JP2017026569A - Base isolation member response estimation device and base isolation member response estimation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a base isolation member response estimation device and a base isolation member response estimation method enabling response estimation to be easily performed to distortion of a base isolation member.SOLUTION: A base isolation member response estimation device 1 capable of estimating response of a base isolation member from relationship between a characteristic of an excitation source and a vibration characteristic of the base isolation member, includes: an input unit 2 configured to input a dominant frequency fof the excitation source, an input acceleration A of the excitation source, a mass Mof the excitation source, an equivalent damping constant hof the base isolation member, a dominant frequency of the base isolation member, and a mass M of the base isolation member; a calculation unit 3 configured to calculate distortion γ of the base isolation member by at least any one of specific formulas, in a case where relationship between the dominant frequency fof the excitation source and the dominant frequency f of the base isolation member satisfies the following: f≥f, on the basis of each numerical value input from the input unit 2; and an output unit 4 configured to output the distortion γ of the base isolation member calculated by the calculation unit 3.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a seismic isolation member response estimation apparatus and a seismic isolation member response estimation method for estimating response of a seismic isolation member.

  Conventionally, when performing response estimation for an excitation problem for a seismic isolation member whose rigidity varies, it is common to perform a time history response analysis of the seismic isolation member (see Non-Patent Document 1).

Yasuo Takenaka, Kazuhiko Yamada, Kazuhide Yoshikawa, “Curve-type history restoring force model of laminated rubber bearing for seismic isolation:“ modified HD model ””, Architectural Institute of Japan Technical Report, December 2001, No. 14, p. 87-92

  However, in order to perform time history response analysis of the seismic isolation member, it is necessary to confirm the correspondence with the actual behavior through experiments and the like, and it was not possible to easily estimate the response of the seismic isolation member.

  An object of this invention is to provide the seismic isolation member response estimation apparatus and the seismic isolation member response estimation method which can estimate response easily of the distortion of a seismic isolation member.

The seismic isolation member response estimation apparatus according to the present invention is:
A seismic isolation member response estimation device capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

An input unit for inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
When the relationship between the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member is f _e ≧ f based on the numerical values input from the input unit, at least the following formula (1) A calculation unit for calculating the strain γ of the seismic isolation member by any one of the formulas (3),
An output unit that outputs the strain γ of the seismic isolation member calculated by the calculation unit;
It is characterized by providing.

In the seismic isolation member response estimation apparatus according to the present invention,
The input unit includes a selection unit that selects any one of the formulas (1) to (3).

The seismic isolation member response estimation method according to the present invention is:
A seismic isolation member response estimation method capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

Inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
Based on each input numerical value, the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member
If the relationship with f _e ≧ f, the step of calculating the strain γ of the seismic isolation member by at least one of the following formulas (1) to (3):
Outputting the calculated strain γ of the seismic isolation member;
It is characterized by having.

The seismic isolation member response estimation method according to the present invention is:
It has the step which selects either of said Formula (1)-(3), It is characterized by the above-mentioned.

The seismic isolation member response estimation apparatus according to the present invention is:
A seismic isolation member response estimation device capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

An input unit for inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
When the relationship between the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member is f _e ≧ f based on the numerical values input from the input unit, at least the following formula (1) A calculation unit for calculating the strain γ of the seismic isolation member by any one of the formulas (3),
An output unit that outputs the strain γ of the seismic isolation member calculated by the calculation unit;
So that
The response γ of the seismic isolation member can be easily estimated.

In the seismic isolation member response estimation apparatus according to the present invention,
Since the input unit includes a selection unit that selects any one of the formulas (1) to (3),
It is possible to adjust the estimated performance of the distortion γ of the seismic isolation member.

The seismic isolation member response estimation method according to the present invention is:
A seismic isolation member response estimation method capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

Inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
Based on each input numerical value, the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member
If the relationship with f _e ≧ f, the step of calculating the strain γ of the seismic isolation member by at least one of the following formulas (1) to (3):
Outputting the calculated strain γ of the seismic isolation member;
So that
It is possible to easily estimate the response of the seismic isolation member.

The seismic isolation member response estimation method according to the present invention is:
Since there is a step of selecting any one of the formulas (1) to (3),
It is possible to adjust the estimated performance of the distortion γ of the seismic isolation member.

The seismic isolation member response estimation apparatus of this embodiment is shown. The model for calculating | requiring the approximate expression used for the seismic isolation member response estimation apparatus of this embodiment is shown. The relationship between the input acceleration of a vibration source and the distortion of a seismic isolation member in the seismic isolation member response estimation apparatus of this embodiment is shown. The relationship between the standardized input acceleration and the distortion of a seismic isolation member when the dominant frequencies in the seismic isolation member response estimation apparatus of this embodiment differ is shown. The relationship between the normalized input acceleration and the distortion of a seismic isolation member when the surface pressure of the seismic isolation member in the seismic isolation member response estimation apparatus of this embodiment differs is shown.

  Hereinafter, an embodiment of a seismic isolation member response estimation apparatus 1 according to the present invention will be described with reference to the drawings.

