary displacement using the equation (6), in the formula (6), [delta] ₂ is the secondary displacement, [delta] ₁ is due to the primary vibration mode of the building, It is a primary displacement of the upper structure relative to the lower structure in the horizontal direction, β ₁ may be a stimulation coefficient of the primary vibration mode, and β ₂ may be a stimulation coefficient of the secondary vibration mode. According to this step, a horizontal displacement for obtaining the second equivalent elastic modulus can be obtained.

The step of obtaining the secondary displacement calculates the secondary displacement using Equation (7). In Equation (7), δ ₂ is the secondary displacement, and δ ₁ is caused by the primary vibration mode of the building, Is the horizontal displacement of the upper structure relative to the lower structure, γ ₁ is the stimulation function of the first mass element in the primary vibration mode, and γ ₂ is the first mass element in the secondary vibration mode. The stimulation function may be According to this step, a horizontal displacement for obtaining the second equivalent elastic modulus can be obtained.

The third function is Equation (8), where m ₁ ′ is the mass of the inertial mass part, _kr is the second equivalent elastic modulus, and k ₂ is the elasticity of the upper elastic element. A coefficient, m ₁ may be the mass of the first mass element, and m ₂ may be the mass of the second mass element. According to this equation (8), it is possible to obtain an inertial mass (m ₁ ′) that can suitably reduce the displacement caused by the secondary vibration mode.

  ADVANTAGE OF THE INVENTION According to this invention, the method of designing the base isolation structure which can improve base isolation performance, and the said base isolation structure is provided.

It is a figure which shows the building where the seismic isolation structure which concerns on 1st Embodiment of this invention was applied. (A) A part is a figure which shows the viscoelastic apparatus shown by FIG. 1, (b) part is a figure which shows the rotary mass apparatus shown by FIG. It is the figure which showed the building and seismic isolation structure shown in FIG. 1 as a vibration model. It is a figure which shows typically the deformation | transformation corresponding to each vibration mode of the building modeled as a two-degree-of-freedom system. It is a flowchart which shows the main steps of the method of designing the seismic isolation structure which concerns on 1st Embodiment of this invention. Part (a) is a graph showing the relationship between the attenuation coefficient and the attenuation constant, and part (b) is a diagram showing the relationship between the attenuation constant and the natural period. It is a graph which shows an example of the acceleration response spectrum of the building with respect to an earthquake. Part (a) is the result of the response analysis of the base isolation structure according to the comparative example, and part (b) is the result of the response analysis of the base isolation structure designed by the design method according to the first embodiment. It is a figure which shows the building where the seismic isolation structure which concerns on 2nd Embodiment of this invention was applied. It is a figure which shows the structure of the laminated rubber bearing apparatus containing a lead plug shown by FIG. It is the figure which showed the building and seismic isolation structure which were shown by FIG. 9 as a vibration model. It is a flowchart which shows the main steps of the method of designing the seismic isolation structure which concerns on 2nd Embodiment of this invention. It is a graph which shows the deformation load characteristic of the laminated rubber bearing apparatus containing a lead plug. It is the figure which showed the seismic isolation structure which concerns on the modification as a vibration model. It is a flowchart which shows the main steps of the method of designing the seismic isolation structure which concerns on a modification. It is a graph which shows the displacement frictional force characteristic of a sliding bearing.

[First Embodiment]
DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted.

  As shown in FIG. 1, the building 100 includes a seismic isolation structure 1, a lower structure 2, and an upper structure 3. The lower structure 2 is a foundation that is spaced apart from the upper structure 3 and is fixed to the ground 101. The upper structure 3 is a casing disposed on the lower structure 2 via the seismic isolation structure 1. The upper structure 3 includes a frame structure 4 including pillars 4 a and beams 4 b and a floor structure 6.

  The seismic isolation structure 1 attenuates horizontal vibration transmitted from the lower structure 2 to the upper structure 3. The seismic isolation structure 1 includes a sliding support device 7, an elastic rubber 8 (lower elastic portion), a viscoelastic device 9 (viscoelastic portion), and a rotating mass device 11 (inertial mass portion).

  The sliding support device 7 supports a vertically downward load based on the upper structure 3. This load is a combination of the weight of the frame structure 4 of the upper structure 3 and the weight of the floor structure 6. The plurality of sliding support devices 7 are arranged in a matrix on the main surface 2 a of the lower structure 2. The sliding support device 7 is disposed directly below the column 4a that constitutes the upper structure 3. The sliding support device 7 includes a building-side sliding portion 7 a fixed to the lower surface of the floor structure 6, and a foundation-side sliding portion 7 b fixed to the main surface 2 a of the lower structure 2. The sliding support device 7 causes a horizontal slip between the sliding portion 7a and the sliding portion 7b. By this sliding, the floor structure 6 can move relative to the lower structure 2 in the horizontal direction.

  The elastic rubber 8 functions as a so-called horizontal spring, and is arranged so that a vertically downward load based on the upper structure 3 does not act. The elastic rubber 8 is connected to the lower structure 2 and the floor structure 6. When the floor structure 6 moves relative to the lower structure 2 in the horizontal direction, the elastic rubber 8 undergoes shear deformation. Due to this shear deformation, the elastic rubber 8 exhibits a restoring force in the horizontal direction.

