JP2005213887A - Designing method and design support system, design support program, body of revolution and building structure - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a designing method and a design support system controlling an earthquake response by controlling a participation factor and a vibration mode by optimally arranging an inertial connecting element, a design support program, a body of revolution and a building structure. <P>SOLUTION: A method for designing the structure has a plurality of layers, on which members moving at a high speed in response to the displacement differences of nodes without being subject to the effect of an earthquake ground motion are loaded. The method for designing the structure is composed of a step of computing eigenvalues from the masses of the components of each layer of the structure and the spring constants of the components of each layer, a step, of computing the participation factors from the masses, the spring constants and the eigenvalues, and a step of computing inertial masses by the members from the masses and the participation factors. In the method, the participation factors are selected and controlled so that the earthquake response of the structure composed of a plurality of the layers is formed only in a primary mode. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a design method, a design support system, a design support program, a rotating body, and a building structure for controlling a response by controlling the period and vibration mode of a vibration system of a building structure.

  In recent years, the design of buildings against earthquake motion has been carried out by adjusting the rigidity and proof stress, and in recent years, artificially adding damping. This is an attempt to control the seismic response of a structure by manipulating the stiffness matrix or damping matrix in the vibration equation. In this case, the mass matrix was often considered to be constant as a diagonal matrix of the mass of a given vibration system.

  In addition, if the response control is performed by controlling the period and vibration mode of the vibration system by manipulating and manipulating the mass matrix artificially, the response of the type of vibration system that is difficult to achieve only by controlling the stiffness and damping Control is possible.

  Therefore, in order to couple and operate the mass matrix without changing the true mass, the inertial element by the rotating part will be examined with reference to FIG.

As shown in FIG. 21, a rotating body 254 having an integrated inner ring 250 and outer ring 252 whose mass is concentrated on the outer ring 252 is rotated by applying force to the inner ring 250 in the tangential direction. Think. The displacement, speed, and acceleration of the outer ring 252 with respect to the inner ring 250 are the ratio of the radius of the inner ring 250 and the outer ring 252.
It is.
Therefore, when the inner ring is moved in the tangential direction with an acceleration α, the magnitude of the inertial force for accelerating the mass m _f of the outer ring is
(5) As shown in the equation, the force R to push the inner ring is
That is, for the acceleration α applied to the inner ring from the outside of the system
An inertial force having a magnitude corresponding to the equation (7) is generated.

Here, consider a vibration system in which the above rotating body is incorporated in a one-mass point vibration system as shown in FIG. The rotational motion of the rotating body is only affected by the displacement X of the mass point from the ground, and is not directly affected by the ground motion y. Here, the kinetic energy of the entire system is T, the energy dissipation function is F, and the potential energy is V.
And the Euler-Lagrange equation is
It becomes. Here, an element that connects the nodes of the vibration system such as the rotating body and generates kinetic energy according to the velocity difference between the nodes is called an inertial connection element (mass-point pseudo mass). Also, this inertial mass is not an actual nodal mass, so put a dash
Is written.
of
The ratio γ to is referred to as inertial connection mass ratio.

  From equation (14), it is predicted that the inertial connection element has a response control effect such as extending the period of the vibration system, lowering the damping constant, and exerting an input reduction effect on the ground motion acceleration. Other control of the vibration system by such auxiliary mass is known.

FIG. 23 shows a lever mechanism with an auxiliary mass shown in Non-Patent Document 1. If the auxiliary mass is m _d and the amplification factor of the insulator is β _d , the kinetic energy T of the entire system in this case is

Therefore, from the Euler-Lagrange equation, the vibration equation of this system is
It becomes. Compared with equation (13), there is a difference in the right term representing the influence of ground acceleration. This is because, in the case of the lever mechanism with auxiliary mass of FIG. 23, the movement of the auxiliary mass is directly affected by the ground motion, but not in the rotating body mechanism. If the lever mechanism is toggled so that the direction of motion of the auxiliary mass is perpendicular to the ground motion, the influence is eliminated, and equation (18) becomes the same form as equation (13). If a spring or a damping device is incorporated at the displacement amplification point, a spring reaction force or damping force that is a square of the displacement amplification factor can be obtained in the same manner as the inertial mass amplification.

  Considering an actual structure, it is often easier to incorporate a control mechanism of type (13) than to incorporate a control mechanism of type (18). Non-Patent Document 2 realizes an “inertia connection element” of the type (13) with a mechanism such as an opposed piston type and a rack and pinion type, and utilizes the fact that the displacement transmission rate becomes 0 at a specific frequency. Proposed connection mechanism.

Shinji Ishimaru: Overview of Earthquake Response Control of Structures, “Applied Mechanics Series 2 Design Mechanics and Control Dynamics of Building Structures”, Architectural Institute of Japan, pp.199-202, 1994.11 Atsushi Okumura: Vibration isolation connection mechanism, “Waseda University Technology Series”, NO.TLO 2000-02, 2000.3

  When utilizing the inertial connection element, it is desirable that the inertial connection element be generated without depending on the magnitude of the ground motion acceleration or its change. However, in the model shown in FIG. 23, the auxiliary mass that performs the rotational motion has an influence because the acceleration of the mass point varies according to the ground motion acceleration, so that there is a problem that a sufficient inertia effect cannot be obtained.

  On the other hand, the “vibration cutoff connection mechanism” shown in Non-Patent Document 2 has a displacement transmission rate of 0 at a specific frequency. For this reason, with respect to the vibration caused by the artificial device that can always predict the occurrence of a specific frequency, the effect of limiting the vibration to the vibration is sufficiently obtained. However, in the case of having a plurality of frequency components as in an earthquake, a sufficient effect cannot be obtained because a frequency other than a specific frequency is transmitted.

  Conventionally, a method for controlling the seismic response by controlling the vibration mode and a control by the stimulation coefficient have not been proposed so far in the case of a multi-mass system.

  Therefore, an object of the present invention is to provide a design method, a design support system, a design support program, a rotating body, and a building structure that control an earthquake response by controlling a stimulation coefficient and a vibration mode by optimizing the arrangement of inertial connection elements. It is in the provision of things.

In order to achieve the above object, a design method according to the present invention is a method for designing a structure having a plurality of layers on which members that move at high speed according to a difference in displacement of a node without being affected by a seismic motion,
A spring coefficient k _i and inertia connecting element m _{i 'on} the ground, the acceleration structure is arranged in the ground of the mass m _i to be supported on the damping device c _i
Is selected for the inertial connection element so that the stimulation coefficient of the higher-order vibration mode is 0 and m ′ _n = 0 for the vibration equation for the ground motion of the n-mass system input to the structure To do.
Further, the method for selecting and controlling the inertial connection element may be configured such that the first-order natural period becomes an optimum value without changing the eigenvector of the vibration equation.
Further, the method of selecting and controlling the inertial connection element includes a step of calculating an eigenvalue from a mass of each layer component of the structure and a spring constant of the component of each layer, and the mass, the spring constant, and the eigenvalue. Selecting a stimulation coefficient so that the seismic response of a multi-layered structure is only in the primary mode, comprising calculating a stimulation coefficient and calculating an inertial mass due to the member from the mass and the stimulation coefficient. Control.

Further, this design method, the primary step of calculating an eigenvalue ₁ omega ^2, the structure of each layer of the mass m _i and each of the spring when second or stimulation coefficient with the addition of inertial clause element is 0 From the constant k and the number n of layers, Equation 19 can be followed.

Furthermore, in this design method, the step of calculating the first-order stimulation coefficient η _i includes the step of calculating the mass m _i , the spring constant k, and the eigenvalue when the second-order or higher stimulation coefficient is 0 due to the addition of an inertial node element. and calculating from ₁ omega ² Tokara formula 20.

Next, this design method is characterized in that the step of calculating an inertial connection element calculates an inertial connection element m _i ′ by the member from Equation 3 from the mass m _i and the stimulation coefficient η _i .

