JPH0472094B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a vibration isolating device for controlling low frequency vibrations of structures such as buildings and elevated roads. In general, buildings and elevated roads are considered to be vibration systems with low damping and low natural frequencies.
It is known that vibrations at the natural frequency are excited by the application of external forces such as earthquakes and running vehicles, and that vibration levels increase due to resonance phenomena. This invention includes an actuator that adds an additional mass in the direction of vibration of a structure and generates a control force in the additional mass according to the vibration of the structure, and absorbs the vibration energy of the structure with the additional mass. , provides a vibration isolator that damps multiple natural vibrations of a structure. By the way, if a structure is considered as a vibration system with one degree of freedom and one natural frequency, it becomes a vibration model as shown in Fig. 1, and the equation of motion of the structure in this case can be considered as Equation (1). m ₁ x¨ ₁ +C ₀ x〓 ₁ +K ₁ x ₁ =F...(1) However, x ₁・x〓 ₁・x¨ ₁ : Vibration displacement, velocity, acceleration of the structure m ₁ : Mass of the structure C ₀ : 〃 Damping constant K ₁ : 〃 Spring constant F: External force Here, the vibration displacement x ₁ of the structure is normalized by the static displacement x _s (=F/K ₁ ) using the equation of motion shown in equation (1). Figure 2 shows the frequency characteristics expressed in the form of resonance magnification.
The horizontal axis shows the vibration frequency ω, and the vertical axis shows the resonance magnification x ₁ /x _s . As shown in Figure 2, such a vibration system with one degree of freedom has the same natural frequency ω of the structure.

It has a resonance characteristic with a peak at [Formula], and is known to vibrate sustainably at the natural frequency of the structure in response to a step-like external force, for example. Conventionally, as a countermeasure for suppressing vibrations of such a structure, an additional mass body is supported on the structure via a spring, and the resonant frequency of the spring and the additional mass body is matched to the natural frequency of the structure. Therefore, so-called dynamic vibration absorbers are known that suppress vibrations of structures. However, with this method, the damping effect can only be achieved in a narrow frequency range near the natural frequency of the structure as an external force, so there is a problem that a damping effect cannot be expected for multiple natural frequencies of the structure. . Conventionally, as a means to solve this problem, for example, the publication "JOINT AUTOMATIC
CONTROL CONFERENCE OF THE
AMERICAN AUTOMATIC COUNCIL”
(June 1973 The Institute Of Electrical and
"COMPARISON OF OPTIMIZED ACTIVE" published in Electronics Engineers, Inc.)
AND PASSIVE VIBRATION ABSORBER”
Active Vibration shown in Fig.3 on page 934 of
There is an absorber (vibration absorber). This vibration absorber installs vibration detectors on the building and the additional mass that vibrate in response to external forces, detects the vibration acceleration generated in the building and the additional mass, and then integrates each acceleration to determine the vibration velocity. get a signal,
In addition, the vibration velocity signal is integrated to obtain a vibration displacement signal, and the relative displacement is obtained from the vibration displacement of the building and the vibration displacement of the additional mass. control an actuator installed in a building based on four types of signals made through gains K ₁ to _{K 4} , each consisting of a vibration velocity signal and a relative displacement signal,
This damps the vibrations of the building by driving the additional mass. By the way, the above publication is about the optimization of vibration absorbers, and all feedback and constants are PI.