  Since the elastic rubber 8 is a separate body from the sliding support device 7, the sliding support device 7 and the elastic rubber 8 can be arranged at desired positions, respectively. Therefore, the freedom degree of arrangement | positioning of the sliding support apparatus 7 and the elastic rubber 8 can be raised. The elastic rubber 8 may be arranged in an arbitrary number between the lower structure 2 and the upper structure 3 in an arbitrary place. Accordingly, since the seismic isolation structure 1 has a high degree of freedom in arrangement of the elastic rubber 8, the arrangement of the elastic rubber 8 makes it easy to align the upper structure 3 with the center of gravity of the upper structure 3. According to such a structure, when the force to a horizontal direction is added to the upper structure 3 by an earthquake etc., generation | occurrence | production of the problem that the upper structure 3 becomes easy to be damaged by twisting the building 100 can be suppressed.

  The elastic rubber 8 can be freely deformed in the horizontal direction. In other words, the elastic constant of the elastic rubber 8 in the horizontal direction is constant regardless of the direction of deformation. Therefore, the natural period of the seismic isolation structure 1 is also constant regardless of the direction. The natural period of the seismic isolation structure 1 is set to, for example, not less than 10 seconds and not more than 15 seconds based on the viewpoint of improving the input blocking performance of shaking to the floor structure 6. Various rubbers can be adopted as the elastic rubber 8. Therefore, it is possible to make it difficult for creep to occur in the elastic rubber 8.

  The viscoelastic device 9 attenuates the shaking of the upper structure 3 in the horizontal direction. That is, the viscoelastic device 9 reduces relative displacement along the horizontal direction of the floor structure 6 with respect to the lower structure 2. The viscoelastic devices 9 are arranged at positions that are point-symmetric or line-symmetric with respect to each other on a horizontal plane. The viscoelastic device 9 is separate from the sliding support device 7 and the elastic rubber 8.

  As shown in part (a) of FIG. 2, the viscoelastic device 9 includes a spring mechanism 12 (connection elastic part) and an oil damper 13 (connection attenuation part). The spring mechanism 12 and the oil damper 13 are connected in series with each other. Thus, the viscoelastic device 9 in which the damping element such as the oil damper 13 is connected in series to the elastic element such as the spring mechanism 12 is a so-called Maxwell type damping device. The spring mechanism 12 is connected to the main surface 2 a of the lower structure 2 via the clevis 16 and the first bracket 14. A spherical bearing is provided inside the clevis 16, and the inclination of the spring mechanism 12 with respect to the first bracket 14 is absorbed by the spherical bearing. The spring mechanism 12 generates an urging force corresponding to the horizontal displacement of the floor structure 6 relative to the lower structure 2. The oil damper 13 connected to one end of the spring mechanism 12 is connected to the lower surface 6 a of the floor structure 6 via the second bracket 17. The oil damper 13 includes a cylinder in which oil is sealed and a rod that protrudes and protrudes with respect to the cylinder.

  In the viscoelastic device 9, the spring mechanism 12 is connected to the floor structure 6 via the first bracket 14 and the oil damper 13 is connected to the lower structure 2 via the second bracket 17. Good.

  As shown in part (b) of FIG. 2, the rotary mass device 11 exhibits an inertial force corresponding to the acceleration along the horizontal direction of the floor structure 6 with respect to the lower structure 2. According to this inertial force, the acceleration along the horizontal direction is reduced. Similarly to the viscoelastic device 9, the rotary mass device 11 is arranged at positions that are point-symmetric or line-symmetric with each other on the horizontal plane. The rotary mass device 11 is separate from the sliding support device 7, the elastic rubber 8 and the viscoelastic device 9.

  The rotary mass device 11 is connected to the main surface 2 a of the lower structure 2 through the third bracket 18 and is connected to the lower surface 6 a of the floor structure 6 through the fourth bracket 19. The fourth bracket 19 has a swinging part 19 a and connects the rotary mass device 11 to the floor structure 6 so as to be swingable.

The rotary mass device 11 includes a flywheel 21 and a rod 22. One end of the rod 22 is connected to the fourth bracket 19 via the swinging portion 19 a, and the other end is connected to the flywheel 21. The rod 22 is movable relative to the flywheel 21 in the axial direction thereof. The flywheel 21 has a cylindrical mass body, and converts the linear motion of the rod 22 in the axial direction into the rotational motion of the mass body around the axis. That is, when horizontal acceleration acts on the upper structure 3, the rod 22 moves in the horizontal direction with respect to the flywheel 21 via the floor structure 6 and the fourth bracket 19. This movement of the rod 22 causes the mass body of the flywheel 21 to rotate. Since the rotating body has an inertia moment based on its diameter and mass, the rod 22 moves relative to the flywheel 21 while receiving a reaction force caused by the inertia moment. The flywheel 21 is connected to the lower structure 2 via a screw-penetrating clevis. The flywheel 21 has an inertial mass (m ₁ ′) using the diameter and mass of the rotating mass body as design variables.

  In the rotary mass device 11, the third bracket 18 may be connected to the floor structure 6 and the fourth bracket 19 may be connected to the lower structure 2.

FIG. 3 illustrates the building 100 as a vibration model. As shown in FIG. 3, the building 100 is shown as a two-mass system vibration system in which the floor structure 6 is treated as a first mass element and the frame structure 4 is treated as a second mass element. Hereinafter, the mass of the floor structure 6 is shown as mass (m ₁ ). Moreover, the mass of the housing structure 4 is shown as mass (m < ₂ >). The frame structure 4 and the floor structure 6 are connected by an upper elastic element. The upper elastic element is caused by components such as the column 4 a and the beam 4 b of the frame structure 4. Hereinafter, the elastic coefficient of the upper elastic element in the housing structure 4 is shown as an elastic coefficient (k ₂ ).