  FIG. 1 shows a seismic isolation member response estimation apparatus 1 according to this embodiment. FIG. 2 shows a model 10 for obtaining an approximate expression used in the seismic isolation member response estimation apparatus 1 of the present embodiment.

  The seismic isolation member response estimation apparatus 1 of the present embodiment includes an input unit 2, a calculation unit 3, and an output unit 4, and performs response analysis from the relationship between the characteristics of the excitation source and the vibration characteristics of the seismic isolation member. Without doing so, it is possible to simply estimate the response of the seismic isolation member. As shown in FIG. 2, a model 10 for obtaining an approximate expression used in the calculation unit 3 of the seismic isolation member response estimation apparatus 1 is obtained by placing an excitation source 13 on a floor 11 via a seismic isolation member 12. It is.

Input unit 2, predominant frequency f _e of the vibration source 13, the input acceleration A of the vibration source 13, mass M _e of vibration source 13, the equivalent damping constant h _eq seismic isolation member 12, the seismic isolation member 12 The spring constant K _eq , the dominant frequency f of the seismic isolation member 12 and the mass M of the seismic isolation member 12 are input.

Based on the numerical values input from the input unit 2, the calculation unit 3 is at least the following when the relationship between the dominant frequency _fe of the excitation source 13 and the dominant frequency f of the seismic isolation member 12 is _fe ≧ f. Equations (1) to (3)
The strain γ of the seismic isolation member 12 is approximately estimated by any one of the equations. Any one of the expressions (1) to (3) may be stored and used for the calculation. Alternatively, the input unit 2 may include a selection unit 21, and the selection unit 21 may select Equations (1) to (3) so that the strain γ of the seismic isolation member 12 can be calculated using the selected equation.

  The output unit 3 outputs the distortion γ of the seismic isolation member 12 calculated by the calculation unit 2. In addition, when Formula (1) or Formula (2) is used, distortion (gamma) of the seismic isolation member 12 is represented as what exists in a predetermined range.

  FIG. 3 shows the relationship between the input acceleration of the excitation source 13 and the strain γ of the seismic isolation member 12 in the seismic isolation member response estimation apparatus 1 of the present embodiment.

In the seismic isolation member response estimation apparatus 1 of the present embodiment, the calculation result assuming an excitation experiment of the seismic isolation member 12 is shown in FIG. In the example shown in FIG. 3, the calculation is performed by virtually changing the excitation source 13 having a mass M _e = 0.2 ton at an input acceleration A = 50 to 1000 cm / s ² . The frequency _fe of the sine wave to be excited was changed from 2 to 10 Hz. As shown in FIG. 3, the input acceleration A of the vibration source 13 increases and the distortion γ of the seismic isolation member 12 increases. However, the degree of change depends on the dominant frequency f _{e of the} vibration source 13. Different.

FIG. 4 shows the relationship between the normalized input acceleration (α · _Me · A / M) and the strain γ of the seismic isolation member 12 when the dominant frequency _fe is different in the seismic isolation member response estimation apparatus 1 of the present embodiment. Indicates.

If the relationship between the dominant frequency f _e and predominant frequency f of the seismic isolation member 12 of the vibration source 13 is f _e ≧ f, ie if not resonate, scaled input acceleration (α · M _e · A / M) and distortion γ of the seismic isolation member 12
The following relationship (1) is satisfied even when the dominant frequency _fe is different.
0.03 (α ・_Me・ A / M) ^0.8 ≦ γ ≦ 0.3 （α ・_Me
・ A / M) ^0.8 (1
)

When the dominant frequency fe is selected, the normalized input acceleration (α ⁴ Me ⁴

・ A / M) ^0.8 (2)

Furthermore, the relationship between the normalized input acceleration (α · _Me · A / M) and the strain γ of the seismic isolation member 12 may be rephrased as substantially satisfying the following expression (3).
γ = 0.05 (α ・_Me・ A / M) ^0.8 (3)

Thus, the relationship between the dominant frequency f _e of the excitation source 13 and the dominant frequency f of the seismic isolation member 12 is expressed as f _e ≧ f
For, if i.e. not resonate, simply by inputting the scaled input acceleration _{(α · M e · A /} M), without the need for time history analysis and frequency response analysis, the predominant frequency f _e Even if they are different, the strain γ of the seismic isolation member 12 can be easily estimated.

FIG. 5 shows the normalized input acceleration (α · _Me · A / M) and the strain γ of the seismic isolation member 12 when the surface pressure of the seismic isolation member 12 is different in the seismic isolation member response estimation apparatus 1 of the present embodiment. The relationship is shown.