It is intended to be determined on the condition that the integral value called (Performance index) is minimized. This will be explained below. PI is shown in formula (9) on page 934 of the above publication. This is shown below. Here, the vibration displacement of the building is
x ₁ and the vibrational displacement of the additional mass body were x ₂ . PI=∫ ^∞ ₀ (x ₁₂ + ρ ² (x ₂ − x ₁ ) ² + ρ _u2 u ² )dt In the above equation, ρ and ρ _u are constants and are called weighting factors. In other words, the PI deals with the vibrational displacement of the building x ₁ , the relative displacement between the additional mass and the building (x ₂ - x ₁ ), and the control force u, but which of these three should be given more importance? Whether the design should be designed can be determined by arbitrarily selecting the sizes of the two parameters ρ and ρ _u . In other words, gains K ₁ , K ₂ , K ₃ , and K ₄ are selected such that the relative displacement (x ₂ − x ₁ ) decreases when ρ is increased, and the control force u decreases when ρ _u is increased. , and to reduce the vibration displacement x ₁ of the building, conversely, ρ and ρ _u should be reduced. However, when trying to specifically determine the gains K ₁ , K ₂ , K ₃ , and K ₄ in order to determine PI in this way, the motion of the vibration system from t = 0 to t = ∞ of the integral is There is a problem that it cannot be applied unless the external force is predicted in advance, and that the expected vibration damping effect cannot be obtained if the vibration system moves differently than expected. In addition, when trying to use an optimal control system using PI in actual hardware, all state quantities of the system to be controlled (in this example, the vibration displacement of the building,
There is a constraint that the vibrational displacement, velocity, and vibrational displacement of the additional mass body must all be known (free since each of these four is subject to feedback gains K ₁ to _{K 4} ). In this example, all of this is done by integrating the output of accelerometers attached to the building and the additional mass, but in reality,
In doing this, there are difficulties, such as how to provide an initial value when performing integration, and how to suppress integration errors that occur each time integration is performed. In addition, in this example, the building is simply expressed as a vibration system with one degree of freedom, but in the case of a vibration system with one degree of freedom, the independent variable of the vibration system is 2N + 2 (N is the number of degrees of freedom of the building, 1). Specifically, there are 2 independent variables for the building and 2 independent variables for the additional mass, for a total of 4 independent variables. Therefore, there are four variables to be observed for optimal control using PI, and since gains (K ₁ to K ₄ ) are added to each variable, four gains are also required. Therefore, when applying this example to a vibration system with multiple degrees of freedom, the total of the independent variables is, for example, 6, 8, when N is 2, 3, 4, 5...
10, 12, etc., and as the number of degrees of freedom N increases, the gain also increases, making it more difficult to apply to buildings with multiple natural frequencies. Although the above publication does not mention that the resonant frequency of the additional mass is set lower than the natural frequency of the building, in an optimal control system using PI,
For example, even if two parameters, gains K ₂ and K ₄ , are selected from the gains K ₁ to K ₄ , damping of a vibration system with multiple degrees of freedom that is difficult using four parameters can be simply reduced to K ₂ , _K4 , we cannot expect any vibration damping effect. The present invention was made to solve these problems, and aims to obtain a vibration reduction effect for a plurality of natural frequencies using a method that is easier to implement than the conventional method. The present invention will be explained in detail with reference to the figures below. Figure 3 shows that by adding an additional mass to a structure and applying a control force between the additional mass and the structure according to the vibration of the structure, the damping of the structure is increased and the vibration is reduced. This shows one embodiment of the vibration isolating device according to the present invention, which will be described below using a building as an example of a structure. In the figure, 1 is a building, 2 is an additional mass that moves freely in the vibration direction of the building, 3 is an accelerometer that detects the vibration acceleration of the building, 4 is a displacement meter that detects the relative displacement between the building and the additional mass, and 5 6 is a control device that receives signals from the accelerometer 3 and displacement meter 4 to drive the actuator, and 6 is a linear motor or the like that receives the output signal from the control device 5 and applies a control force between the additional mass body 2 and the building. This is a typical actuator. FIG. 4 shows an embodiment of the configuration of the control device shown in FIG. 3, in which 51 is an integrator that converts an acceleration signal into a speed signal, 52 is a speed signal amplifier, and 53 is an integrator for converting an acceleration signal into a speed signal.