Between the lower structure 2 and the floor structure 6, three vibration elements, that is, an elastic rubber 8, a viscoelastic device 9, and a rotating mass device 11 are arranged. The elastic rubber 8 is a lower elastic element, the viscoelastic device 9 is a viscoelastic element, and the rotary mass device 11 is an inertial mass element. Further, in the viscoelastic device 9, the spring mechanism 12 is a connecting elastic element, and the oil damper 13 is a connecting damping element. These lower elastic elements, viscoelastic elements, and inertial mass elements are not connected in series with each other, and are disposed in parallel between the lower structure 2 and the floor structure 6. The elastic coefficient of the elastic rubber 8 as the lower elastic element is shown as an elastic coefficient (k ₁ ). The elastic coefficient of the spring mechanism 12 as the connecting elastic element is shown as an elastic coefficient (k _c ). A damping coefficient of the oil damper 13 as a coupling damping element is shown as a damping coefficient (C). The mass of the rotary mass device 11 as an inertial mass element is shown as mass (m ₁ ′).

The building 100 that is a two-degree-of-freedom vibration system has a primary natural period (T ₁ ) and a secondary natural period (T ₂ ). When the vibration based on the earthquake is input to the building 100, the building 100 is deformed according to the vibration mode corresponding to each natural period (T ₁ , T ₂ ). Specifically, the deformation of the building 100 is expressed by the addition of the deformation corresponding to the primary vibration mode and the deformation corresponding to the secondary vibration mode. For example, FIG. 4 shows a result of mode analysis of the building 100. The horizontal axis represents the normalized displacement in the horizontal direction, and the vertical axis represents the height of the building 100 in the vertical direction. As shown in FIG. 4, the building 100 has a deformation mode (see graph G1) in which the upper structure 3 moves horizontally with respect to the lower structure 2 by deformation according to the primary vibration mode. Further, the building 100 has a deformation mode (see graph G2) in which a predetermined position in the vertical direction is a node by deformation according to the secondary vibration mode.

In this seismic isolation structure 1, an increase in deformation caused by the primary vibration mode that can occur when the primary natural period (T ₁ ) of the building 100 is lengthened is reduced by the oil damper 13 of the viscoelastic device 9. Therefore, the influence caused by the primary vibration mode that may occur when an earthquake is applied to the building 100 is reduced. Furthermore, in the seismic isolation structure 1, an increase in acceleration due to the secondary vibration mode is reduced by the rotating mass device 11. Therefore, the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building 100 is reduced. Therefore, according to the seismic isolation structure 1, since the influence resulting from the primary vibration mode and the secondary vibration mode can be reduced, the seismic isolation performance can be improved.

Next, a method for designing a seismic isolation structure will be described with reference to FIGS. 5, 6, 7, and 8 as appropriate. The building 100 has seven design variables. Specifically, the seven design variables are mass (m ₁ ), mass (m ₂ ), elastic coefficient (k ₁ ), elastic coefficient (k ₂ ), elastic coefficient (k _c ), and damping coefficient (C). And mass (m ₁ ′). Note that the sliding support device 7 is treated as being hardly resistant to relative movement in the horizontal direction.

First, the primary natural period (T ₁ ) of the building 100 is set (step S1). The natural period (T ₁ , T ₂ ) is determined by the elastic coefficient (k ₁ ), the elastic coefficient (k ₂ ), the mass (m ₁ ), and the mass (m ₂ ). Specifically, when an expected seismic wave is input to the building 100, a primary natural period (T ₁ ) at which the response acceleration of the building 100 is equal to or less than a predetermined value is determined. The mass (m ₁ ) and the mass (m ₂ ) are set in advance. Accordingly, the elastic coefficient (k ₁ ) and the elastic coefficient (k ₂ ) are determined from the primary natural period (T ₁ ), the mass (m ₁ ), and the mass (m ₂ ).

式（９）において、ωは式（１０）に示される円振動数である。Ｎは弾性係数（ｋ_１）に対する弾性係数（ｋ_ｃ）の比を示す剛性比（ｋ_ｃ／ｋ_１）である。 Next, an optimum attenuation coefficient (C ₀ ) is obtained (step S2). Part (a) of FIG. 6 shows the relationship between the attenuation coefficient (C) and the attenuation constant (h). The graph G3 shows the relationship between the damping coefficient (C) corresponding to the primary vibration mode and the damping constant (h), and the graph G4 shows the relationship between the damping coefficient (C) corresponding to the secondary vibration mode and the damping constant (h). It is. These relationships are obtained by performing complex eigenvalue analysis. Here, the value required for the design of the seismic isolation structure is the optimum damping coefficient (C ₀ ) that maximizes the damping constant (h) in the graph G3. This optimum attenuation coefficient (C ₀ ) is obtained by the following equation (9) (first function) and equation (10).

In equation (9), ω is the circular frequency shown in equation (10). N is the rigidity ratio showing the ratio of the elastic modulus _{(k c)} for elastic modulus _{(k 1) (k c /} k 1).