The member may include a rotating body having an inner ring and an outer ring having different radii on the same axis and having a mass concentrated on the outer ring from the inner ring.
In addition, the rotating body described in this design method includes first and second connecting members that are connected to each other so as to be relatively displaceable. The first connecting member has a guide screw portion formed at least on the connection side. A first rod, a guide nut that engages with the guide screw portion and is rotatably supported on the guide screw portion based on relative displacement with the guide screw portion, and larger than the first rod. The second connecting member is formed of a cylindrical rotating body having a diameter and an axial length sufficiently larger than the diameter, and is rotatably inserted through the guide nut. In a damping device comprising a cylindrical casing that accommodates a rotating body and a guide nut, a damping viscous body and / or viscoelastic body is provided at least in a gap between the inner wall of the cylindrical casing and the cylindrical rotating body. Hama to.

  In this design method, the cylindrical rotating body is formed of a cylindrical body having one end portion extrapolated to the guide nut and the other end portion closed, and one side portion of the guide nut and the rotating inner cylinder facing the cylindrical nut. The closed end is rotatably supported.

  The cylindrical rotating body is a tubular rotating body having one end portion extrapolated to a guide nut and the other end portion being an open end, and both sides of the guide nut are rotatably supported and the viscous body And / or a viscoelastic body is filled also in the hollow part of a tubular rotary body.

  Further, the rotating body includes first and second connecting members that are connected to each other so as to be relatively displaceable. The first connecting member includes a first rod having a guide screw portion formed on the connecting side thereof, and A guide nut that is engaged with the guide screw portion and pivotally slidable on the guide screw portion based on a relative displacement with the guide screw portion, and has a diameter sufficiently larger than the first rod; It comprises a disk-shaped rotating body that is inserted so as to be able to rotate and slide through a guide nut, and the second connecting member is a second rod, and the rotating body and guide nut formed on the connection side thereof. In the damping device comprising a cylindrical casing for accommodating the damping body, a gap between the inner wall of the cylindrical casing and the rotating body is filled with a damping viscous body and / or a viscoelastic body.

  Moreover, the rotating body is integrally formed so as to extend radially outward from the outer periphery of the guide nut.

Next, the rotating body is provided at a position spaced apart from the guide nut in the axial direction, and is formed to engage with one side portion of the guide nut.
The members are mainly composed of a main mass portion supported by a spring portion provided on the ground, and an auxiliary mass portion connected to an auxiliary mass support rod pin-coupled on a fixed main shaft standing on the ground. It may be configured by a toggle-type auxiliary mass mechanism coupled by a mass support rod, and the auxiliary mass portion may be further supported on the ground by the second spring portion and the damping portion.
Further, the member is connected to a first auxiliary mass support bar connected to a main mass portion supported by a spring portion provided on the ground and a first auxiliary mass support rod pin-coupled to the top of a fixed main shaft standing on the ground. A mass part is coupled to the main mass part by a first main mass support bar, and a second auxiliary mass part connected to a second auxiliary mass support bar pin-coupled to an intermediate part of the fixed main shaft A toggle type auxiliary mass mechanism coupled to the main mass part by a two main mass support rod may be configured, and the first auxiliary mass part and the second auxiliary mass part may include a connecting spring part and a connecting damping part. It may be connected via.

The design program according to the present invention is a design program for a structure having a plurality of layers on which a member that moves at high speed according to a displacement difference of a node without being affected by a ground motion,
A spring coefficient k _i and inertia connecting element m _{i 'on} the ground, the acceleration structure is arranged in the ground of the mass m _i to be supported on the damping device c _i
Is selected for the inertial connection element so that the stimulation coefficient of the higher-order vibration mode is 0 and m ′ _n = 0 for the vibration equation for the ground motion of the n-mass system input to the structure To do.
In the design system of a structure consisting of a plurality of layers in which members that move at high speed according to the displacement difference of the nodes without being affected by the member earthquake motion from the mass and the stimulation coefficient,
An input means for inputting in advance the mass of each layer of the structure and the spring constant of each layer; a storage means for storing the input data; an operation program stored in advance in the storage means and describing a calculation method; A step of calculating an eigenvalue from the mass of the component of each layer of the structure and the spring constant of the component of each layer, comprising a central processing unit for calculating according to the calculation program and an output means for outputting the calculation result;
Calculating a stimulation coefficient from the mass, the spring constant and the eigenvalue;
Comprising the step of calculating the inertial mass due to the member from the mass and the stimulus coefficient, the stimulus coefficient is selected and controlled so that the seismic response of the multi-layered structure is only the primary mode.

The rotating body of each layer according to the present invention includes an inner ring and an outer ring which are designed by the above-described design method and have different radii on the same axis, and an inertia connecting element is generated by the rotating body whose mass is concentrated on the outer ring from the inner ring. It is set as follows.
The building structure according to the present invention is a member of each layer that is designed so that an inertia connecting element is generated by a member that is designed by the above-described design method and that moves at a high speed according to a displacement difference of a node without being affected by a ground motion. Then, the seismic response of the structure consisting of a plurality of layers on which the members are mounted is controlled so as to be only in the primary mode.

  The design method of the present invention can be realized by manufacturing a device having an inertial mass effect whose inertial connection element is much larger than the actual mass by using a deformation amplification mechanism such as a rotation mechanism. Since the mass related to vibration is increased without changing the mass, characteristic fluctuations such as a period expansion fluctuation, an attenuation reduction fluctuation, and an input reduction fluctuation effect are induced in the vibration system. Further, the inertia connecting element couples the mass matrix in the vibration equation, and a rigid mode of “acceleration directly transmitted via the inertia connecting element” appears in the response to the ground motion. On the other hand, it is possible to control the eigenvalues and eigenvectors of the vibration system by adjusting the values of the inertial connection elements of each layer. Specifically, it is possible to control response to earthquake motion, such as changing the natural period of each order without changing the eigenvector of the vibration system, or setting the stimulation coefficient of the higher order mode to 0. This method can enable a new seismic response control of a structure that cannot be achieved only by conventional rigidity and damping control.

While describing this invention using FIGS. 1-20, a design method, a design support system, a design support program, a rotary body, and a building structure are demonstrated in the following order.
(1) Response characteristics of multi-mass system with inertial connection element (2) Properties of n + 1 order mode of system with inertial connection element (3) Eigenvalue change without changing eigenvector (4) Other than primary mode (5) Zero stimulation coefficients for all higher modes (6) Cylinder-type damping piece (7) Disk-type damping piece (8) Auxiliary mass (9) Design system (10) Design flow ( Examples 1-2)

That is, (1) to (5) show the principle of the present invention, (6) and (7) show application examples to the attenuation piece according to the present invention, and (8) and (9) relate to the present invention. The design system and its method and program are described. Finally, Examples 1-2 will be described.
(1) Response characteristics of multi-mass systems with inertial connection elements

FIG. 1 shows a model diagram in which the principle of the present invention is applied to a multi-mass point system. A structure having a mass m _i supported by a spring coefficient k _i , an inertia connecting element m _i ′ (indicated by a circle in the drawing) and a damping device c _i is arranged on the ground, and an acceleration is applied to the ground.
It is assumed that a disturbance is input to this structure. The vibration equation for ground motion of n-mass system with inertial connection elements is expressed by the following equation.
here,

Is a mass matrix with nodal mass only

Is the mass matrix of inertia connection elements only

Indicates an attenuation coefficient.

Indicates a spring constant.

Indicates a vector representing the action of an external force.

The difference between Eq. (22) and the general vibration equation for ground acceleration is that the vector representing the action of external force is
not
It is to be.
And
Represents a kind of input reduction variation effect. This effect arises from the fact that the ground acceleration acts only on the nodal mass to generate kinetic energy.

Equation (22) can also be interpreted as follows. Ground acceleration in vibration system
Since the acceleration is transmitted directly through the inertia connecting element when
Occurs. When viewed from the ground, each node has
Acceleration occurs,
Inertial force is generated. Therefore, the dynamic force balance equation is shown in equation (29).
Alternatively, the vibration equation for the ground motion of the n-mass system having the inertia connecting element is the same as in the case of the 2-mass vibration system, with the dummy mass point m ₀ representing the ground motion added, and the (n + 1) -th row in the equation (19), The n + 1th column is added and expressed by the following equations (30) to (36).
Here, each item is shown in the following equation.

Is a mass matrix of only the node mass, and is shown in the equation (33).

