JPH0941715A - Vibration mitigation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To regulate natural vibration characteristics of a vibration mitigator real time by making it correspond with vibration characteristics of a vibration mitigation object varying from hour to hour when the object is mitigated with the vibration periodical control type or synchronous type mitigation such as semi-active type TMD method, joint vibration mitigation method, cable vibration control method, etc. SOLUTION: When vibration of an object is mitigated with a vibration periodical control type or a synchronous type mitigation such as semi-active type TMD method, joint vibration mitigation method, cable vibration mitigation method, etc., in order to use the vibration mitigation method for controlling natural vibration characteristics of the mitigator by making it corresponding with natural vibration characteristics of the vibration mitigating object varying from hour to hour in details of vibration from the beginning to the end, at least elastic modulus and damping coefficient of the object in a vibration equation of vibration system consisting of the vibration mitigation object and mitigator make as unknown quantities, and a vibration state of vibration system is detected in a plurality of times by a detector in the details. Simultaneous equations with several unknowns from two or more vibration equations are established, and solution of the unknown quantities in the simultaneous equations is identified the vibration characteristics of the object.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a vibration control system of a semi-active type, such as a TMD method, a coupled vibration control method, a cable vibration control method or the like, for controlling a vibration target by a vibration period adjusting type or a tuning type vibration damping device. The present invention relates to a vibration damping method capable of adjusting a natural vibration characteristic of a vibration damping device in real time by following a vibration characteristic of a vibration damping target which changes every moment.

[0002]

Generally, in addition to the inertial effect of the mass such as an additional mass and the spring, when damping is performed by a semi-active type vibration damping device constituted by a damper, the vibration damping is performed. In order to enhance the effect, it is necessary to adjust the natural vibration cycle of the vibration damping device to an optimum cycle corresponding to the natural vibration cycle of the object to be damped, for example, the structure, or a cycle in synchronization with the cycle. . As a vibration damping method for performing such period adjustment, for example, the TMD method,
There are the consolidated vibration control method and the cable vibration control method.

In these vibration damping methods, the natural vibration characteristics of the vibration damping target, which are originally determined by the mass, the damping coefficient, and the elastic coefficient of the vibration damping target, are grasped in advance, and then the additional mass of the vibration damping device, etc. The mass, the damping coefficient and the elastic coefficient are set in advance to optimize the natural vibration characteristics of the vibration damping device.

Here, the structure will be described as an example of the object of vibration suppression. As shown in FIG. 1, in the vibration suppression corresponding to the vibration caused by a small earthquake or a wind, only the mass m of the structure 1 is measured. However, it may be considered that the damping coefficient c and the elastic coefficient k are also constant. Therefore, the above-described period adjustment type or tuning type vibration damping device exhibits a sufficient vibration damping effect due to the preset natural vibration characteristics.

On the other hand, when a large earthquake that may collapse the structure 1 is taken into consideration, the damping coefficient c and the elastic coefficient k of the structure 1 are caused by a large amplitude caused by the large earthquake. Then, a partition wall, which is a secondary structural member that constitutes the structure 1, is worn away by friction, or a primary structural member such as a pillar or a beam is partially plasticized,
It changes non-linearly (k → k _x , c → c _x ). Such a situation is not limited to the structure 1, and the same applies to other vibration damping targets. At this time, in the above-described period adjusting type or tuning type vibration damping device, the damping coefficient of the vibration damping target is set because the natural vibration characteristics based on the mass, damping coefficient, and elastic coefficient of the vibration damping target are set in advance. If the elastic modulus changes and the natural vibration characteristics change, it becomes impossible to exert sufficient vibration damping effect. Therefore, the period adjustment type or tuning type vibration damping device is not effective against a large earthquake. It was said to be absent.

As described above, when the damping coefficient or elastic coefficient of the object to be damped changes, the elastic coefficient of the spring or the damping coefficient of the damper constituting the vibration damping device is correspondingly dealt with.
It is possible to adjust these in order to change the inertial effect due to the mass. However, for this adjustment, it is necessary to observe the vibration state of the vibration suppression target that changes from moment to moment and identify the damping coefficient and elastic coefficient of the vibration suppression target based on this observation result. If such an evaluation process is not performed, the vibration characteristics of the vibration damping device, that is, its natural vibration period cannot be optimally adjusted.

Generally, a response waveform indicating a vibration state of a vibration damping target is observed, and an elastic coefficient or a damping coefficient of the vibration damping target is estimated by the periodicity appearing in the response waveform to obtain a vibration characteristic of the vibration damping target. It is possible to grasp the changes in But,
Since this method can be used only after obtaining the response waveform of the object to be damped due to an earthquake, etc., the damping device can be adjusted only for the result after the earthquake is over, and the It is difficult to adjust the natural vibration characteristics of the damping device in real time with respect to the target. Furthermore, since this response waveform is data that includes the effect of vibration suppression by the vibration damping device, it is difficult to evaluate the vibration characteristics of the vibration suppression target itself. Even if it is used for adjusting the vibration damping device, there is a problem that a good vibration damping effect cannot be obtained.