Incidentally, FIG. 7 shows an acceleration response spectrum of the building 100 when an earthquake is input to the building 100. The horizontal axis is the natural period (T) of the building 100, and the vertical axis is the response acceleration. For example, according to the graph G7 of FIG. 7, when it is the natural period (T ₀ ) of the building 100, the response acceleration (R ₀ ) is obtained. When it is the primary natural period (T ₁₎ natural period determined in step S1 that sets the (T ₁₎ is response acceleration (R ₁₎ is obtained. Since the response acceleration (R ₁ ) is smaller than the response acceleration (R ₀ ), it can be seen that the response acceleration can be reduced by increasing the period.

As described above, the building 100 has a primary natural period (T ₁ ) and a secondary natural period (T ₂ ). The secondary natural period (T ₂ ) is shorter than the primary natural period (T ₁ ). Therefore, in the building 100, when it is the primary natural period (T ₁ ), it may be the secondary natural period (T ₂ ). In this case, the influence of the primary vibration mode corresponding to the primary natural period (T ₁ ) is suppressed. However, in the secondary natural period (T ₂ ), it is the response acceleration (R ₂ ), which is larger than the response acceleration (R ₁ ). Therefore, the influence of the secondary vibration mode cannot be ignored. Therefore, the inertial mass (m ₁ ′) of the rotary mass device 11 is set from the viewpoint of reducing the secondary vibration mode.

To determine the inertial mass (m ₁ ′) that reduces the secondary vibration mode, that is, brings the secondary vibration mode close to zero, Expression (11) (second function) is used. Here, ka in the equation (11) is _a first equivalent elastic coefficient to be described later, and is represented by the equation (12).

When Expression (11) is used in the design method of the present embodiment, for example, if the spring mechanism 12 is simply ignored (k _c = 0), the secondary vibration mode cannot be suitably suppressed. The part (a) in FIG. 8 is an analysis result when (k _a = k ₁ ) in the expression (11). The graph G8 shows the acceleration response in the housing structure 4. The graph G9 shows the acceleration response in the floor structure 6. As shown in the graph G9, the acceleration in the floor structure 6 is not sufficiently suppressed. Therefore, in handling the formula (11), handling of the spring mechanism 12 becomes a problem.

Part (b) of FIG. 6 shows the relationship between the attenuation coefficient (C) and the natural period (T). When the damping coefficient (C) is zero, the primary vibration mode is a natural period (T ₁ ), and the secondary vibration mode is a natural period (T ₂ ). When the damping coefficient (C) increases, in the primary vibration mode, the natural period (T ₁ ) significantly decreases with the damping coefficient (C ₀ ) as a boundary and converges to the natural period (T ₁ ′). On the other hand, in the secondary vibration mode, the natural period (T ₂ ) significantly decreases with the damping coefficient (C ₁ ) as a boundary, and converges to the natural period (T ₂ ′). The damping coefficient (C ₀ ) at which the natural period (T ₁ ) of the primary vibration mode decreases is larger than the damping coefficient (C ₁ ) at which the natural period (T ₂ ) of the secondary vibration mode decreases.

As already described, in step S2, the damping coefficient (C) of the oil damper 13 is set to the optimum damping coefficient (C ₀ ). Referring to the graph G6, the optimal natural damping coefficient (C ₀ ) corresponds to the secondary natural period (T ₂ ′). This state is a state in which the spring mechanism 12 functions effectively against vibration. We introduce the first equivalent elastic coefficient indicating the modulus of the seismic isolation structure 1 (k _a). In a state where the spring mechanism 12 functions effectively with respect to vibration, the elastic element in the seismic isolation structure 1 is one in which the elastic rubber 8 and the spring mechanism 12 are connected in parallel as shown in the equation (12). Can be handled as Therefore, by calculating the sum of the elastic coefficient (k ₁ ) and the elastic coefficient (k _c ), the first equivalent elastic coefficient (k _a ) in the seismic isolation structure 1 is obtained (step S3).

Then, the first equivalent elastic modulus (k _a ), elastic modulus (k ₂ ), mass (m ₁ ), and mass (m ₂ ) obtained by equation (12) are substituted into equation (11). Thus, the inertial mass (m ₁ ′) is obtained (step S4).

  The seismic isolation structure 1 is designed by the above steps S1, S2, S3, and S4.

In the seismic isolation structure 1, an increase in deformation caused by the primary vibration mode that can occur when the natural period (T) of the building 100 is lengthened is reduced by the oil damper 13 of the viscoelastic device 9. The characteristics of the oil damper 13 are determined so as to correspond to the damping of the primary vibration mode of the building 100 in step S2 for obtaining the optimum damping coefficient (C ₀ ). According to this method, it is possible to obtain the optimum damping coefficient (C ₀ ) that can suitably reduce the influence caused by the primary vibration mode that can occur when an earthquake is applied to the building 100. Furthermore, in the seismic isolation structure 1, the increase in deformation due to the secondary vibration mode is reduced by the rotating mass device 11. The characteristic of the rotating mass device 11 is that the elastic coefficient (k ₁ ) of the elastic rubber 8 and the elastic coefficient (k _c ) of the spring mechanism 12 are obtained in step S3 for obtaining the inertial mass (m ₁ ′) of the rotating mass device 11. It is treated as _a sum (k _a = k ₁ + k _c ). According to this method, it is possible to obtain an inertial mass (m ₁ ′) that can suitably reduce the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building 100. Therefore, according to the method of designing the base isolation structure, it is possible to design the base isolation structure 1 that can improve the base isolation performance by reducing the influence caused by the primary vibration mode and the secondary vibration mode.