54 is a displacement signal amplifier, 54 is an adder that adds the speed signal and the displacement signal, and 55 is a power amplifier that drives the actuator 6. In the vibration isolator of the present invention, when an external force F acts on the building 1 via wind or the ground, vibrations are excited in the building 1. The vibration acceleration of the building 1 is detected by the accelerometer 3, sent to the control device 5, and given to the actuator 6 via the integrator 51, speed signal amplifier 52, and power amplifier 55. The actuator 6 generates a control force between the additional mass body 2 and the building 1 that corresponds to the speed of the building, for example, a control force that is proportional to the speed of the building, and has the role of increasing vibration damping of the building 1. Furthermore, there is a displacement meter 4 between the building 1 and the additional mass body 2 that detects relative displacement, and this relative displacement signal is
Via the displacement signal amplifier 53 in the control device 5,
The signal is input to the adder 54, and similarly to the speed signal, the actuator 6 applies a control force corresponding to the relative displacement between the additional mass body 2 and the building 1, for example, a control force proportional to the relative displacement. In other words, by generating a control force proportional to the relative displacement, it is equivalent to installing a mechanical spring between the building 1 and the additional mass body 2, and by changing the gain of the displacement signal amplifier 53, an arbitrary spring can be generated. An electrical spring with a constant is constructed. Further, in the present invention, the resonance frequency of the additional mass body 2 determined from the spring constants of the additional mass body 2 and the electric spring is selected to be lower than the natural frequency of the building 1. FIG. 5 shows the configuration according to the present invention as a vibration model, and in the figure, m ₁ , K ₁ , and C ₀ represent the mass, spring constant, and damping constant of the building 1, respectively;
m ₂ is the mass of the additional mass body 2 , C ₂₀ is a damping constant represented by friction of the additional mass body 2 , and U is the control force acting between the building 1 and the additional mass body 2 . The equation of motion of the vibration model in FIG. 5 is given by the following equation. m ₁ x¨ ₁ +C ₀ x〓 ₁ +K ₁ x ₁ =F−U …(2) m ₂ x¨ ₂ +C ₂₀ (x〓 ₂ −x〓 ₁ )=U …(3) U=K _n (x ₁ − x ₂ ) + C _n x〓 ₁ ...(4) where, F: External force applied to the building x ₂ , x〓 ₂ , x¨ ₂ : Additional mass, velocity, acceleration _K Constant determined by the gain C _n : Constant determined by the gain of the speed signal amplifier As shown in equation (4), the control force U is determined by K _n (x ₁ - x ₂ ), which acts as an electric spring, and the building 1 It is expressed as the sum of two control forces, C _n・x〓 _1, which give damping to . When considering the control system of a vibration isolator, the frequency characteristics from the control force U of the actuator 6 to the vibration acceleration x¨1 of the building ₁ , and the frequency characteristics from the vibration acceleration x¨1 of the building ₁ to the control force U are the control system. This is an important factor for stability and vibration control effectiveness. Here, the frequency characteristics from the control force U to the vibration acceleration x ₁ indicate the characteristics of the building 1, and the frequency characteristics from the vibration acceleration x to the control force U indicate the characteristics of the vibration isolator. From equation (2), the transfer function Z _s (s) from the control force U to the vibration acceleration x ₁ is given by the following equation. Z _s (s) = X ₁ (s) / U (s) = s ² /m ₁ s ² +C ₀ s + K ₁ ...
...(5) where s: Laplace operator U(s): _Function obtained by Laplace transform of control force U X¨1 (s): Function obtained by Laplace transform of vibration acceleration x¨1 Also, (3), (4 ₎ ), the transfer function Z _c (s) from the vibration acceleration x¨ ₁ to the control force U is Z _c (s) = U (s) / X ₁ (s) = m ₂ (C _n s + K _n ) / m _2s ²
+C ₂₀ s + K _n ...(6) It is expressed as follows. FIG. 6 shows a control block diagram of the vibration isolator expressed by equations (2), (3), and (4). Now, when the transfer function Z _c (s) of equation (6) is set to be the control force U proportional to the vibration velocity x ₁ of the building 1, the transfer function C _M (s) of the control system is It is expressed by equation (7). C _M (s)=s・Z _c (s)=m ₂・s・(C _n s + K _n )/m ₂
s ² +C ₂₀ s+K _n =m ₂・s・{s/(K _n /C _n )+1}/1+
2ξ ₂₀ [s/ω ₂ ] + [s/ω ₂ ] ² ...(7) Here, ω ₂ : Resonance frequency of the additional mass

[Formula] ξ ₂₀ : Damping ratio of the additional mass body [=C ₂₀ /2m ₂ ω ₂ ] The Bode diagram of the transfer function C _M (s) in equation (7) is expressed as the seventh
As shown in the figure. As is clear from FIG. 7, the transfer function C _M (s) of the control system is determined by the vibration velocity _x〓 1 of the building 1 in the frequency range higher than the resonance frequency ω ₂ of the additional mass 2.