The present invention was made in view of the above circumstances, and its object is to provide a semi-active type T
When damping a damping target with a vibration period adjustment type or tuning type damping device such as the MD method, the coupled damping method, the cable damping method, etc., the vibration characteristics of the damping target that change from moment to moment are followed. Another object of the present invention is to provide a vibration damping method that enables adjustment of the natural vibration characteristic of the vibration damping device in real time.

[0009]

SUMMARY OF THE INVENTION The present invention is intended to suppress a vibration target by a vibration period adjusting type or a tuning type vibration damping device such as a semi-active type TMD method, a coupling damping method, a cable damping method. In order to adjust the natural vibration characteristics of the vibration damping device in response to the natural vibration characteristics of the vibration suppression target, which changes moment by moment in the process of occurrence and termination of vibration, At least the elastic coefficient and the damping coefficient of the vibration suppression object in the vibration equation of the vibration system including the vibration suppression object and the vibration suppression device are unknowns, and the vibration state of the vibration system is detected by the detecting means a plurality of times in the history. It is characterized in that a multi-dimensional simultaneous equation consisting of two or more vibration equations is created, and a solution of the unknown of the multi-dimensional simultaneous equation is obtained to identify the vibration characteristic of the vibration suppression target.

Further, it is characterized in that the mass to be damped is an unknown quantity.

Further, the multidimensional simultaneous equations are characterized by being analyzed by a statistical method such as a least square method.

Further, the damping object is modeled as a one-mass system model or a multi-mass system model.

Further, when the vibration suppression target is modeled as a model of a multi-mass system, in order to extract a vibration mode to be suppressed from a plurality of vibration modes that can occur, a detection value by the detection means is detected. Of these, a bandpass filter that passes a detection value near the peak frequency of the vibration mode to be damped is applied, and the vibration equation is created for the result.

Furthermore, when the vibration suppression target is modeled as a model of a multi-mass system, in order to extract a vibration mode to be suppressed from a plurality of vibration modes that can be generated, detection by the detection means is performed. Among the values, a mode filter that allows detection values corresponding to the vibration mode to be damped to pass is applied, and the vibration equation is created for the result.

Therefore, the vibration damping method of the present invention is a semi-active type vibration damping device of a period adjustment type or a tuning type which exerts a damping effect by adjusting the characteristic vibration characteristic. Initial settings are made in correspondence with known data, and when vibration characteristics of the object to be dampened change due to this, it is constantly changing for vibration damping devices that are difficult to exert sufficient vibration damping performance. It is possible to identify the values of the elastic coefficient and the damping coefficient of the vibration damping target that are going to be detected from the values detected by the detection means. As a result, the natural vibration characteristic of the vibration damping device can be adjusted to the optimum characteristic in real time from the time when the vibration is generated until the vibration is terminated. At this time, the elastic coefficient and damping coefficient of the object to be damped can be identified instantaneously by a computing means such as a computer from a multi-dimensional simultaneous equation based on the vibration equation. This makes it possible to make the natural vibration characteristics of the above-mentioned vibration damping device follow the changes in the vibration characteristics of the vibration suppression target, such as during a large earthquake when the elastic coefficient or damping coefficient of the vibration suppression target changes. However, it is possible to exert an effective vibration damping effect on the vibration damping device.

The unknown value of the object to be damped can include its mass as necessary, and even if the change in the mass of the object to be damped must be taken into consideration, the present method can be applied. You can

If a statistical method is used for obtaining the solution of the simultaneous equations, it is possible to eliminate the influence of noise at the time of detection.

By modeling the vibration suppression target in a mass system,
The analysis work can be facilitated.

Among the detection values detected by the detection means, a bandpass filter for passing the detection values in the vicinity of the peak frequency of the vibration mode to be damped, and the detection values corresponding to the vibration mode to be damped among the detection values detected by the detection means. By using the mode filter that passes the detection noise, the detection value necessary for the analysis can be extracted while removing the observation noise, and the accuracy of the analysis work can be improved.

[0020]

2. Description of the Related Art As mentioned above, in addition to the inertial effect of the mass of the additional mass and the spring, when the vibration is damped by the semi-active type vibration damping device constituted by the damper, the vibration damping effect is obtained. In order to increase the frequency, the natural vibration cycle of the vibration damping device is adjusted to an optimum cycle corresponding to the natural vibration cycle of the vibration suppression target, or is adjusted to a cycle in synchronization with the cycle. Examples of vibration damping methods for which the period adjustment is performed include the TMD method, the coupled vibration damping method, and the cable vibration damping method.

In the TMD method, as shown by modeling in FIG. 2, a damper 3 installed on a damping target 2 having a mass m, a damping coefficient c, and an elastic coefficient k to damp the vibration is a damping target. 2 is connected to an additional mass 5 mounted via a spring 4, and the inertial force generated by the additional mass 5 vibrating in response to the vibration of the damping target 2 is used as a reaction force of the damper 3, As a result, the damping force of the damper 3 acts on the damping target 2 to damp it. Then, the natural vibration cycle of the vibration system 6 configured by the damper 3, the spring 4, and the additional mass 5 that are collectively mounted on the vibration suppression target 2 is made to match the natural vibration cycle of the vibration suppression target 2 in advance. The damping effect is obtained at the peak of the vibration transfer function of the damping target 2.