Is a mass matrix of inertia connection elements only and is shown in equation (34).

here,
Indicates each matrix of equation (22). However,
Assume that A vector representing the action of ground motion is given by Eqs. (22) and (30).
From
It has changed to. This is because a dummy node is provided, and since there is no inertia connecting element below, formally, ground motion acceleration is not directly transmitted to each node via the inertia connecting element.
And the right side of equation (30) is
From the equation (28), it becomes the same as the right side of the equation (22). However, in the equation (30), the acceleration of the dummy node m ₀ that actually moves in the same manner as the ground is transmitted to the upper part through the inertia connecting element.

Considering the dynamic force balance, the ground motion acceleration is not directly transmitted to each node, so the dynamic force balance equation is
It can be expressed.

The eigenvalue and the stimulation function for the expression (30) under the condition that the frequency is made infinite, the 1st to nth modes are called “response to a reduced input having a significant frequency and damping constant”. The n + 1 order mode is
It has a rigid mode. This can be confirmed by the following method. The s-order eigenvalue in the eigenvalue problem of equation (30)
, The eigenvector
As
far. Now, if the eigenvalue problem is constructed ignoring the viscous damping term, it is expressed by equation (41).
From the conditions of equations (41) and (40), the eigenvalue problem for equation (22) is
Is configured. here,
It is.

When the equation (42) is taken into consideration, the stimulation coefficient for the equation (41) becomes the equation (43).
because,
On the other hand, the stimulation coefficient for equation (22) is
However, in equation (28)
By the definition of
Therefore, the equations (44) and (46) coincide with each other, and the equation (43) is established. That is, even if the equation (30) is solved under the condition of the equation (40), the result is the same as the result of solving the equation (22).

next
in the case of,
Whether or not is true. Similarly to the case of the two mass point system, the equation (42)
Substituting can be expanded as follows.
About n lines from the top of the above formula,
If we arrange as, we get the following formula.
Therefore, the equation (43) is also established. The sum of all orders of the stimulation function in equation (22) is
Therefore, the sum of the stimulation functions of all orders in equation (30) is the value except for the dummy mass point value.
It is. However, the sum for all orders is
Since the (n + 1) th order stimulation coefficient of equation (30) is 1, equation (45) is also a dummy mass point stimulation function.

Hereinafter, unless otherwise specified, attenuation is assumed to be proportional attenuation, and sth order (1 ≦ s ≦ n) broad mass in the formulas (22) and (30).
, Wide rigidity
, Broad damping coefficient
Are equal since _s u ₀ = 0, and are respectively as follows.

(2) Properties of n + 1 order mode of a system having an inertial connection element Equations (22) and (30), which are vibration equations for ground motion of an n mass system having an inertial connection element, have the same 1st to nth orders. By the way, the equation (30) has an n + 1 order mode. This mode represents acceleration transmitted directly through the inertial connection element. The conditional expression of the n + 1 order eigenvector is shown in Expression (55).
Expression (56) is obtained from the condition for satisfying Expression (55).
here,
Then, equation (56) is
Indicated,
It becomes. Therefore, the following recurrence formula holds.
In addition, the stimulation coefficient in this mode is 1 as follows.

As described above, the (n + 1) th order mode of the equation (30) has an eigenvector having only a mass term that is not related to the stiffness term. coefficient
Is
And the eigenvector
Is
And can be obtained in order from the bottom. Inertial connection element in one layer
Then all the layers above it
It becomes.

(3) Change of eigenvalues without changing eigenvectors When considering seismic response control of structures, inertial connection elements have several useful uses. The s-th order (s = 1 to n) eigenvalues and eigenvectors of equation (22)
Then, equation (62) is established.
Here on both sides of equation (62)
Is added.
Here is a matrix of inertial connection elements
The stiffness matrix
And the shape is the same,
The inertia connection element
Assuming that
Is established. That is, the inertia connecting element proportional to the rigidity of each layer is added to the vibration system of equation (22).
When s is added, the eigenvector of the sth order (s = 1 to n) does not change, and the new eigenvalue

Is
Can be controlled to be This operation increases the s-order broad-sense mass, but the eigenvector does not change, so the s-order broad-sense rigidity and broad-sense damping coefficient do not change. In addition, the s-order broad mass before adding the inertia connecting element
(It may have an inertial connection element.) The s-order broad inertial connection element mass of the inertial connection element to be added
Then the inertia mass ratio for one mass system
In the n-mass system, when adding an inertial connection element proportional to the rigidity of each layer, the sth-order inertial connection mass ratio for this addition is added.
The
Can be defined. The next eigenvalue of this operation
, Damping constant
, Stimulation coefficient
The change of is expressed by the following equation.
However, s = 1 ~ n

  The value of inertial connection mass ratio varies depending on the order. The total decrease in the 1st to nth order stimulation functions is the increase in the n + 1th order stimulation function in the equation (30).

  As a special case, when the inertial connection element of each layer is proportional to the rigidity of each layer, the eigenvector is the same as the eigenvector of the system without the inertial connection element. In addition, this means that there are innumerable combinations of inertial connection elements in each layer where the 1st to nth order eigenvectors are the same. This shows that the coefficient, n + 1 order stimulation function can be operated.

(4) Zeroing the stimulus coefficient other than the first-order mode Consider the control of changing the eigenvector of the vibration system by adding an inertial connection element. Aside from special purpose mode control, when considering general response control to earthquake motion, it is one of the important usages to make the stimulation coefficient of a mode zero by using this property.

In equation (22)
By adding eigenvalues
, Eigenvector
However,
, Is assumed to hold. That is,
Only the top three lines remain in this formula,
And
Is not related to the value of. Here, when the sum of the equations (71) is taken,
And ask
So
And
Therefore, since the numerator of the equation (45) is 0 from the equation (46), the stimulation coefficient in this mode is 0.
Is known, the equation (71)
This is a ternary system of simultaneous equations, and since the number of unknowns and the number of equations match, they can be solved uniquely.

Next, in equation (22)
By adding eigenvalues
, Eigenvector
However,
, Is assumed to hold. That is,
Only the top four lines remain in this formula,
And
Is not related to the value of. Here, when the sum of the expression (78) is taken,
And ask
So
And
Therefore, since the numerator of the equation (45) is 0 from the equation (46), the stimulation coefficient in this mode is 0.
Is known, Eq. (78)
This is a quaternary quadratic simultaneous equation, and if each expression is independent, it can be solved algebraically. Although the calculation in the middle is omitted, when equation (78) is solved, ω ² becomes the solution of the following quadratic equation.

As well
With eigenvalues
, Eigenvector
However,
, Is established. If the conditions at this time are arranged in the same way,
here,
Is the equation (22)
(N-i + 1) -row (n-i + 1) -column submatrix from the upper left of
Is the equation (22)
(N-i + 1) -row (n-i + 1) -column submatrix from the upper left of
Is the equation (22)
(N-i + 1) rows of partial vectors from above. The sum of each line in equation (85) is
Since u _i−1 = ui ₋₂ =... = U ₁ = 0, the stimulation coefficient in this mode in which the numerator of the equation (45) is 0 from the equation (46) is still 0. When m ′ _n ,..., m ′ _{i + 1} are known, the equation (85) is an (n−i + 2) element (ni) order simultaneous equation. (82) Equation 1 is an (n-i + 1) -order ordinary general eigenvalue problem,
Since both are symmetric and positive definite matrices, they have (n−i + 1) positive ω ² solutions regardless of the value of m ′ _i . Accordingly, the simultaneous equations with the second equation (85) have (ni) solutions of positive value ω ² . Each solution of ω ^{2 corresponds to} a ^2nd to (n−i + 1) th order mode excluding the first order in the equation (85).
This operation can be repeated from m ′ _n−1 to m ′ ₁ . However, in the case of m ′ ₁ , it is necessary to add the following expression as a condition.
As a result, the solution of the inertial connecting elements m _'i of the stimulation index of a mode 0 is shown in Table ^{1 (n-1) 2/} 2 pieces are required. The table represents the mode shape of the eigenvector corresponding to the solution (how to repeat the eigenvector positive or negative). View of this table, for example, looking at i = n-2 line, m 'when the stimulation index by controlling the _n-2 to try 0, m' _n-2 is 2 solutions exist, two The stimulation coefficient of the mode can be set to 0, and the shape of the eigenvector at that time is read as a cubic and a quadratic form. The colored part shows the combination of solutions that makes the stimulation coefficient of all higher modes 0.