This gives a constant control gain C _n proportional to . In other words, the vibration isolator of the present invention achieves vibration isolation by setting the constant K _n determined by the gain of the displacement signal amplifier so that the resonant frequency ω ₂ of the additional mass body 2 is lower than the natural frequency ω of the building 1. The control force U output by the device acts as a damping force that reduces the vibration of the building 1 in proportion to the vibration velocity x ₁ of the building 1. Figure 8 shows the vibrational displacement x ₁ of the building 1 and the displacement x ₂ of the additional mass body 2 in the equations of motion shown in equations (2), (3), and (4), expressed as resonance magnification (static displacement x _s1 =F/ This is an example of frequency characteristics shown in the form of K ₁ , x _s2 = displacement normalized by F/K _n . In the figure, the horizontal axis is the vibration frequency ω, the solid line A curve is the resonance magnification of the building 1 (x ₁ / x _s1 ), and the dotted line B curve is the resonance magnification of the additional mass body 2 (x ₂ / x _s2 ). show.
By setting the resonant frequency ω ₂ of the additional mass body 2 to be lower than the natural frequency ω of the building 1, the resonance magnification of the building 1 is determined by the damping force C _n proportional to the vibration speed x〓 ₁ of the building 1.
It becomes lower because x〓 ₁ acts. Figure 9 is a diagram (frequency characteristic diagram of a multi-degree-of-freedom vibration model) showing an example of the effect of reducing the resonance magnification of building 1, which has multiple natural frequencies ω ^{( 1)} , ω ⁽²⁾ , and ω (3). can be,
In the figure, the solid line A curve shows an example of the resonance magnification of the building 1 without a vibration isolator, and the dotted line C curve shows an example of the resonance magnification of the building 1 when the vibration isolator of the present invention is added. Even in a building 1 that has multiple natural frequencies, by setting the resonant frequency ω ₂ of the additional mass body 2 lower than the lowest primary natural frequency ω ⁽¹⁾ of the building 1,
Conventionally, it is possible to simultaneously reduce the vibrations of a building 1 having a plurality of natural frequencies without increasing the number of gains according to the number of degrees of freedom of the building. As described above, this invention selects two gains, K _n and C _n , and adjusts the resonance frequency of the additional mass body 2 determined from the spring constant K _n of the additional mass body 2 and the electric spring to the characteristic characteristic of the building 1. By setting a value lower than the vibration frequency, there is no need to predict the motion of the vibration system in advance, including external forces, and this method is simpler than conventional methods, making it possible to control buildings for multiple natural frequencies, which was difficult to achieve in the past. This makes it possible to implement a vibration means. In the embodiments of this invention, a building is used as an example of a structure. Although the example has been explained, it is clear that the present invention can also be applied to vibration isolators for two or more vibration directions by providing similar vibration isolators on the axes in other vibration directions.

[Brief explanation of the drawing]

Figure 1 is a diagram showing a structure as a vibration model with one degree of freedom, Figure 2 is a diagram showing the frequency characteristics of the vibration model with one degree of freedom, and Figures 3 and 4 are configurations of embodiments of the present invention. , FIG. 5 is a diagram showing the present invention as a vibration model, FIG. 6 is a control block diagram of the vibration isolator of the present invention, FIG. 7 is a Bode diagram of the transfer function C _M (s), and FIG. Figure 8 is a frequency characteristic diagram of the one-degree-of-freedom vibration model of this invention, and Figure 9 is a frequency characteristic diagram of a multi-degree-of-freedom vibration model.
is an additional mass body, 3 is an accelerometer, 4 is a displacement meter, 5 is a control device, 6 is an actuator, 51 is an integrator,
52 is a speed signal amplifier, 53 is a displacement signal amplifier,
54 is an adder, and 55 is a power amplifier. Note that the same or corresponding parts in the figures are indicated by the same reference numerals.

Claims (1)

[Claims] 1. Vibration detection means for detecting the vibration of a structure that vibrates in response to an external force, an additional mass installed in the structure and moving in the vibration direction of the structure, and relative displacement between the structure and the additional mass. and a control force corresponding to the vibration velocity occurring in the structure and a control force corresponding to the relative displacement between the structure and the additional mass between the structure and the additional mass. an actuator to be applied, a control force corresponding to the vibration velocity generated in the structure in response to an output signal from the vibration detection means, and a control force corresponding to the vibration velocity generated in the structure in response to an output signal from the relative displacement detection means; a control device that controls the actuator to generate a control force corresponding to the displacement between the structure and the additional mass, and a control device that controls the actuator to generate a control force corresponding to the relative displacement between the structure and the additional mass. an electric spring that supports the additional mass by acting between them, and setting the resonant frequency of the additional mass supported by the electric spring to be lower than the natural frequency of the structure. Features a vibration isolator.