As shown in FIG. 3, the coupled damping method is a method of coupling two damping objects 11 and 12 having different natural vibration periods, and the masses m ₁₁ and m ₁₂ of both damping objects 11 and ₁₂ are It can be used as a reaction force for damping and is effective in this respect. At this time, in order to optimally suppress both damping objects 11 and 12 simultaneously, the connecting spring 13 and the damper 1
Period adjustment using 4 is performed, and both damping targets 1
The vibrations of 1 and 12 are controlled at once. It should be noted that this cycle adjustment is performed only for one vibration mode.

As an example of the cable damping method, two configurations are shown below. The former shown in FIG. 4 is disclosed in JP-A-4-1769.
No. 74 (E04H 9/02, E04B 1/34), and this device is schematically shown in the figure
Between a structure 22 such as a high-rise / super-high-rise building or a warehouse rack constructed on 1 and a damper 23 fixedly provided on the ground 21, only a tensile force is transmitted as a vibration transmitting material and a compressive force is transmitted. Tensile members 24a, 24 such as wires that do not transmit
b is stretched, and horizontal shaking generated in the structure 22 due to an earthquake, wind, or the like, that is, horizontal vibration of the structure 22 is transmitted to the damper 23 via the tension members 24a and 24b pulled by the structure 23, and the structure is transmitted. It is configured to damp the vibration of 22.

In the illustrated example, the left and right ends 2 of the top of the structure 22 where the vibration displacement is most noticeable in the vibration of the first mode.
One end of each of the pair of tension members 24a and 24b is connected to each location. And these pair of tension members 24a, 2
4b is obliquely downwardly crossed and guided to the base of the structure 22 and is hung around a pair of pulleys 25a and 25b arranged at the left and right ends of the structure 22 to form a structure. It is guided to the center of 22 bases.
On the other hand, in the center of the base of the structure 22, a laminated rubber type damper 23 that is fixed to the ground 21 separately from the structure 22 and absorbs energy by shear deformation is provided. The other ends of the pair of tension members 24a and 24b are connected to each other.

When the structure 22 vibrates in the horizontal direction, one of the tension members 24a is damped by the damper 23 in accordance with the vibration.
And the damper 23 is sheared and deformed.
At this time, the other tension member 24b is the damper 2 that undergoes shear deformation.
3 causes the structure 22 to be pulled between the top of the structure 22 and the vibration of the structure 22 is transmitted to the damper 23 and attenuated by such an action.

The latter shown in FIG. 5 relates to Japanese Patent Application No. 7-177307 filed earlier by the applicant of the present application.
Between a structure 32 such as a high-rise / super-high-rise building or a warehouse rack constructed on 1 and a damper 33 fixedly provided on the ground 31, as a vibration transmitting material, only tensile force is transmitted and compressive force is transmitted. Tensile members 34a, 3 such as cables that do not transmit
4b is stretched, and horizontal shaking generated in the structure 32 due to an earthquake or wind, that is, horizontal vibration of the structure 32,
This is configured to be transmitted to the damper 33 via the tension members 34a and 34b that are pulled, and to damp the vibration of the structure 32.

Also in this example, one end of the pair of tension members 34a, 34b is connected to each of two left and right ends of the top of the structure 32 where the vibration displacement is most prominent in the first mode vibration. Then, the pair of tension members 34a, 34a
b is crossed diagonally downward and is guided to the base of the structure 32, and is wound around pulleys 35 arranged at both left and right ends of the base of the structure 32, so that the structure 32
You will be guided to the center of the base.

On the other hand, at the base of the structure 32, a hydraulic cylinder type damper 33 is provided separately from the structure 32 and fixed to the ground 31. The cylinder 33a of this damper 33 is connected to the ground 31, and the piston rod 3
3b has a general structure that absorbs energy by causing a pressure loss in the flow of hydraulic oil associated with the forward / backward movement of 3b. The damper 33 and the tension members 34a and 34b are connected to a rotary shaft 38, which is rotatably supported by the ground 31, and has a considerable outer diameter. Thus, a plurality of arms 36 are provided, and additional masses 37 are provided at the respective tips of these arms 36. And a plurality of dampers 3 fixed to the ground 31
3 are connected to one of the additional masses 37, respectively. Further, tension members 34a and 34b are wound around the rotary shaft 38.

When the structure 32 vibrates in the horizontal direction, one of the tension members 34a is pulled, whereby the rotating shaft 38 is rotated at a considerable swinging rotation angle, whereby the additional mass 37 is passed through the arm 36. Is being shaken. Accordingly, the piston rod 33b of the damper 33
Is pushed in or pulled out to cause a flow in the hydraulic oil of the damper 33. At this time, the other tension member 34b is wound around the rotary shaft 38 and pulled between the top of the structure 32 and the top. Such an action is alternately generated in the pair of tension members 34a and 34b according to the vibration of the structure 32, and the tensile force of the tension members 34a and 34b causes the additional mass 3 to pass through the rotary shaft 38.
The vibration of the structure 32 is damped by swinging 7 in the reciprocating direction and operating the damper 33.