In this table, the solution has the following properties.
1. The solution in each square in the table is not related to the stiffness and mass (including inertial connection elements) below that layer, but the value changes when an inertial connection element is added to a layer above that layer.
2. There can be only one solution at a time on a line.
3. Even if multiple solutions are selected in one row, only the uppermost solution is valid because the upper solution includes the lower solution.
If this property is satisfied, there can be a combination of multiple layers of inertial connection elements with different mode stimulation coefficients of zero.

Here, consider the case of i = 1 in Table 1. Equations (85) and (87), which are conditions at this time, are just equations for the n mass point vibration system having an inertial connection element to have a mode having a stimulation coefficient of zero. The original form of Equation (2) is the same as Equation (3).
In order for these to have a solution of ω ² ≠ 0,
Need to be. When u ₁ ≠ 0, m ′ ₁ needs to exist, and the solution is n−1 solutions obtained when i = 1.

Next, when u ₁ = 0, the condition is i = 2 in the equation (85). In order for this to have a solution of ω ² ≠ 0, as in the case of i = 1,
Need to be. When u ₂ ≠ 0, m ′ ₂ needs to exist, and the solution is n−2 solutions obtained when i = 2. In the same manner, when i = n, it is obvious that the stimulation coefficient cannot be 0 when u ₁ = u _i−2 =… = u _n−1 = 0 and u _n ≠ 0, so m 'Stimulation factor is not 0 in any mode when only _n is added.

  From the above, a solution that makes the stimulation coefficient of any mode 0 by adding an inertia connecting element cannot be a solution other than the types shown in Table 1. However, even if an inertia connecting element proportional to the rigidity of each layer is added to this solution, there are any number of individual solution values.

(5) Zeroing the stimulation coefficients of all higher-order modes Consider the control to make the stimulation coefficients of all higher-order modes of the vibration system zero by adding inertia connection elements. The combination of inertial connecting elements, which is the solution, can be obtained by calculating the solution in which the eigenvector is quadratic in order from m ' _n-1 to m' ₁ by the method shown in the previous section. When the number increases, it is necessary to solve higher order simultaneous equations, which requires a lot of calculation. Here is another way to find this combination.

Now the first-order eigenvector of the system of (1) is
Suppose that In this case, the stimulation coefficient of the sth order (s ≠ 1) is expressed by the equation (91), and this value becomes 0 due to the orthogonality of the eigenvectors. Therefore, no response other than the first order appears.
This is only the case where the combination of colored parts in Table 1, that is, the combination of quadratic solutions in each row, is selected from the properties of Table 1. Therefore, there is always only one combination of the inertia connecting elements except for the combination of inertia connecting elements proportional to the rigidity of each layer. Here, it is assumed that the 2nd to n-th order stimulation coefficient is 0 by adding a certain combination of inertial connection elements, that is, the relationship of Expression (91) is established. The primary eigenvalue at this time in the form of equation (22) is
It is. On the left side is the definition of {η}
Substituting
It becomes. Therefore,
It becomes. Here, taking the sum of 1 row, 2 rows,..., N rows from the top of equation (94),
And, when organized,
It becomes. Since the right side of each of the equations (96) represents the response layer shear force coefficient of the first-order mode, the addition of a combination of inertial connection elements simultaneously causes the 2nd to nth-order stimulation coefficients to become 0 at the same time. When only the response remains, the response layer shear force coefficient of each layer becomes equal, and the ratio of interlayer displacement of each layer becomes constant. Therefore, if an inertial connection element is added to a vibration system in which the rigidity of each layer is proportional to the sum of the masses above that layer, and the stimulus coefficient of the higher-order mode is set to 0, a vibration system in which the response interlayer displacement of each layer is equal. In addition, if an inertial connection element is added to the vibration system in which the rigidity of each layer is proportional to the value obtained by dividing the sum of the masses above that layer by the floor height to make the higher-order mode stimulation coefficient 0, A vibration system having the same response interlayer deformation angle can be achieved.
Further transforming equation (96),
Because
It becomes. When the 2nd to nth order stimulation coefficients become 0 at the same time due to the addition of the combination of inertial connection elements, and only the primary mode response remains, η ₀ = 0 and η _0n = 1. Is
It becomes.

Now, it is assumed that a combination of inertial connection elements that makes the stimulation coefficient of the 2nd to nth order modes 0 in the n mass point vibration system, where m ′ _n = 0 is obtained. At this time,
It should be. At this time
Is obtained from the values of m _i and k _i according to equation (99).
Is obtained from the equation (97), so {1-η}
Is obtained.
D _i and m ′ _i can be obtained from equation (59). That is, a combination of inertial connection elements that makes the stimulation coefficient of the 2nd to nth order modes 0 can be obtained. This combination is the minimum inertia connection element combination because m ′ _n = 0, and even if an inertia connection element proportional to the rigidity of each layer is added to this combination, the stimulation coefficient of the 2nd to nth order modes is also obtained. Is 0. This method is expressed by the following procedure.

(6) Cylinder-type damping piece Next, an inner ring and an outer ring having different radii on the same axis are used as members that move at high speed in accordance with the displacement difference of the contact without being influenced by the ground movement by the design method according to the present invention. FIG. 3 shows a cylinder-type damping piece 2 which is a rotating body provided with a mass concentrated from the inner ring to the outer ring.

  In FIG. 3, a cylinder-type damping piece 1 that realizes an inertial connecting element according to the present invention includes first and second connecting members 6 that are connected to each other so as to connect two points (objects) 2 and 4 that are relatively displaced. And both of the connecting members 6 and 8 are fixed to one of the two points (objects) 2 and 4 to be displaced relative to each other, and the first connection is made. The member 10 is formed with a guide screw portion 14 on the connection side, and a rotating inner cylinder 20 driven by a guide nut 18 screwed through a ball bearing 16 can be slid on the screw portion 14. The connecting portion of the second connecting member 8 is formed in a fixed outer cylinder 24 for the chamber 22 that accommodates the rotating inner cylinder 20, and a damping viscous body is provided in the chamber 22. And / or filling the viscoelastic body 26 To so that configuration.

Here, the rotating inner cylinder 20 is composed of a closed cylinder whose other end is inserted into the guide nut 18 at one end, and a fixed outer cylinder at one side of the guide nut 18 and the closed end of the rotating inner cylinder 20. By arranging ball bearings 28 and 30 on both the upper and lower contact surfaces with respect to 24, on the guide screw portion 14 corresponding to both compression and tension loads generated from relative displacement between the two points 10 and 12, respectively. Is supported so as to slide in the vertical direction in the figure. Furthermore, polyisobutylene and other synthetic rubbers can be suitably used for the viscous fluid.
In addition, the cylinder type attenuation | damping top used by the design method based on this invention can be changed variously, for example, can be deform | transformed as shown in FIG. That is, in this embodiment, in the embodiment shown in FIG. 3, the rotating inner cylinder 20 is formed as an open cylinder, and the guide nut 18 is attached to the casing 32 fixed to the fixed outer cylinder 24. It is comprised so that it may support through.

  Furthermore, in the third modified example of the cylinder-type damping piece 1 as shown in FIG. 5, the cylinder-type damping piece 1 includes a speed amplification unit 36, a transmission unit 38, and an attenuation unit 40. A guide screw part 14 with a thread groove is inserted into the speed amplifying part 36 from its end, and is screwed into the guide nut 18 via the ball bearing 16 of the linear bearing 42. It is rotatably joined to the outer cylinder 32 of the amplifying unit 36 via a thrust bearing 29.

  The guide nut 18 is joined to the rotating inner cylinder 20 in the transmission portion 38 and rotates in the damping portion 40. A viscous body 26 is enclosed between the outer cylinder 24 and the rotating inner cylinder 20 of the attenuation portion 40 and sealed with a seal 28 at the end of the outer cylinder 24, so that the viscous body 26 does not leak.

  Moreover, the cylinder-type damping piece can be applied to a building structure composed of a plurality of floors by the design method according to the present invention. Then, next, the Example at the time of applying the damping device which uses the said damping rod based on this invention to a building structure is described below.