  Part (b) of FIG. 8 is an analysis result of the seismic isolation structure designed by the design method of the present embodiment. The graph G10 shows the acceleration response in the housing structure 4. The graph G11 shows the acceleration response in the floor structure 6. As can be seen from the graph G11, the acceleration in the floor structure 6 can be sufficiently reduced. Therefore, according to the method of designing the seismic isolation structure of this embodiment, it has been found that the acceleration response due to the secondary vibration mode can be sufficiently reduced.

[Second Embodiment]
Next, a method for designing the base isolation structure and the base isolation structure according to the second embodiment will be described. As shown in FIG. 9, the seismic isolation structure 1 </ b> A according to the present embodiment is different from the elastic rubber 8 and the viscoelastic device 9 in that the seismic isolation structure 1 </ b> A is a laminated rubber bearing device with lead plugs (hereinafter referred to as LRB23: Lead Rubber). It differs from the seismic isolation structure 1 of 1st Embodiment by the point provided with a bearing. Other configurations of the seismic isolation structure 1A according to the second embodiment are the same as those of the seismic isolation structure 1 according to the first embodiment.

  The building 100A includes a seismic isolation structure 1A. The seismic isolation structure 1 </ b> A includes a rotary mass device 11 and an LRB 23. The LRB 23 supports the loads of the frame structure 4 and the floor structure 6, functions as a horizontal rubber, and further has a damping function. That is, the LRB 23 has the functions of the sliding support device 7, the elastic rubber 8, and the viscoelastic device 9 of the first embodiment.

  As shown in FIG. 10, the LRB 23 is formed by alternately stacking a plurality of steel plates 23a and a plurality of rubber sheets 23b in the vertical direction. The steel plate 23a functions to support a load in the vertical direction. Also. The rubber sheet 23b exhibits the function of a horizontal rubber. Furthermore, the steel plate 23a and the rubber sheet 23b are provided with holes penetrating in the stacking direction. A lead plug 23c is disposed in this hole. When the steel plate 23a and the rubber sheet 23b are deformed in the horizontal direction, the lead plug 23c is plastically deformed. Since this plastic deformation consumes vibration energy, the damping function is exhibited.

  In this seismic isolation structure 1A, the increase in deformation caused by the primary vibration mode that can occur when the primary natural period of the building 100A is lengthened is reduced by the LRB 23. Therefore, the influence caused by the primary vibration mode that can occur when an earthquake is applied to the building 100A is reduced. Furthermore, in the seismic isolation structure 1 </ b> A, an increase in acceleration due to the secondary vibration mode is reduced by the rotating mass device 11. Therefore, the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building 100A is reduced. Therefore, according to the seismic isolation structure 1A, the influence caused by the primary vibration mode and the secondary vibration mode can be reduced, so that the seismic isolation performance can be improved.

Next, a method of designing the seismic isolation structure 1A that is a vibration model as shown in FIG. 11 will be described with reference to FIG. The building 100A has seven design variables. Specifically, the design variables include the mass (m ₁ ) of the floor structure 6, the mass (m ₂ ) of the housing structure 4, the elastic modulus (k ₂ ) of the housing structure 4, and the inertial mass (m ₁ ) of the rotating mass device 11. '), an elastic coefficient of LRB23 _{(k r)} and damping coefficient of LRB23 (C).

First, the primary natural period (T ₁ ) of the building 100A is obtained (step S1). The primary natural period (T ₁ ) is determined by the elastic coefficient (k _r ), the elastic coefficient (k ₂ ), the mass (m ₁ ), and the mass (m ₂ ). Specifically, when an expected seismic wave is input to the building 100A, a primary natural period (T ₁ ) at which the response acceleration of the building 100A is equal to or less than a predetermined value is determined. Next, the optimum attenuation coefficient (C ₀ ) of the LRB 23 is obtained (step S2). This step S2 is executed by the same process as step S2 of the first embodiment.

Next, after obtaining a second equivalent elastic modulus (k _r ) (step S3A), an inertial mass (m ₁ ′) is obtained using the second equivalent elastic modulus (k _r ) (step S4A). As shown in FIG. 13, the elastic coefficient of the LRB 23 is not a unique value, and can take various values depending on the deformation amount or the load. FIG. 13 shows the deformation load characteristics of the LRB 23. The horizontal axis is the amount of deformation in the horizontal direction, and the vertical axis is the load. As shown in FIG. 13, the LRB 23 has a hysteresis property called a so-called bilinear loop. The elastic coefficient (k _r ) of the LRB 23 having such characteristics can be expressed as secant rigidity. The secant rigidity in this case can be treated as the slope (k _s ) of the straight line L1 connecting the origin O to the point A. Therefore, how to handle the second equivalent elastic modulus (k _r ) used when determining the inertial mass (m ₁ ′) becomes a problem. As a result of intensive studies, the inventors obtained a suitable inertial mass (m ₁ ′) that can reduce the influence of the secondary vibration mode according to the second equivalent elastic modulus (k _r ) obtained by the following procedure. ) Was obtained.

In order to derive the second equivalent elastic modulus (k _r ), the secondary displacement (δ ₂ ) corresponding to the secondary vibration mode is used. Specifically, first, a primary displacement (δ ₁ ) corresponding to the primary vibration mode is obtained (step S3a). Then, a secondary displacement (δ ₂ ) corresponding to the secondary vibration mode is derived from the primary displacement (δ ₁ ) (step S3b). For this derivation, equation (13) is used. In Expression (13), δ ₂ is the secondary displacement of the floor structure 6 corresponding to the secondary vibration mode, δ ₁ is the primary displacement amount of the floor structure 6, and β ₁ is the first stimulus in the primary vibration mode. Is a coefficient, and β ₂ is the second stimulation coefficient in the secondary vibration mode.