[0030]

BEST MODE FOR CARRYING OUT THE INVENTION In the above-described semi-active type TMD method, coupled damping method, cable damping method, or other periodic adjustment type or tuned type damping method, a damping device is added to a damping target. The force generated by the load sensor, such as a load cell, is directly estimated, and the acceleration detected by a displacement sensor, a speed sensor, an acceleration sensor, etc. is estimated by assuming that the mass of the additional mass of the vibration damping device is known. Therefore, it is possible to indirectly and further detect and observe with other detecting means. Further, the seismic input and the response of the vibration control target thereto can be detected and observed by various detection means similar to those used in the vibration control device.

The inventor of the present invention pays attention to the fact that the elastic performance and damping performance of the object of vibration control change moment by moment in the process of starting and ending vibration after an earthquake or the like is input. Then, the vibration state of the vibration suppression target or the vibration suppression device is detected by the detection means, and the value of the elastic coefficient or the damping coefficient of the changing vibration suppression target, and thus the natural vibration characteristic is identified from the detected value,
As a result, the elastic effect of the spring that constitutes the damping device, the damping coefficient of the damper, and the inertial effect due to the mass of the additional mass,
Similar to the setting in the adjustment of the natural vibration characteristics in the initial stage, it is intended to be able to adjust in real time to the optimum value for damping, and the identification of the elastic coefficient and damping coefficient of the damping target at this time is performed. This can be performed by instantaneously analyzing a multi-dimensional simultaneous equation consisting of two or more vibration equations by a computing means such as a computer, which makes it possible to adjust the natural vibration characteristics of the above-described vibration damping device in real time. It has been found that it is possible to exhibit sufficient vibration damping effect in the above-mentioned period adjustment type or tuning type semi-active type vibration damping device by following the change in the vibration characteristics of the vibration damping target. Is.

The basic idea of this method for identifying the elastic coefficient and damping coefficient of the object to be damped will be explained with reference to FIG. 6 above by exemplifying the case where the object to be damped 50 is treated as a single mass system. , The vibration equation in that case is as follows. Reference numeral 60 is a vibration damping device.

[0033]

[Equation 1] Here, m is the mass of the damping target, c is the damping coefficient of the damping target, k is the elastic coefficient of the damping target, and F is the damping force input to the damping target from the damping device.

In this equation (1), if the force term is arranged on the right side, it can be rewritten as the equation (2).

[0035]

[Equation 2] Now, it can be generally assumed that the mass m of the vibration suppression object is constant, while the elastic coefficient k and the damping coefficient c of the vibration suppression object can change from moment to moment.
It is appropriate to treat it as an unknown number. However, the mass m of the vibration suppression target may be an unknown number. When the elastic coefficient k and the damping coefficient c of the vibration suppression target are unknowns, there are two unknowns, so at least two vibration equations are naturally obtained from the above equation (1) or equation (2). By creating and solving these multi-dimensional simultaneous equations, it is possible to obtain a solution for these two unknowns k and c, and by this, it is possible to identify the vibration characteristics of the vibration suppression target that are changing every moment. .

For the simultaneous equations, it is possible to use the vibration equation at a moment t _k where there is a vibration suppression target in the vibration state and the vibration equation at the time t _k−1 sampled immediately before that. This is shown in the following equation.

[0037]

(Equation 3) Here, the mass m of the vibration suppression target is known as an initial value,
And it is assumed to be constant. And at these times t _k-1 , t
_{Between k} and _k , the elastic coefficient k and the damping coefficient c of the damping target are
By assuming that does not change, it is possible to uniquely determine the elastic coefficient k and the damping coefficient c, which are unknowns, from the equation (2a). This assumption can be satisfied without any problem by making the sampling time width as small as possible. If the elastic coefficient k and the damping coefficient c change during the sampling time width, the solution of the simultaneous equations is obtained as an average value of the value at the time t _{k-1 and} the value at the time t _k . It will be. Theoretically, the elastic coefficient k and the damping coefficient c of the vibration damping target are obtained every moment by such a method, and the vibration characteristic of the vibration damping target is identified by these solutions, and this is identified by the characteristic of the vibration damping device. It can be reflected in the adjustment of vibration characteristics. In reality, in order to eliminate the influence of noise in observation, sampling is performed three times or more, three or more equations of vibration are obtained, and the elastic coefficient k and the damping coefficient are calculated by a statistical method such as the least square method. It is preferable to obtain c. As a sampling time width, for example, about 1/100 second to 10/100 second is considered to be appropriate.

Numerical values other than the unknown elastic coefficient k and damping coefficient c in the above equations (1), (2), and (2a) can be measured. The displacement, velocity and acceleration can be detected by a general sensor. Further, the damping force F can be obtained by detecting the displacement, velocity or acceleration of the additional mass 5 with a sensor, for example, in the damping device of the TMD method of FIG. 2, since the mass of the additional mass 5 is known. . Since the mass of the additional mass 37 is known even in the cable damping method of FIG. 5, the cables 34a, 34
A sensor detects movement displacement, movement speed, movement acceleration of b, rotation angle, rotation angular velocity or rotation angular acceleration of the arm 36, and connects the cables 34a, 34b to the structure 32 at the cables 34a, 34b. It is also possible to directly detect the acting tensile force by measuring it with a load cell or the like. More specifically, the damping force F of the damping device will be described by taking the TMD method of FIG. 2 as an example.