First, in FIG. 6, the damping rod 50 is disposed between the mounting plates 74 a and 74 b at the opposite corners of the structural frame 74 of the building structure 72 so as to be compressible and tensionable via connecting members 50 a and 50 b, respectively. ing. Therefore, the strain energy in the structural frame 74 is absorbed by the damping effect of the damping rod 50 that is expanded and contracted by the strain displacement of the structural frame 74 caused by an earthquake or the like, and the vibration of the building structure 70 is effectively controlled. However, the design method according to the present invention further artificially couples and operates the mass matrix, and if response control is performed by controlling the period and vibration mode of the vibration system, rigidity and damping This makes it possible to control the response of a type of vibration system that is difficult to achieve with only this control.
In the design method according to the present invention, the mass for each layer is calculated from the building structure 72 and the spring constant for each layer is calculated. From these masses and spring constants, eigenvalues and stimulation coefficients when the stimulation coefficient other than the primary mode becomes 0 are calculated, and inertial connection elements between the respective layers are calculated from these stimulation coefficients and masses. By arranging the damping rod 50 capable of generating the inertia connecting element in each layer, the building structure 72 capable of mode control of each layer is designed.

(7) Disc type damping piece FIG. 7 shows an example in which the damping piece is used as a member that moves at high speed according to the displacement difference of the contact without being influenced by the ground motion in the design method according to the present invention. First, basically, first and second connecting members connected to each other to connect two points (objects) 90 and 92 that are relatively displaced, that is, a first rod 94 and a tubular second rod 96. Consists of. The rods 94 and 96 are fixed at one end to one of the two points 90 and 92, respectively. The first rod 94 is formed with a guide screw portion 98 on the connection side, and a rotary piece 104 driven by a guide nut 102 screwed through a ball bearing 100 is slid on the screw portion 98. Insert it in a movable manner. The second rod 96 forms a casing 108 defining a chamber 106 for accommodating the rotary piece 104 on the connection side, and a damping viscous body and / or a viscoelastic body 110 is provided in the chamber 106. Fill.

  The guide nut 102 is generated from the relative displacement between the two points 90 and 92 by disposing ball bearings 112 and 114 on the upper and lower facing surfaces of the casing 108 surrounding the guide nut 102, respectively. Corresponding to both compression and tension loads, it is pivotally supported so as to rotate on the guide screw portion 98 and slide in the vertical direction in the figure. The rotary piece 104 is composed of an integral rotary part 104 extending radially outward from the outer periphery of the guide nut 102. Furthermore, other synthetic rubbers such as polyisobutylene can be suitably used for the viscous fluid.

  The attenuation piece of the present invention can be changed variously. For example, it can be modified as shown in FIG. In the first modification, as shown in FIG. 8, the first connecting member is changed from the tubular rod 96 to the normal rod 120, and the rotating piece is changed from the integral rotating portion 104 and from one side portion of the guide nut 102. The configuration is changed to a separate rotating unit 122 that is separated and extends in parallel in the radial direction. That is, the separate rotating part 122 is accommodated in the chamber 106 in the first casing 122 formed on the connection side of the rod 120 (second connecting member), and the guide nut 102 is in the second casing 124. It is supported by ball bearings 112 and 114 inside. Note that it is obvious that the same effect as in the previous embodiment is exhibited in this modified example.

As shown in FIG. 9, a further modification example includes first and second connecting members that are connected to each other so as to be relatively displaceable. The first connecting member has a guide screw portion 130 formed on the connection side. The inner tube 132 is engaged with the screw portion and has a sufficiently larger diameter than the inner tube 132, and is inserted on the guide screw portion so as to be slidable on the guide screw portion based on relative displacement with the screw portion 130. It consists of a disk-shaped rotating body. This rotating body is composed of 134, a disk-shaped main body 136, and a flange 138 that extends radially outward from the outer periphery of the disk-shaped main body 136 and is thinner than the disk-shaped main body 136. The second connecting member includes an outer tube 140 and a cylindrical casing 142 that houses the rotating body 134 formed on the connection side thereof. Further, the rotating body 134 is supported in a substantially cylindrical casing 142 via a plurality of ball bearings 144 so as to be able to rotate and slide. A gap between the inner wall of the cylindrical casing 142 and the rotating body 134 is filled with a damping viscous body and / or a viscoelastic body 146. It is obvious that the same effect as in the previous embodiment is exhibited in this modified example.
As described above, in the design method according to the present invention, when a damping top is used, an inertial force and a damping force can be applied with one device, and each is set independently. In addition, although the utilization method was shown about the attenuation | damping piece and the attenuation | damping rod from the above as a member in this invention, it is not limited to these.
(8) Auxiliary Mass FIGS. 10 and 11 show an example in which the auxiliary mass is applied to the design method according to the present invention as a member that moves at high speed according to the displacement difference of the contact without being affected by the ground motion. FIG. 10A shows a first toggle type auxiliary mass mechanism in which a damping term provided on the ground 150 is c, and a main mass portion 154 whose mass is m by a spring portion 152 whose spring constant is k. Is supported. On the other hand, a fixed main shaft 156 is also erected on the ground 150. An auxiliary mass support rod 160 pin-coupled to the top of the fixed main shaft 156 is connected to an auxiliary mass portion 162 having a mass of md. Further, the main mass portion 154 and the auxiliary mass portion 162 are connected by the main mass support rod 164.
The second toggle auxiliary mass mechanism shown in FIG. 10B is a main mass part whose mass is m by the spring part 152 whose attenuation term is provided on the ground 150 and whose spring constant is k. 154 is supported. On the other hand, a fixed main shaft 156 is also erected on the ground 150. A first auxiliary mass support bar 168 that is pin-coupled to an intermediate portion of the fixed main shaft 156 is connected to a first auxiliary mass portion 173 having a mass m _d / 2. The first auxiliary mass unit 173 is connected to the main mass unit 154 via the first main mass support rod 170. On the other hand, the second auxiliary mass support rod 176 pin-coupled to the top that is above the middle portion of the fixed main shaft 156 is connected to the second auxiliary mass portion 174 having a mass of md / 2. The second auxiliary mass unit 174 is connected to the main mass unit 154 via the second main mass support rod 176.
In particular, if the second toggle type auxiliary mass mechanism is used, the inertial forces due to the vertical movements of the auxiliary masses 173 and 174 are canceled with each other by the auxiliary masses, and the reaction force becomes only the horizontal force. Form the same mechanical mechanism. Such a mechanism can be easily manufactured by forming a toggle with a steel frame and attaching a metal weight to the toggle. When the above configuration is represented by a vibration equation, the equation (103-1) is obtained.
FIG. 11A shows a model in which the second toggle auxiliary mass mechanism is stacked. That is, if it is arranged on each floor of a multi-layer building, response control by multi-mass point mode control becomes possible.
Further, FIG. 10 and the damping device 182 decay constant is c _d between the auxiliary mass 162 and the ground 150 in (a), the spring constant k _d a a spring 180 is inserted spring damped toggle auxiliary mass mechanism Is shown in FIG. Further, FIG. 10 decay constant between the auxiliary mass 173 and 174 in (b) is a damping device 186 is c _d, spring constant k _d a a spring 184 is inserted spring damped toggle auxiliary mass mechanism Is shown in FIG. If a spring or a damping device is incorporated at the amplification point of the displacement, an amplified spring reaction force and damping force can be obtained in the same manner as the amplification of the mass term. The vibration equation of this mechanism is shown in Formula (103-2).

(9) Design System FIG. 12 shows an attenuation top design system according to the present invention based on the above theory.

  The attenuation top design system 200 includes a central processing unit CPU 202 that controls the system, a main memory 204 that stores a control program such as an OS, a file device 206 that is a second storage device, an input device 208, and an output device. 210 and a network input / output device 230, the CPU 202 is electrically connected to the bus 212 so as to be able to transmit and receive, the main memory 204 is also electrically connected to the bus 212 so as to be able to receive and transmit, and the file device 206 is also connected to the bus 212. The input device 208 is electrically connected to the bus 212 for transmission, the output device 210 is electrically connected for reception, and the network input / output device 230 is electrically connected for transmission / reception. Connected to.

  The CPU 202 reads various operations and the OS from the main memory 204, and performs input / output control in the file device 206, input control of the input device 208, output device 210, and output control to the network connection device 230.