By using the secondary displacement (δ ₂ ) obtained from the equation (13) and the displacement load characteristic shown in FIG. 13, the secant stiffness as the second equivalent elastic modulus (k _r ) is obtained. Specifically, a point B on the loop P1 corresponding to the secondary displacement (δ ₂ ) is obtained. Next, a straight line L2 connecting the point B and the origin O is obtained. Then, the inclination of the straight line L2 is obtained (step S3c). Then, this inclination is determined as the second equivalent elastic modulus (k _r ) (step S3d).

Next, an inertial mass (m ₁ ′) is obtained using the second equivalent elastic modulus (k _r ) (step S4A). This step S4A uses Expression (14) which is the third function.

  The seismic isolation structure 1A is designed by the above steps S1 to S4A.

In the seismic isolation structure 1A, an increase in deformation due to the primary vibration mode that can occur when the natural period (T) of the building 100A is lengthened is reduced by the LRB 23. The characteristics of the LRB 23 are determined so as to correspond to the damping of the primary vibration mode of the building 100A in step S2 for obtaining the optimum damping coefficient (C ₀ ). Therefore, the influence caused by the primary vibration mode can be suitably reduced. Furthermore, in the seismic isolation structure 1 </ b> A, the increase in deformation due to the secondary vibration mode is reduced by the rotating mass device 11. This characteristic of the rotating mass device 11 is handled as the second equivalent elastic modulus (k _r ) based on the deformation load characteristic of the LRB 23 in step S4 for obtaining the mass (m ₁ ′) of the rotating mass device 11. According to this method, it is possible to determine the inertial mass (m ₁ ′) that can suitably reduce the influence caused by the secondary vibration mode that can occur when an earthquake is applied to the building 100A. Therefore, according to the method of designing the seismic isolation structure 1A, it is possible to design the seismic isolation structure 1A that can improve the seismic isolation performance by reducing the influence caused by the primary vibration mode and the secondary vibration mode.

  In addition, embodiment mentioned above shows an example of the method of designing the base isolation structure and base isolation structure which concern on this invention. The seismic isolation structure and the method of designing the base isolation structure according to the present invention are not limited to the design of the base isolation structure and the base isolation structure according to the embodiment, and the scope not changing the gist described in each claim. Thus, it may be modified or applied to other things.

In the method of designing the seismic isolation structure of the first embodiment, the sliding bearing device 7 is handled as having little influence on the relative displacement in the horizontal direction. However, as shown in FIG. 14, the method of designing the base isolation structure may incorporate the effect of sliding, that is, the frictional force in the sliding support device 7 as the friction element. In the actual seismic isolation structure 1B, a frictional force as a resistance force is generated between the sliding portion 7a and the sliding portion 7b. This frictional force is caused by the weight of the structure supported by the sliding support device 7 and the friction coefficient, and is handled using the relationship between the horizontal displacement and the frictional force when the displacement occurs. It is also possible. Therefore, the influence of the friction that can be generated by the sliding bearing device 7 is shown as an equivalent rigidity of the relationship between the displacement in the horizontal direction and the friction force at that time. FIG. 14 shows a vibration model incorporating the equivalent rigidity (k _f ) of the sliding bearing device 7. The base isolation structure 1B further includes a sliding support device 7 as a vibration element in addition to the vibration element shown in the base isolation structure 1B.

As shown in FIG. 15, in the method for designing a base-isolated structure according to the modification, step S1 for determining the natural period (T ₁ ) of the building 100B and the optimum damping coefficient (C ₀ ) of the oil damper 13 are determined. In addition to step S2, the step S3B for obtaining the equivalent stiffness (k _f ) of the sliding bearing is performed, and then the step S4B for setting the inertial mass (m ₁ ′) of the rotary mass device 11 is performed. Step S1 and step S2 are the same as in the first embodiment.

Step S3B obtains an equivalent stiffness (k _f ) using the displacement frictional force characteristics shown in FIG. The displacement frictional force characteristic is the relationship between the displacement in the horizontal direction and the frictional force in the sliding bearing device 7. As shown in FIG. 16, the equivalent stiffness (k _f ) of the sliding bearing is not the only value, and can take various values depending on a combination of displacement or frictional force. Therefore, sliding bearings of equivalent stiffness _{(k f),} as well as the method of calculating the elastic modulus of LRB23 described above _{(k r),} calculates an equivalent stiffness _{(k f)} as secant stiffness.

Specifically, first, the primary displacement (δ ₁ ) of the floor structure 6 corresponding to the primary vibration mode of the building 100B is obtained (step S3e). Next, a secondary displacement (δ ₂ ) is obtained from the primary displacement (δ ₁ ) using the following formula (15) (step S3f). In equation (15), β ₁ is the first stimulation coefficient in the primary vibration mode, and β ₂ is the second stimulation coefficient in the secondary vibration mode.

Then, by using the secondary displacement (δ ₂ ) obtained from the equation (15) and the displacement frictional force characteristic shown in FIG. 16, the secant stiffness as the equivalent stiffness (k _f ) of the sliding bearing is obtained ( Step S3g). Specifically, a point C on the loop P2 corresponding to the secondary displacement (δ ₂ ) is obtained. A straight line L3 connecting the point C and the origin O is obtained. The slope of this straight line L3 is secant rigidity. Then, the secant rigidity is set to the equivalent rigidity (k _f ) of the sliding support device 7 (step S3h).