(Equation 4) And the damping force F is calculated by using the equation (3) or (3a).
Can be calculated.

By the way, if the cable damping method of FIG.

(Equation 5) Is expressed as

In the above equations (3), (3a) and (3b), m ₀ is the mass of the additional mass of the vibration damping device, k ₀ is the elastic coefficient of the vibration damping device, and c ₀ is the damping coefficient of the vibration damping device. Yes, these are known. Further, Φ is an inclination angle of the cables 34a and 34b with respect to the horizontal plane in the case of the cable damping method.

By using this method, it is possible to identify the values of the elastic coefficient k and the damping coefficient c of the changing vibration damping object, that is, the vibration characteristics of the vibration damping object, and to configure the vibration damping device. It is possible to adjust the natural vibration characteristics of the vibration damping device by adjusting the elastic effect k _{0 of the} spring, the damping coefficient c _{0 of the} damper, and the inertial effect due to the mass m ₀ to a value optimum for damping in real time. Thus, the optimum vibration damping effect can be obtained.

To give an example of how to adjust the components such as the damper in the vibration damping device, for example, in the case of a hydraulic damper, the flow resistance of the hydraulic oil may be changed, and for the additional mass, the cable control shown in FIG. If the swing method, additional mass 37
There are various methods such as changing the radius of gyration.

In the above example, the damping coefficient c and the elastic coefficient k of the vibration suppression target are two unknowns. However, in consideration of the change of the mass m of the vibration suppression target, this is also treated as an unknown number. For this, a multidimensional simultaneous equation with three unknowns is used.

As described above, the period adjustment type or tuned type semi-active type vibration damping device that exerts the vibration damping effect by adjusting the natural vibration characteristic, and the known data to be damped is known. The initial setting is made in response to the above, and when the vibration characteristics of the vibration suppression target change, it is difficult to achieve sufficient vibration suppression performance for the vibration suppression device and the vibration suppression device. At least the elastic coefficient and damping coefficient of the object to be damped in the vibration equation of the vibration system including the device are unknowns, and the vibration state of the vibration system is detected by the detection means a plurality of times in real time, and a multi-dimensional simultaneous equation including two or more vibration equations is detected. By applying this method, which creates an equation and identifies the vibration characteristics of the vibration suppression target by obtaining the unknown solution of this multi-dimensional simultaneous equation, the vibration of the vibration suppression target that changes moment by moment Can be identified value of the coefficient k and the damping coefficient c from the detection value by the detecting means. As a result, the natural vibration characteristic of the vibration damping device can be optimally adjusted in real time from the time when the vibration is generated until the vibration is terminated. At this time, the elastic coefficient k and the damping coefficient c of the vibration suppression target can be identified instantaneously by a computing means such as a computer from a multi-dimensional simultaneous equation based on the vibration equation. This makes it possible to make the natural vibration characteristics of the above-mentioned vibration damping device follow the changes in the vibration characteristics of the vibration suppression target, such as during a large earthquake when the elastic coefficient or damping coefficient of the vibration suppression target changes. However, it is possible to exert an effective vibration damping effect on the vibration damping device.

Next, a case in which the vibration suppression target 50 is treated more realistically and practically as a multi-mass system will be described with reference to FIG. In the case of a multi-mass system modeled by n masses, there are multiple vibration modes from the first-order mode to the n-th order mode. Therefore, as a mathematical treatment, the modal coordinate system is used. It is easy to create the above vibration equation with. Further, here, the masses m _i , i = 1 to n of the vibration suppression target, the elastic coefficients k _i , i = 1 to n, and the damping coefficients c _i , i = 1 to n are set as unknowns. Reference numeral 60 is a vibration damping device.

The vibration equation of the multi-mass system is expressed by the following equation.

[0047]

(Equation 6) Here, [m] = D _iag (m _i ) i = 1 to n, and i represents the number of mass _points and their positions. Similarly, [c] = D
_iag (c _i ) i = 1 to n, [k] = D _iag (k _i ) i =
1 to n. Further, {m} is the mass at each mass point i = 1 to n, and {F} is the damping force input at the position at each mass point i = 1 to n. Further, x and y are the same as above and are physical quantities in the physical coordinate system.

The following equation is used to convert this equation (4) into a modal coordinate system.

[0049]

(Equation 7) [U] is a matrix representing the vibration modes from the first-order mode to the n-th order mode as shown in FIG. 8, and according to the equation (5), each mass point position i of the vibration suppression target modeled in the multi-mass system is expressed.
It will be simply shown that the horizontal response displacement x _{i of the above} is a superposition of the horizontal response displacement q _j due to a plurality of vibration modes from the 1st to the nth order. Here, j represents the order of the vibration mode. [U] is called a mode vector, is a function that connects a physical quantity and a mode quantity, and is a matrix having orthogonality. Further, q _j is a mode quantity indicating a horizontal direction response displacement in each vibration mode from the 1st to the nth order on the mode coordinate system.

When this equation (5) is applied to the equation (4), it becomes as follows.