If the relationship between the dominant frequency f _e and predominant frequency f of the seismic isolation member 12 of the vibration source 13 is f _e ≧ f, ie if not resonate, scaled input acceleration (α · M _e · A / M) and distortion γ of the seismic isolation member 12
The following relationship (2) is satisfied even when the surface pressure of the seismic isolation member 12 is different.
0.03 (α ・_Me・ A / M) ^0.8 ≦ γ ≦ 0.07 （α ・_Me
・ A / M) ^0.8 (2
)

Furthermore, the relationship between the normalized input acceleration (α · _Me · A / M) and the strain γ of the seismic isolation member 12 may be rephrased as substantially satisfying the following expression (3).
γ = 0.05 (α ・_Me・ A / M) ^0.8 (3)

Thus, the relationship between the dominant frequency f _e of the excitation source 13 and the dominant frequency f of the seismic isolation member 12 is expressed as f _e ≧ f
In this case, that is, when there is no resonance, the input of the standardized input acceleration (α · _Me · A / M) is required, and the surface of the seismic isolation member 12 is not required to perform time history response analysis or frequency response analysis. Even if the pressures are different, the strain γ of the seismic isolation member 12 can be easily estimated.

As mentioned above, according to the seismic isolation member response estimation apparatus 1 of this embodiment, the seismic isolation member response estimation which can estimate the response of the seismic isolation member 12 from the relationship between the characteristic of the excitation source 13 and the vibration characteristic of the seismic isolation member 12 is possible. an apparatus 1, predominant frequency f _e of the vibration source 13, the input acceleration a of the vibration source 13, the vibration source mass M _e of 13, the equivalent damping constant h _eq seismic isolation member 12, the seismic isolation member 12 Prevailing frequency f and mass M of the seismic isolation member 12
When the relationship between the dominant frequency f _e of the excitation source 13 and the dominant frequency f of the seismic isolation member 12 is f _e ≧ f based on the input unit 2 for inputting , At least the following formula (1)
A calculation unit 3 that calculates the strain γ of the seismic isolation member 12 according to any one of the equations (3) and an output unit 4 that outputs the strain γ of the seismic isolation member 12 calculated by the calculation unit 3. Therefore, the response γ of the seismic isolation member 12 can be easily estimated.

  Moreover, according to the seismic isolation member response estimation apparatus 1 of the present embodiment, the input unit 2 includes the selection unit 21 that selects any one of the formulas (1) to (3). It is possible to adjust the estimated performance of.

Furthermore, according to the seismic isolation member response estimation method of the present embodiment, the seismic isolation member response estimation method capable of estimating the response of the seismic isolation member 12 from the relationship between the characteristics of the excitation source 13 and the vibration characteristics of the seismic isolation member 12. a is, predominant frequency f _e of the vibration source 13, the input acceleration a of the vibration source 13, mass M _e of vibration source 13, the equivalent damping constant h _eq seismic isolation member 12, excellence of seismic isolation member 12 Based on the step of inputting the frequency f and the mass M of the seismic isolation member 12 and the input numerical values, the relationship between the dominant frequency _{fe of the} excitation source 13 and the dominant frequency f of the seismic isolation member 12 is When f _e ≧ f, the step of calculating the strain γ of the seismic isolation member 12 according to at least one of the following formulas (1) to (3), and the calculated strain γ of the seismic isolation member 12 are output. Therefore, it is possible to easily estimate the response of the seismic isolation member 12.

  Moreover, according to the seismic isolation member response estimation method of this embodiment, since it has the step which selects any of Formula (1)-(3), adjusting the estimation performance of distortion (gamma) of the seismic isolation member 12 is possible. It becomes possible.

  In addition, this invention is not limited by this embodiment. That is, in describing the embodiment, many specific details are included for illustration, but those skilled in the art may add various variations and changes to these details.

DESCRIPTION OF SYMBOLS 1 ... Seismic isolation member response estimation apparatus 2 ... Input part 3 ... Calculation part 4 ... Output part 10 ... Model 11 ... Floor 12 ... Seismic isolation member 13 ... Excitation source

Claims (4)

A seismic isolation member response estimation device capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

An input unit for inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
When the relationship between the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member is f _e ≧ f based on the numerical values input from the input unit, at least the following formula (1) A calculation unit for calculating the strain γ of the seismic isolation member by any one of the formulas (3),
An output unit that outputs the strain γ of the seismic isolation member calculated by the calculation unit;
A seismic isolation member response estimation device comprising:

The seismic isolation member response estimation apparatus according to claim 1, wherein the input unit includes a selection unit that selects any one of the equations (1) to (3). A seismic isolation member response estimation method capable of estimating the response of the base isolation member from the relationship between the characteristics of the excitation source and the vibration characteristics of the base isolation member,
The excitation source of the predominant frequency f _e, an input acceleration A of the vibration source, the mass of the vibration source M _e

Inputting the equivalent damping constant h _{eq of} the base isolation member, the dominant frequency f of the base isolation member, and the mass M of the base isolation member;
Based on each input numerical value, the dominant frequency f _{e of the} excitation source and the dominant frequency f of the seismic isolation member
If the relationship with f _e ≧ f, the step of calculating the strain γ of the seismic isolation member by at least one of the following formulas (1) to (3):
Outputting the calculated strain γ of the seismic isolation member;
A seismic isolation member response estimation method characterized by comprising:

The seismic isolation member response estimation method according to claim 3, further comprising a step of selecting any one of the equations (1) to (3).

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