Next, an inertial mass (m ₁ ′) is obtained using the equivalent rigidity (k _f ) of the sliding bearing (step S4B). In this step S4B, the following equation (16) is used. Here, the first equivalent elastic coefficient (k _a ) is the sum of the elastic coefficient (k ₁ ), the elastic coefficient (k _c ), and the equivalent stiffness (k _f ) of the sliding bearing as shown in the equation (17). (K ₁ + k _c + k _f ).

According to the method for designing a base-isolated structure according to the modification, it is possible to set the inertial mass (m ₁ ′) in consideration of the friction of the sliding support device 7. Therefore, since the inertial mass (m ₁ ') is set based on a model that is closer to the vibration characteristics of the seismic isolation structure 1B that is actually constructed, it is possible to design a seismic isolation structure that can exhibit good seismic isolation performance. it can.

In the modification of the first embodiment, the secondary displacement (δ ₂ ) is obtained using the stimulation coefficients (β ₁ , β ₂ ) in step S3f. Similarly, in the second embodiment, the secondary displacement (δ ₂ ) is obtained using the stimulation coefficients (β ₁ , β ₂ ) in step S3b. In the step of obtaining the secondary displacement (δ ₂ ), a stimulation function (γ ₁ , γ ₂ ) may be used instead of the stimulation coefficient (β ₁ , β ₂ ). Equation (18) is a calculation equation for obtaining the secondary displacement (δ ₂ ) from the primary displacement (δ ₁ ) using the stimulation function (γ ₁ , γ ₂ ). In Expression (18), γ ₁ is a stimulation function of the floor structure 6 in the primary vibration mode, and γ ₂ is a stimulation function of the floor structure 6 in the secondary vibration mode. The secondary displacement in the horizontal direction can be suitably obtained also by the stimulation function.

  Moreover, in the said embodiment, although the lower structure 2 was a foundation and the upper structure 3 was a frame structure, it is not limited to this. Both the lower structure 2 and the upper structure 3 may have a frame structure. For example, in a 20-story building, the lower structure 2 may have a frame structure from the first floor to the 10th floor, and the upper structure 3 may have a frame structure from the 11th floor to the 20th floor. That is, the seismic isolation structure may be disposed between the 1st to 10th floor structures and the 11th to 20th floor structures. Furthermore, the seismic isolation structure and the method of designing the base isolation structure according to the present invention may be used as a structure for a bridge structure or a railway structure.

DESCRIPTION OF SYMBOLS 1,1A, 1B ... Seismic isolation structure, 2 ... Lower structure, 3 ... Upper structure, 4 ... Housing structure, 6 ... Floor structure, 7 ... Slide bearing device, 8 ... Elastic rubber (lower elastic part), 9 ... Viscoelastic device (viscoelastic part), 11 ... rotational mass device (inertial mass part), 12 ... spring mechanism (connected elastic part), 13 ... oil damper (connected damping part), 23 ... laminated rubber bearing device with lead plug, 100 ... Building, 101 ... Ground.

Claims (13)

A seismic isolation structure applied to a building including an upper structure and a lower structure,
A lower elastic portion connected to the upper structure and the lower structure and exhibiting a restoring force in a horizontal direction;
A viscoelastic part connected to the upper structure and the lower structure and having a connected elastic part and a connected damping part connected in series with each other and according to Maxwell's viscoelastic model;
An inertial mass unit coupled to the upper structure and the lower structure and exhibiting an inertial force based on acceleration acting in a horizontal direction on the upper structure;
The lower elastic part, the viscoelastic part, and the inertial mass part are arranged in parallel with each other, and each is connected to the upper structure and the lower structure.   2. The seismic isolation structure according to claim 1, further comprising a sliding bearing that is mounted on the lower structure and connected to the upper structure, and exerts a horizontal frictional force with the lower structure. A method of designing a seismic isolation structure applied to a building,
The building is
A superstructure comprising a first mass element, a second mass element, and an upper elastic element connecting the first mass element to the second mass element;
A lower structure that is spaced downward from the upper structure;
The lower part including a lower elastic element, an inertial mass element, a viscoelastic element including a connecting elastic element and a connecting damping element, the connecting damping element being connected in series to the connecting elastic element, and arranged in parallel to each other Each of an elastic element, the viscoelastic element, and the inertial mass element connected to the first mass element and the substructure, and
Using the first function including the elastic coefficient (k ₁ ) of the lower elastic element, the elastic coefficient (k _c ) of the coupled elastic element, and the mass (m ₁ ) of the first mass element, the coupling Obtaining a damping coefficient (C ₀ ) of the damping element;
Using the elastic modulus (k ₁ ) of the lower elastic element and the elastic coefficient (k _c ) of the connecting elastic element to obtain _a first equivalent elastic coefficient (k _a );
The mass (m ₁ ) of the _first mass element, the mass (m ₂ ) of the second mass element, the first equivalent elastic modulus (k _a ), and the elastic modulus (k ₂ ) of the upper elastic element. Obtaining a mass (m ₁ ′) of the inertial mass element using a second function including: a method of designing a base-isolated structure. The building further includes a friction element that is mounted on the lower structure and connected to the upper structure, and exerts a horizontal frictional force with the lower structure,
Obtaining the equivalent stiffness (k _f ) of the friction element;
The step of obtaining the equivalent stiffness (k _f ) results from a secondary vibration mode of the building, and obtains a horizontal secondary displacement of the upper structure relative to the lower structure; Obtaining a secant stiffness using a displacement frictional force characteristic indicating the relationship between the horizontal displacement of the superstructure relative to the object and the frictional force and the secondary displacement; and dividing the secant stiffness into an equivalent of the friction element Determining as stiffness (k _f ),
The step of obtaining the first equivalent elastic coefficient (k _a ) includes the elastic coefficient (k ₁ ) of the lower elastic element, the elastic coefficient (k _c ) of the connecting elastic element, and the equivalent stiffness (k _f ) of the friction element. ) by using, to obtain the first equivalent elastic modulus (k _a), a method of designing a seismic isolation structure according to claim 3. The step of obtaining the secondary displacement calculates the secondary displacement using Equation (1),
In the formula (1), δ ₂ is the secondary displacement, and δ ₁ is a primary displacement in the horizontal direction of the upper structure relative to the lower structure due to the primary vibration mode of the building. , Β ₁ is the stimulation coefficient of the primary vibration mode, and β ₂ is the stimulation coefficient of the secondary vibration mode.