[0051]

(Equation 8) Further, in order to orthogonalize the matrix in this mode coordinate system, the transposed matrix [U] ^T of the mode vector [U] is multiplied from the left side. As a result, the following equation is obtained.

[0052]

[Equation 9] [U] ^T [m] in the first term on the left side of the equation (6)
[U] and [U] ^T [k] [U] in the third term are
Due to the orthogonality of the eigenmodes, it is a diagonal matrix. Also, with respect to the second term, it can often be said that the damping coefficient c _i is also orthogonal because of the orthogonality of the mass m _i and the elastic coefficient k _i . In particular, in the case of Rayleigh type damping, a diagonal matrix is used. Become. However, although the second term is generally not a diagonal matrix and thus the analysis is complicated, a solution can be found.

If all the first to third terms of equation (6) are diagonal matrices, they can be written as the following equation.

[0054]

(Equation 10) Here, [M] = D _iag (M _j ) _{j = 1, n} , [K] = D
_iag (K _j ) _{j = 1, n} , [C] = D _iag (C _j ) _{j = 1, n} ,
It is.

Considering, for example, the damping by the TMD method or the like with respect to the equation (7), this damping method limits the vibration mode to be damped, and therefore the equation (7) If only the vibration mode to be damped is extracted from, and the mass position where the vibration damping device is installed is set to the i-th position (for example, the i-th floor of the structure), the force balance of the following equation Should be considered. In other words, when only one vibration mode is selected as the target vibration control, the mass point position to be controlled is considered,
It is better to select only specific vibration modes.

[0056]

[Equation 11] That is, in the equation (8), the j-th vibration mode of the vibration suppression target is extracted in the state converted to the mode coordinate system, where the first term on the left side is the mass M _{j of the} vibration suppression target (mode mass). ) Is multiplied by the horizontal response acceleration of the damping target, and the second term is the damping coefficient C _j (modal damping coefficient) of the damping target.
Is multiplied by the horizontal response speed of the object to be damped, and the third term is that the elastic coefficient K _j (modal elastic coefficient) of the object to be dampened is multiplied by the horizontal response displacement of the object to be dampened, and these are added together. , The vibration state in the j-th vibration mode to be damped is shown on the left side. On the other hand, the first term on the right side is the number of n mass points that make up the multi-mass system, and the state where each mass with mass m _i vibrates in the jth vibration mode is converted into the modal coordinate system. It is expressed as the sum of U _{i, j} m _i by using the used mode vector [U], and by multiplying this by the ground motion acceleration, the earthquake input is expressed. The second term on the right side is that the state in which the damping force from the damping device provided at the i-th mass point position is input corresponding to the j-th vibration mode uses the mode vector [U]. U _{i, j} F _i
It is represented as

Here, looking at the equation (8), the mode quantity and the physical quantity are mixed. In order to sort this out, with respect to the mode vector [U] of the equation (5), the i-th mass point position (i-th row of [U]) where the vibration damping device is installed is standardized to 1.0, and Only the j-th vibration mode at the i-th position is extracted. That is, in this case, the equation (5) is represented by the following equation (9).

[0058]

(Equation 12) According to the equation (9), by using, as the mode vector [U], the matrix in which the i-th row, which means the i-th mass point position where the vibration damping device is installed, is normalized to 1.0, It is understood that the actual response x _i in the physical coordinate system measured at the i-th mass point position is the superposition of the modal responses q _j of the vibration modes from the 1st to the nth order, which is as described above. Is. Further, since the mode vector [U] has orthogonality as described above, it is possible to multiply this matrix by any numerical value, and the i-th row is treated as 1.0 so that the formula can be simplified there. Good.

By applying the equation (9) to the equation (8), the damping force F _i of the vibration damping device coincides with the value of the physical coordinate system as the basis. At this time, the modal mass M _j , the modal damping coefficient C _j , and the modal elastic coefficient K _j in the equation (8).
Is in balance with the damping force and seismic input from the damping device in the physical coordinate system. In that sense, these values M _j ,
It can be said that C _j and K _j are the effective mass, the effective damping coefficient, and the effective elastic coefficient of the jth vibration mode.

Here, the vibration mode to be damped is, for example, j
In the case of the next vibration mode, when observing the content of the equation (8) with a waveform, it is complicated because all the vibration modes from the 1st to the nth order are included, but if this is analyzed by the frequency, The peak of a particular vibration mode can be found and can be treated separately. Therefore, if a band-pass filter is applied here, it is possible to take out by passing through the filter in the form of increasing the response component of the j-th order vibration mode to be obtained. As a result, regarding the j-th order vibration mode, the physical coordinate system on the left side of the equation (8) and the mode coordinate system on the right side coincide with each other. On the assumption that this is the case, the rewritten expression (8) is converted into the following expression (1
0).