  The main memory 204 is a memory that stores a control program such as an OS in conjunction with the CPU 202 such as a main cache, and is configured by a semiconductor RAM or the like.

  The file device 206 is composed of, for example, a hard disk such as a magnetic disk used for data storage and application software storage. As data, a building structure specification file 214, an original vibration data file 216, and a result file 218 are recorded. Further, an attenuation top design program 224 is stored as application software.

Building structure specification file 214 includes a hierarchical mass data m _i, composed of a hierarchical spring constant data k _i.

Stratified mass data m _i is the mass a and the unit of each layer of the building to be constructed is (ton). The hierarchy-specific spring constant data k _i is a spring constant for each layer of the building to be constructed, and its unit is (kN / m). In Example 1, Table 2 corresponds, and in Example 2, Table 6 corresponds.

The original vibration data file 216 includes a natural period T, a natural frequency ω, and a damping constant h in each vibration mode when no damping device is arranged when a target vibration such as an earthquake is applied to a building. And a file made up of the stimulation coefficient β and the eigenvector u _i . In Example 1, Table 3 corresponds, and in Example 2, Table 7 corresponds.

The result file 218 is a file for storing calculated data. When the calculated inertial connection element m ′ _i and the damping device are arranged, the calculated data includes the natural period T, the natural frequency ω, the damping constant h, the stimulation coefficient, and the calculated vibration modes. It is a file composed of β and eigenvector u _i . In Example 1, Tables 4 and 5 and FIGS. 15 and 17 are applicable, and in Example 2, Tables 8 and 16 and 18 to 20 are applicable.

  The input device 208 includes at least a keyboard, a mouse, and a 10 keyboard. In addition, any device that can input numerical values or the like is any of position information input such as trackball, microphone, camera, and scanner, audio input, and image input. It may be a device.

  The output device 210 includes at least a display, and further includes a printer and a speaker.

  The network connection device 230 is connected to the Internet 234 through the line 232.

  On the other hand, the manufacturing terminal 242 is connected to the Internet 234 via the connection device 238. The manufacturing terminal 242 has a function of accumulating and storing parameters in the manufacturing machine and sending the parameters to control the manufacturing machine.

(10) Design Flow FIG. 13 shows a design flow according to the present invention using the above design system according to the present invention.

First, in the design system of the present invention, when the design program 224 is activated (A2), the CPU 202 displays an input acceptance screen on the display. Thereafter, when the building structure specification data and the original vibration data predetermined by the operator are input from the keyboard as the input device (A4, A6), the CPU 202 uses the input data as the building structure specification of the file device 206. The file 214 and the device specification file 216 are recorded. Numerical such as specifications that are entered here, the mass m _i and the spring constant k _i of each layer of the building structure, if no damping device is a raw vibration data arranged at all, and the natural period T in each vibration mode, a natural frequency omega, which is a parameter for solving the damping constant h, and stimulated coefficient beta, the eigenvectors u _i and subsequent expression. That is, the mass _mi and the spring constant k _i of each layer of the building structure correspond to the data in Table 2 in Example 1, and the data in Table 6 in Example 2. The original vibration data corresponds to Table 3 in the first embodiment and Table 7 in the second embodiment.

  Subsequently, the CPU 202 calculates a stimulation coefficient from the mass, the spring constant, and the eigenvalue (A8). The formula used at this time is formula (101). In Example 2, the fifth column in Table 7 is calculated.

Further, CPU 202 calculates the middle equation _{D n} from the stimulation index (A10). The formula used at this time is formula (102). In Example 2, the seventh column in Table 7 is calculated.

Then, CPU 202 calculates the inertia connecting element according to the rotary body from the middle equation _{D n} (A12). The formula used at this time is formula (103). In Example 2, the eighth column in Table 7 is calculated.

  Thereafter, the CPU 202 calculates the parameters of the inertial top of each layer from the inertial connection element (A14). The formula used at this time is formula (103). By arranging a damping top capable of generating this inertia connecting element in each layer by such a method, it is possible to design a building structure capable of mode control of each layer.

  14 and 15 and Tables 1 to 4 show the results of mode control of the two-mass point vibration system using inertial connection elements for a building structure designed using the design method according to the present invention.

A vibration system model is shown in FIG. A mass point m ₁ is connected to the ground via a spring constant k ₁ , an inertia connection element m ′ ₁ , and a damping coefficient c ₁ , and further a mass point via a spring constant k ₂ , inertia connection element m ′ ₂ and a damping coefficient c _2. m ₂ is connected. The original vibration y, mass, respectively, the distance _{x 1} and _{x 2} moves. The case where the mass inertia connection element ^{m′2 = m′1 = 0} is referred to as the original vibration system. Table 2 shows the mass of each mass point and the spring constant. The damping coefficients ^c1 and ^c2 were given in proportion to the rigidity of each layer so that h = 0.05 with respect to the primary vibration of the original vibration system.
Table 3 shows the eigenvalue analysis results obtained by adding the dummy mass point m ₀ to the original vibration system and forming the equation (30). Values from the first-order mode to the third-order mode are described for the natural period T, eigenvalue ω, damping constant h, stimulation coefficient β, and eigenvector u ₀ due to the original vibration. Since there is no inertial connection element, the third order mode is meaningless.

As an example of the control vibration system 1, an embodiment is shown in which a vibration control device having an inertial connection element calculated based on the design method according to the present invention is added to the original vibration system to perform control to make the secondary mode stimulation coefficient zero. . Assuming that n = 2 in the equations (71) to (73) and calculating based on the design method of the present invention, the minimum combination of inertia connecting elements is
It is. Table 4 shows the eigenvalue analysis results in this case. The stimulation coefficient is 1 only in the first-order mode, and the second-order mode and the third-order mode are 0. Therefore, even if the eigenvector exists, the product becomes the vibration mode, so the vibration is actually only the first-order mode. .

  Next, an example is shown in which control is performed so that the natural period of the primary mode is further extended to 1.5 seconds using the design method according to the present invention as the control vibration system 2.

Control is performed to extend the natural period of the primary mode to 1.5 seconds while keeping the secondary stimulation coefficient of the control vibration system 1 at 0. The broad mass of the control vibration system 1 is
From equation (64), the eigenvector does not change even if an inertial connection element proportional to k _i in FIG. 14 is added. For example, suppose that m ′ ₂ = 600 tons and m ′ ₁ = 1000 tons are added. In this case
From the formulas (52) and (66)
It is. On the other hand, it is necessary for the control to extend the natural period.
From equation (64)
It becomes. Therefore, m ′ ₂ = 0 ton and m ′ ₁ = 705.88 ton of the control vibration system 1 may be changed to the following inertial connection element.
Table 5 shows the eigenvalue analysis results of the system to which this inertial connection element is added. The stimulation coefficient of the secondary mode remains 0, and the period of the primary mode is 1.5 seconds. Compared to the control vibration system 1, the third-order stimulus function is increased.

FIG. 15 shows a comparison of the results of time history response analysis using the EL CENTRO 1940 NS (Amax = 510.8 cm / s ² ) of the original vibration system and the control vibration systems 1 and ² as input earthquake motion. By adding the inertia connecting element, the upper acceleration, displacement, interlayer displacement, layer shear force, inertia connecting element half force, response acceleration are reduced, and the response layer shear force coefficient is the same in all layers. It can be seen that it exhibits a unique and effective response control effect.

The result of mode control of the multi-mass point vibration system by the inertia connecting element for the building structure designed by using the design method according to the present invention is shown in FIGS. 16, 17, 18, 19, and 20 and Tables 6-8. As a model of a building structure, the model shown in FIG. 1 is assumed, and n = 8, that is, a building composed of 8 stories is assumed. Table 6 shows m _i and k _i of a vibration system of n = 8 (referred to as the original vibration system) appropriately set so that the primary period is 1 second in this model. Table 6 shows a calculation method including the mass of the inertia connecting element in the equations (100), (101), (102), and (103) from the mass of each mass point and the spring constant in the design method according to the present invention. The progress and result of finding the combination of inertial connection elements that make the stimulation coefficient of the higher-order mode excluding all the first-order modes of the original vibration system 0 are shown. The solution of m ′ ₈ ≠ 0 is obtained by adding an inertia connecting element proportional to the rigidity of each layer to the solution of Table 6, and the eigenvalue at that time is obtained by equation (67).