The step of obtaining the secondary displacement calculates the secondary displacement using Equation (2),
In the formula (2), δ ₂ is the secondary displacement, and δ ₁ is a primary displacement in the horizontal direction of the upper structure relative to the lower structure due to the primary vibration mode of the building. , Γ ₁ is a stimulation function of the first mass element in the primary vibration mode, and γ ₂ is a stimulation function of the first mass element in the secondary vibration mode. How to design.

The first function is Equation (3),
In the equation (3), C ₀ is a damping coefficient of the coupling damping element, k ₁ is a modulus of elasticity of the lower elastic element, k _c is a modulus of elasticity of the coupling elastic element, and ω is a formula ( 4), where N is the stiffness ratio (k _c / k ₁ ) as the ratio of the elastic modulus (k _c ) of the coupled elastic element to the elastic coefficient (k ₁ ) of the lower elastic element. There, m ₁ is the mass of the first mass element, a method of designing a seismic isolation structure according to any one of claims 3-6.

The second function is Equation (5),
In the formula (5), m ₁ ′ is the mass of the inertial mass element, k _a is the first equivalent elastic modulus, m ₁ is the mass of the first mass element, and m ₂ is wherein the mass of the second mass element, k ₂ is the elastic modulus of the upper elastic element, a method of designing a seismic isolation structure according to any one of claims 3-7.

A seismic isolation structure applied to a building including an upper structure and a lower structure,
Laminated rubber bearings with lead plugs connected to the upper structure and the lower structure and exhibiting restoring force and damping force in the horizontal direction;
An inertial mass unit coupled to the upper structure and the lower structure and exhibiting an inertial force based on acceleration acting in a horizontal direction on the upper structure;
The lead-plug laminated rubber bearing and the inertial mass portion are arranged in parallel with each other, and each is connected to the upper structure and the lower structure. A method of designing a seismic isolation structure applied to a building,
The building is
A superstructure comprising a first mass element, a second mass element, and an upper elastic element connecting the first mass element to the second mass element;
A lower structure that is spaced downward from the upper structure;
An inertial mass element and a laminated rubber bearing with a lead plug, and the inertial mass element and the laminated rubber bearing with a lead plug arranged in parallel with each other are connected to the first mass element and the lower structure, respectively. With a seismic isolation structure,
Obtaining a second equivalent elastic modulus (k _r ) of the lead plug-containing laminated rubber bearing using a deformation load characteristic indicating a relationship between deformation and load of the lead plug-containing laminated rubber bearing;
The second equivalent elastic modulus (k _r ), the mass of the first mass element (m ₁ ), the mass of the second mass element (m ₂ ), and the elastic modulus (k ₂ ) of the upper elastic element. Obtaining a mass (m ₁ ′) of the inertial mass element using a third function comprising:
Obtaining the second equivalent elastic modulus (k _r ), obtaining a secondary displacement in the horizontal direction of the upper structure relative to the lower structure due to a secondary vibration mode of the building; Obtaining a secant stiffness using the deformation load characteristic and the secondary displacement; and determining the secant stiffness as the second equivalent elastic modulus ( _kr ) of the laminated rubber bearing with lead plug; How to design a seismic isolation structure. The step of obtaining the secondary displacement calculates the secondary displacement using Equation (6),
In the formula (6), δ ₂ is the secondary displacement, and δ ₁ is the primary horizontal displacement of the upper structure relative to the lower structure due to the primary vibration mode of the building. , Β ₁ is the stimulation coefficient of the primary vibration mode, and β ₂ is the stimulation coefficient of the secondary vibration mode.

The step of obtaining the secondary displacement calculates the secondary displacement using Equation (7),
In the equation (7), δ ₂ is the secondary displacement, and δ ₁ is a primary displacement in the horizontal direction of the upper structure relative to the lower structure due to the primary vibration mode of the building. , Γ ₁ is the stimulation function of the first mass element in the primary vibration mode, and γ ₂ is the stimulation function of the first mass element in the secondary vibration mode. How to design a structure.

The third function is Equation (8),
In the equation (8), m ₁ ′ is the mass of the inertial mass element, _kr is the second equivalent elastic modulus, k ₂ is the elastic modulus of the upper elastic element, and m ₁ is The method of designing a base-isolated structure according to any one of claims 10 to 12, wherein the mass of the first mass element is m ₂ and the mass of the second mass element is m ₂ .

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