[0061]

(Equation 13) Here, the subscript _fj indicates that the result is obtained by passing the jth-order natural vibration frequency (peak frequency) band through a bandpass filter. As described above, using the band-pass filter that passes the natural vibration frequency band in which the peak of the vibration mode of the j-th vibration mode of the vibration suppression target is passed, the vibration of the j-th vibration vibration target of the vibration suppression target is obtained from the physical response x _i detected by the detection means. Extract mode response. With the bandpass filter described above, only the response of the mass point position to be detected needs to be detected, so the sensor counts the number of mass points to be detected, that is, 1 if there is one mass point.
It is economical, and it is economical to use observations at multiple points to increase reliability. In this case, the force term on the right-hand side of equation (8) may be left as it is, but if a filter is used, the phase will rotate, so a bandpass filter is similarly applied to the observed component of the force term on the right-hand side. I am going to pass. Here, as can be seen by comparing the equations (1) and (10), the equation (1
0)

[Equation 14] Since there is no match with, the number of unknowns is 3 to 4. Then, in Equation (10), at least four times are sampled in time series.

(Equation 15) By solving the simultaneous equations using the detected values of

(Equation 16) Can be requested.

From this result, as in the case of the one mass system,
Optimizing the natural vibration characteristics of a period adjustment type or tuning type semi-active type vibration damping device that exerts a vibration damping effect by adjusting the natural vibration characteristics in real time from the occurrence of vibration to the end It becomes possible to adjust. This makes it possible for the natural vibration characteristics of the vibration damping device described above to follow changes in the vibration characteristics of the vibration damping target,
Even in the event of a large earthquake in which the elastic coefficient or damping coefficient of the damping target changes, the damping device can exert an effective damping effect.

Particularly in the case of creating a multi-element simultaneous equation in the case of a multi-mass system, it is preferable to create a multi-element simultaneous equation consisting of the balance of forces of two or more vibration equations at a plurality of times.

Obtaining an exact solution in this method will be further described. For example, in obtaining an exact solution for the jth-order vibration mode, the responses of all mass points to be damped are observed, and the modal response q _j in equation (8) is

[Equation 17] From the relationship,

(Equation 18) Ask for the solution.

Here, [G _{i, j} ] = [U _{i, j} ] ⁻¹ , where [U _{i, j} ] ⁻¹ is the inverse matrix of the mode vector [U] in equation (5). is there.

This equation gives the modal response q _{j of the} modal coordinate system.
Is represented by the response x _i of the physical coordinate system. At this time, all the physical responses x _i at each mass point position are used to obtain the mode response q _j . Therefore, in this method, it is necessary to observe the response at all mass point positions in the multi-mass system, and therefore, the sensors are installed at all mass point positions. This has the advantage that the accuracy of analysis can be increased, but the above-mentioned bandpass filter only needs to observe the response of the mass point position where the damping force is input, so the sensor can detect the number of mass points to be observed. That is, it can be said that the present method is uneconomical, as compared with the case where one mass point is sufficient and one is economical.

This method is a general method as a mode filter. This method does not require the use of the previous bandpass filter. For example, in the case of a low-rise structure, since it is easy to measure the response on all floors, the above exact solution can be obtained using a mode filter.
However, from the viewpoint of removing the observation noise, it is preferable to additionally use a bandpass filter that can pass the natural vibration frequency band in which the peak of the jth vibration mode of the vibration suppression target appears.

On the other hand, in the case of a high-rise / super-high-rise structure,
By using this mode filter to filter in the mode coordinate system and also using a bandpass filter, it is possible to eliminate the influence of modes that are close together in the frequency region that cannot be eliminated by the bandpass filter, and the solution reliability You can improve your sex.

By the way, as described above, when the mode filter is adopted, detection values detected at all mass point positions are necessary, and measurement of all floors in high-rise / super-high-rise structures, etc. is performed by installing a sensor, etc. In view of the above, and because of the problem of the computer's ability to perform calculations, it may not be economically feasible as described above. In such a case, it is recommended to use a low-dimensional multi-mass point system model represented by the mass point position to be observed in advance at the stage of Expression (4). A mode vector [U] is obtained based on this reduced model, that is, a reduced model, and the mode response q _j of the vibration suppression target is calculated from [G _{i, j} ] of its inverse matrix.
Similar to equation (13),

[Equation 19] Can be set up as In this method, since the dimension is reduced to the m-th order, the detected higher-order vibration mode is removed through the bandpass filter. On the other hand, a mode filter is applied to detection values that come close to each other in the low-order vibration mode. In this way, when the above bandpass filter and mode filter are used together, its vibration equation becomes

(Equation 20) Becomes This method uses a double filter to extract the modal response q _j , and has a great effect in removing influences other than the order of the vibration mode to be damped, and makes the reliability of the solution extremely high. Can be higher.

By these methods,

(Equation 21) Based on this result, the natural vibration characteristics of the vibration damping device
It is possible to make optimal adjustments in real time from the occurrence of vibration to the end. This makes it possible to make the natural vibration characteristics of the above-mentioned vibration damping device follow the changes in the vibration characteristics of the vibration suppression target, such as during a large earthquake when the elastic coefficient or damping coefficient of the vibration suppression target changes. However, it is possible to exert an effective vibration damping effect on the vibration damping device.

In the present method, when the vibration control target, for example, the mass, elastic modulus, damping coefficient of a building or civil engineering structure is changed by the influence of a large earthquake, etc. When damping with a semi-active type tuning type or vibration period adjustment type damping device that can change the elastic coefficient, the vibration characteristics of the damping device are adjusted by following the changes in the vibration characteristics of the damping target. It is possible to identify the mass, damping coefficient, and elastic coefficient of the object to be dampened so that optimum vibration damping can be performed.