Tables 7 and 8 show the eigenvalue analysis results of the original vibration system and the vibration system to which the inertia connecting element is added (referred to as a control vibration system). The stimulus coefficient of the 2nd to 8th order modes of the control vibration system is 0, and the shape of the eigenvector is a quadratic form in which positive and negative appear once each.
FIG. 16 shows a comparison of the results of time history response analysis using the original vibration system and the control vibration system EL CENTRO 1940 NS (Amax = 510.8 cm / s ² ) as input ground motion. Damping is stiffness proportional damping with h = 0.05 for the first order of the system without inertia connecting elements. By adding an inertial connection element, the primary natural period is slightly increased from T = 1.00 seconds to T = 1.11 seconds, but the attenuation constant of the primary mode is reduced from h = 0.05 to h = 0.045. . By adding an inertia connecting element to the response value, the upper response acceleration, response displacement, interlayer displacement, and layer shear force are reduced, and the response layer shear force coefficient is the same for all layers. It can be seen that it exhibits a unique and effective response control effect.

Also, by loading the inertial connection element designed by the design method of the present invention to the vibration system having the same interlayer displacement of each layer, the upper response acceleration, response displacement, interlayer displacement, and layer shear force can be reduced. Is shown in FIG. FIG. 17 shows an effect different from the previous example of “control of interlayer displacement or interlayer deformation angle”.
Here, by adding an inertia connection element to the vibration system in which the rigidity of each layer is proportional to the mass above that layer, the higher order stimulation coefficient is made zero, so that the interlayer displacement of each layer at the time of response is equal. This is a vibration system controlled to be This effect is derived from equation (96).

Further, FIG. 18 shows an example in which an inertia connecting element is connected to a conventional base-isolated building based on the design method according to the present invention. In FIG. 18, symbol O represents the response value of an actual steel structure building using laminated rubber with lead plugs as a seismic isolation bearing. The symbol ▲ is a response value when an inertia connecting element is added so that the higher order mode of the base-isolated building is 0, and the response acceleration is significantly reduced from the symbol O. However, since the laminated rubber with lead plugs exhibits non-linear characteristics, the method of the present invention cannot be accurately applied, and thus approximate calculation based on equivalent rigidity is performed. In addition, the symbol ■ indicates a case where the characteristics of the base isolation layer are changed to a base isolation layer having a linear characteristic that is compatible with the calculation method of the present invention in order to further improve the performance. Not only the response acceleration but also the layer shear force is significantly reduced.
If the inertia connecting element is used in the method of the present invention, the response of the base-isolated building can be further improved, and further, the performance is further improved if the base isolation characteristics are changed to those suitable for the present design method.

Next, FIG. 19 shows the original vibration of the layer collapse factor, that is, the vibration of a model in which some floors are significantly displaced compared to other floors. “Suppression effect of layer collapse” is another important effect of inertial connection elements.
If there is a weak part in a part of the vibration system, energy concentrates on that part and the deformation increases locally. As a result, energy is further concentrated in this portion, and deformation is further increased. In this way, a phenomenon that the structure collapses occurs. It is thought that the layer collapse of buildings during an earthquake often occurs in this way. In fact, there are many cases such as the destruction of the middle floor and the layer collapse in past earthquakes such as the Hyogoken-Nanbu Earthquake.
A model with no inertia connecting element and a vibration model with an inertia connecting element added to make the higher-order stimulation coefficient zero, and a layer that yields with a yield strength of 80% of the yield strength required for response in both models. 19 and 20 are comparisons in which is set.
When there is no inertial connection element, a weak layer with insufficient proof stress is greatly deformed, leading to a phenomenon of layer collapse. On the other hand, in the model having the inertial connection element, the interlayer displacement of the weak layer is slightly increased, but the degree is small, and it is understood that the layer collapse by the weak layer is suppressed and the response of the entire system is stabilized.

It is a model figure which applies the principle of this invention to a multi-mass point system. It is a model figure which applies the principle of this invention to a multi-mass point system, (a) The acceleration applied directly from the ground is shown, (b) The acceleration seen from the ground is shown. It is a schematic diagram of the cylinder type 1st attenuation | damping piece | frame which is a rotary body used for the design method which concerns on this invention. It is a schematic diagram of the cylinder type 2nd attenuation | damping piece | frame which is a rotary body used for the design method which concerns on this invention. It is a schematic diagram of the cylinder type 3rd attenuation | damping piece | frame which is a rotary body used for the design method which concerns on this invention. The Example at the time of applying a damping device to a building structure by the design method which concerns on this invention is shown. It is a schematic diagram of a disk-type first attenuation piece that is a rotating body used in the design method according to the present invention. It is a schematic diagram of a disk-type second attenuation piece that is a rotating body used in the design method according to the present invention. It is a schematic diagram of the disc type 3rd attenuation | damping piece | frame which is a rotary body used for the design method which concerns on this invention. It is a member used for the design method which concerns on this invention, (a) is a 1st toggle type auxiliary mass mechanism, (b) is a 2nd toggle type auxiliary mass mechanism. It is a member used for the design method concerning the present invention, (a) is a block diagram of the model which laminated the 2nd toggle type auxiliary mass mechanism, and (b) is the toggle type auxiliary mass mechanism with the 1st spring damping. Yes, (c) is a toggle type auxiliary mass mechanism with a second spring damping. 1 shows a configuration diagram of a damping top design system according to the present invention. FIG. The design flow figure concerning the present invention using the design system concerning the present invention is shown. It is an acceleration response spectrum in the case of extending the period by adding the inertia connecting element according to the present invention. The comparison figure of the result of the time history response analysis which made EL CENTRO 1940 NS (Amax = 510.8cm / s < ² >) of the original vibration system in 2 mass points and the control vibration systems 1 and 2 by this invention the input earthquake motion is shown. A comparison diagram of the results of time history response analysis using EL CENTRO 1940 NS (Amax = 510.8cm / s ² ) of the original vibration system and the control vibration system at multi-mass points as input ground motion is shown. It is a graph which shows the response acceleration of the upper part at the time of loading the inertial connection element designed by the design method of this invention to the vibration system with the same interlayer displacement of each layer, response displacement, interlayer displacement, and layer shear force. The graph of the example which connects an inertial connection element also to the conventional seismic isolation building based on the design method which concerns on this invention is shown. An original vibration diagram is shown for the layer collapse factor, that is, the vibration of a model in which some floors are significantly more easily displaced than other floors. A vibration response diagram in a case where an inertia connecting element is connected to a model having a layer collapse factor, that is, a floor in which some floors are significantly more easily displaced than other floors based on the design method according to the present invention is shown. The model figure of the rotary body 2 which has the integrated inner ring | wheel 250 and the outer ring | wheel 252 which are the prior art examples, and the mass concentrates on the outer ring | wheel 252 is shown. A model diagram of a vibration system in which the above rotating body is incorporated in a conventional one-mass point vibration system is shown. The model figure of the lever mechanism with an auxiliary | assistant mass which is a prior art example is shown.