That is, the response of the object to be damped, the ground motion, the damping force of the vibration damping device or the response of the object to be damped by it is observed, and the multidimensional simultaneous equations of the vibration equation are processed by a statistical method such as the least square method. The changing mass of the damping target,
Obtain solutions of damping coefficient and elastic coefficient.

As the filter, either a mode filter, a bandpass filter, or both are applied.

[0074]

As described above, according to the vibration damping method of the present invention, a periodic adjustment type or tuning type semi-active type vibration damping that exerts a damping effect by adjusting the natural vibration characteristic. The device is initially set according to the known data of the vibration damping target, and it is difficult to exert sufficient vibration damping performance when the vibration characteristics of the vibration damping target change due to this. With respect to the vibration device, it is possible to identify the values of the elastic coefficient and the damping coefficient of the vibration suppression target, which are changing every moment, from the values detected by the detection means. As a result, the natural vibration characteristic of the vibration damping device can be optimally adjusted in real time from the time when the vibration is generated until the vibration is terminated. At this time, the elastic coefficient and damping coefficient of the object to be damped can be identified instantaneously by a computing means such as a computer from a multi-dimensional simultaneous equation based on the vibration equation. This makes it possible to make the natural vibration characteristics of the above-mentioned vibration damping device follow the changes in the vibration characteristics of the vibration suppression target, such as during a large earthquake when the elastic coefficient or damping coefficient of the vibration suppression target changes. However, it is possible to exert an effective vibration damping effect on the vibration damping device.

As the unknown number of the vibration suppression target, its mass can be included if necessary, and even if the change in the mass of the vibration suppression target must also be taken into consideration, the present method can be applied. You can

If a statistical method is used in obtaining the solution of the simultaneous equations, it is possible to remove the influence of noise at the time of detection.

By modeling the vibration control target in the mass system,
The analysis work can be facilitated.

Among the detection values detected by the detection means, a bandpass filter for passing the detection values in the vicinity of the peak frequency of the vibration mode to be damped, and the detection values corresponding to the vibration mode to be damped among the detection values of the detection means are set. By using the mode filter that passes the detection noise, the detection value necessary for the analysis can be extracted while removing the observation noise, and the accuracy of the analysis work can be improved.

[Brief description of drawings]

FIG. 1 is an explanatory diagram for explaining that a vibration characteristic of a vibration suppression target changes.

FIG. 2 is a schematic view showing a vibration damping device by the TMD method.

FIG. 3 is a schematic diagram showing a vibration damping device according to the coupled vibration damping method.

FIG. 4 is a schematic view showing an example of a vibration damping device by a cable damping method.

FIG. 5 is a schematic view showing another example of the vibration damping device by the cable vibration damping method.

FIG. 6 is a schematic diagram showing a vibration suppression state of a vibration suppression target modeled as a one-mass system.

FIG. 7 is a schematic diagram showing a damping state of a damping target modeled in a multi-mass system.

FIG. 8 is an explanatory diagram for explaining a property of a mode vector [U].

[Explanation of symbols]

 50 vibration control target 60 vibration control device

Claims (6)

[Claims] 1. When a vibration control object such as a semi-active type TMD method, a joint vibration control method, a cable vibration control method or a vibration control apparatus of a vibration period adjusting type or a tuning type is used to control a vibration target, vibration is generated and the vibration is terminated. In order to adjust the natural vibration characteristics of the vibration damping device in response to the natural vibration characteristics of the vibration damping object that change from moment to moment, the vibration damping target and the vibration damping device are used. In the vibration equation of the vibration system consisting of, at least the elastic coefficient and the damping coefficient of the damping target are unknowns, and the vibration state of the vibration system is detected by the detecting means a plurality of times in the history, and is composed of two or more vibration equations. A vibration damping method characterized in that a multi-dimensional simultaneous equation is created, a solution of the unknown of the multi-dimensional simultaneous equation is obtained, and a vibration characteristic of the vibration suppression target is identified. 2. The vibration damping method according to claim 1, wherein the mass of the vibration damping target is also an unknown number. 3. The vibration damping method according to claim 1, wherein the simultaneous equations of multiple elements are analyzed by a statistical method such as a least square method. 4. The one-mass system or multi-mass system model of the damping object is modeled.
The damping method according to any one of item 3. 5. A detection value by the detection means for extracting a vibration mode to be suppressed from a plurality of vibration modes that can occur when the vibration suppression target is modeled as a multi-mass system model. 5. The vibration damping method according to claim 4, wherein a bandpass filter that allows detection values in the vicinity of the peak frequency of the vibration mode to be damped to pass through is applied, and the vibration equation is created for the result. . 6. A detection value by the detection means for extracting a vibration mode to be suppressed from a plurality of vibration modes that can occur when the vibration suppression target is modeled as a multi-mass system model. The vibration damping method according to claim 4 or 5, wherein a mode filter that allows a detection value corresponding to the vibration mode to be damped to pass through is applied, and the vibration equation is created for the result.