Explanation of symbols

1 Cylinder-type damping piece 2, 4 Relatively displaced 2 points (object)
6 First connecting member 8 Second connecting member 10 Connecting member 10, 12 Two points 14 Guide screw 16 Ball bearing 18 Guide nut 20 Rotating inner cylinder 22 Chamber 24 Fixed outer cylinder 26 Viscoelastic body 28, 30 Ball bearing 29 Thrust bearing 32 Casing 36 Speed amplification part 38 Transmission part 40 Damping part 42 Linear bearing 50 50 Damping rods 50a, 50b Connecting member 70 Building structure 72 Building structure 74 Structure frame 74a, 74b Mounting plate 74 Structure frame 76 Foundation 76a, 80a Support column 78 Seismic isolation pad 80 Seismic structure 90, 92 2 points (object)
94 First rod 96 Second rod 98 Guide screw portion 100 Ball bearing 102 Guide nut 104 Rotating top 106 Chamber 108 Casing 110 Viscous and / or viscoelastic body 112, 114 Ball bearing 96 Tubular rod 120 Rod 122 First Casing 124 Second casing 130 Guide screw part 132 Internal pipe 134 Rotating body is 136 Disc-shaped main body 138 Ridge part 140 External pipe 142 Cylindrical casing 144 Ball bearing 146 Viscous and / or viscoelastic body 150 Ground 152 Spring part 154 Main Mass portion 156 Fixed main shaft 160 Auxiliary mass support rod 162 Auxiliary mass portion 164 Main mass support rod 168 First auxiliary mass support rod 173 First auxiliary mass portion 170 First main mass support rod 176 Second auxiliary mass support rod 174 Second auxiliary mass 173,174 auxiliary mass 182 damping device 180 spring 200 damping piece design system 202 central processing unit CPU
204 Main memory 206 File device 208 Input device 210 Output device 212 Bus 214 Building structure specification file 216 Device specification file 222 Parameter file 223 Output file 224 Attenuation frame design program 230 Network connection device 232 Line 234 Internet 242 Manufacturing terminal 238 Connection device

Claims (22)

In the design method of a structure having a plurality of layers on which members that move at high speed according to the displacement difference of the node without being affected by the earthquake motion,
A spring coefficient k _i and inertia connecting element m _{i 'on} the ground, the acceleration structure is arranged in the ground of the mass m _i to be supported on the damping device c _i
Is selected for the inertial connection element so that the stimulation coefficient of the higher-order vibration mode is 0 and m ′ _n = 0 for the vibration equation for the ground motion of the n-mass system input to the structure How to design.   2. The design method according to claim 1, wherein the method of selecting and controlling the inertial connection element is configured such that the first-order natural period becomes an optimum value without changing the eigenvector of the vibration equation. . The method of selecting and controlling the inertia connecting element is as follows:
Calculating an eigenvalue from the mass of the component of each layer of the structure and the spring constant of the component of each layer;
Calculating a stimulation coefficient from the mass, the spring constant and the eigenvalue;
The method includes calculating the inertial mass due to the member from the mass and the stimulation coefficient, and selecting and controlling the stimulation coefficient so that the seismic response of the multi-layer structure is only in the first mode. The design method according to claim 1 or 2. Step includes a spring constant k and the layer number n of each layer of the mass m _i and each layer of the structure when second or stimulation coefficient addition is zero inertial clause elements for calculating the primary eigenvalue ₁ omega ² The design method according to claim 3, wherein:
The step of calculating the first-order stimulation coefficient η _i is based on the equation (2) from the mass m _i , the spring constant k, and the eigenvalue ₁ ω ² when the second-order or higher stimulation coefficient is 0 with the addition of an inertial node element. The design method according to claim 3, wherein the design method is calculated from:
The design method according to claim 3, wherein the step of calculating an inertial connection element calculates an inertial connection element m _i ′ by the member from the mass m _i , the stimulation coefficient η _i, and Equation 3.
  The design method according to any one of claims 1 to 6, wherein the member includes an inner ring and an outer ring having different radii on the same axis and a rotating body whose mass is concentrated on the outer ring from the inner ring.   The rotating body includes first and second connecting members that are connected to each other so as to be relatively displaceable. The first connecting member includes at least a first rod having a guide screw portion formed on the connecting side thereof, A guide nut that is engaged with the guide screw portion and is rotatably supported on the guide screw portion based on a relative displacement with the guide screw portion, and has a larger diameter than the first rod and is sufficiently larger than the diameter. The cylindrical rotating body has a large axial length and is rotatably inserted through the guide nut. The second connecting member accommodates the cylindrical rotating body and the guide nut. 8. The design method according to claim 7, wherein in a damping device comprising a cylindrical casing, at least a gap between the inner wall of the cylindrical casing and the cylindrical rotating body is filled with a damping viscous body and / or a viscoelastic body. .   The cylindrical rotating body is formed of a cylindrical body having one end portion extrapolated to a guide nut and the other end portion closed, so that one side portion of the guide nut and the closed end portion of the rotating inner cylinder opposed thereto are rotatable. 9. The design method according to claim 8, wherein the design method is pivotally supported.   The cylindrical rotating body comprises a tubular rotating body having one end portion extrapolated to a guide nut and the other end portion being an open end. Both side portions of the guide nut are rotatably supported, and the viscous body and / or The design method according to claim 8, wherein the viscoelastic body is also filled in a hollow portion of the tubular rotating body.   The rotating body includes first and second connecting members that are connected to each other so as to be relatively displaceable. The first connecting member includes a first rod having a guide screw portion formed on the connecting side thereof, and the guide. A guide nut that engages with the screw portion and is pivotally supported to rotate and slide on the guide screw portion based on relative displacement with the guide screw portion; and the guide nut having a sufficiently larger diameter than the first rod The second connecting member accommodates the second rod, the rotating body formed on the connection side, and the guide nut. The design method according to claim 7, wherein a damping viscous body and / or a viscoelastic body is filled in a gap between an inner wall of the cylindrical casing and the rotating body.   The design method according to claim 11, wherein the rotating body is integrally formed so as to extend radially outward from an outer peripheral portion of the guide nut.   The design method according to claim 11, wherein the rotating body is provided at a position spaced apart from the guide nut in the axial direction and is engaged with one side portion of the guide nut.   The member is supported by a main mass portion supported by a spring portion provided on the ground and an auxiliary mass portion connected to an auxiliary mass support rod pin-coupled on a fixed main shaft standing on the ground. The design method according to claim 1, comprising a toggle type auxiliary mass mechanism coupled by a rod.   The design method according to claim 14, wherein the auxiliary mass portion is further supported on the ground by the second spring portion and the damping portion.   The member is a first auxiliary mass connected to a main mass portion supported by a spring portion provided on the ground and a first auxiliary mass support rod pin-coupled to the top of a fixed main shaft standing on the ground. And a second auxiliary mass portion connected to a second auxiliary mass support rod that is pin-coupled to an intermediate portion of the fixed main shaft and a second auxiliary mass portion that is coupled to the main mass portion by a first main mass support rod The design method according to claim 1, comprising a toggle auxiliary mass mechanism coupled to the main mass portion by a main mass support rod.   The design method according to claim 16, wherein the first auxiliary mass part and the second auxiliary mass part are connected via a connection spring part and a connection damping part. In a design program for a structure having a plurality of layers on which a member that moves at high speed according to the displacement difference of the node without being affected by the earthquake motion,
A spring coefficient k _i and inertia connecting element m _{i 'on} the ground, the acceleration structure is arranged in the ground of the mass m _i to be supported on the damping device c _i
Is selected for the inertial connection element so that the stimulation coefficient of the higher-order vibration mode is 0 and m ′ _n = 0 for the vibration equation for the ground motion of the n-mass system input to the structure Design program to do. In a design system for a multi-layered structure in which members that move at high speed according to the displacement difference of the nodes without being affected by earthquake motion are mounted on each layer,
An input means for inputting in advance the mass of each layer of the structure and the spring constant of each layer; a storage means for storing the input data; an operation program stored in advance in the storage means and describing a calculation method; A step of calculating an eigenvalue from the mass of the component of each layer of the structure and the spring constant of the component of each layer, comprising a central processing unit for calculating according to the calculation program and an output means for outputting the calculation result;
Calculating a stimulation coefficient from the mass, the spring constant and the eigenvalue;
A structure design system comprising a step of calculating an inertial mass due to the member from the mass and the stimulation coefficient, and selecting and controlling the stimulation coefficient so that the seismic response of the structure composed of a plurality of layers is only in the first mode. .   14. Each layer which is designed by the design method according to claim 1 and has an inner ring and an outer ring having different radii on the same axis, and is configured so that an inertia connecting element is generated by a rotating body whose mass is concentrated on the outer ring from the inner ring. Rotating body.   14. Each layer which is designed by the design method according to claim 1 and has an inner ring and an outer ring having different radii on the same axis, and is configured so that an inertia connecting element is generated by a rotating body whose mass is concentrated on the outer ring from the inner ring. Rotating body.   A member of each layer that is designed by the design method according to claim 1 to be set so that an inertia connecting element is generated by a member that moves at a high speed in accordance with a displacement difference of a node without being affected by a ground motion, and the member A building structure that is controlled by multiple layers with the seismic response of the structure in the primary mode only.