JP5190652B2 - Vibration reduction mechanism and specification method thereof - Google Patents

Description

  The present invention relates to a vibration reduction mechanism for reducing vibration of a structure such as a high-rise building where bending deformation is dominant, and a specification setting method thereof.

In order to suppress the vibration of a structure such as a tower-like high-rise building where bending deformation is dominant, as shown in Patent Document 1, for example, a so-called Tuned Mass Damper is provided at the top of the structure. : TMD) is known. This reduces the response near the resonance point of the structure by connecting the additional mass to the structure via an additional spring and tuning the natural frequency determined by the additional spring and the additional mass to the natural frequency of the structure. It is to let you.
Further, in Patent Document 2, a structure is configured by a core (main structure) and an outer peripheral frame (or outer peripheral wall), and a top girder is provided so as to project over the top of any one of the core, By installing a vibration control device between the outer frame and the outer frame via a top girder, a bending deformation control type vibration control structure that operates the vibration control device to attenuate the vibration when the core is bent and deformed. I have a suggestion.
JP-A 63-156171 Japanese Unexamined Patent Publication No. 7-26786

The conventional general TMD as shown in Patent Document 1 needs to increase the additional mass in order to obtain a sufficient vibration reduction effect, which inevitably becomes large and heavy, It is not preferable to add too much mass, and the larger the TMD, the greater the restrictions on the installation position and installation space. Therefore, the added mass should normally be about 1-2% of the total mass of the structure. Therefore, the vibration reducing effect is naturally limited.
Moreover, in the bending deformation control type damping structure shown in Patent Document 2, the vibration reduction effect is limited and small for giving a large damping because the bending back of the top portion is used.

  In view of the above circumstances, the present invention provides an effective vibration reduction mechanism and its specification setting method that do not require an excessive additional mass like conventional TMD and can dramatically improve the vibration reduction effect. The purpose is to do.

The vibration reduction mechanism and its specification setting method according to the present invention are intended for structures such as high-rise buildings where bending deformation is outstanding, and around the main structure in the structure to be reduced in vibration. A rigid member that protrudes is provided integrally with the main structure, and an axial force member that is independent of the main structure is provided around the main structure to fix one end thereof, and the shaft Between the other end of the force member and the rigid member, a rotational inertia mass damper is provided that generates a rotational inertia mass by rotating the weight when the bending deformation of the main structure is transmitted through the rigid member. In order to synchronize the natural frequency determined by the rotational inertia mass generated by the rotational inertia mass damper and the axial rigidity of the axial force member with the natural frequency of the main structure, the axial rigidity of the axial force member is changed to the rotational inertia. The mass inertia of the mass damper Is the value which was set to be substantially matched to the square of intrinsic primary angular frequency of the main structure.
In the present invention, if necessary, an additional spring for adjusting the axial rigidity of the axial force member may be installed in series with the axial force member.

According to the present invention, the following remarkable effects can be obtained.
Resonance characteristics of the main structure can be sufficiently improved simply by adding a rotary inertia mass damper in series with the axial force member while providing a rigid member to the main structure in a structure with excellent bending deformation. A significant response reduction effect can be obtained, and vibrations can be effectively suppressed against disturbances such as wind and traffic vibrations as well as seismic motion, contributing to improved comfort.
In order to synchronize the frequency determined by the rotary inertia mass and the axial stiffness of the axial force member with the natural frequency of the main structure, the value obtained by dividing the axial stiffness of the axial force member by the rotary inertia mass of the rotary inertia mass damper is the main structure. By substantially matching the square of the natural primary angular frequency of the body, the response of the structure can be greatly reduced. Further, the damper reaction force and the reaction force of the axial force member do not increase even in a high vibration region.
A rotary inertia mass damper can obtain a rotary inertia mass of 10 to 500 times the mass of an actual weight. Therefore, even a small, lightweight and small capacity rotary inertia mass damper with a small mass weight has a large mass such as TMD. Performance equivalent to or better than other vibration reduction mechanisms can be obtained, which is advantageous in terms of cost and installation space.
By installing additional springs in series with the axial force member as necessary, the overall axial rigidity can be set optimally and easily, and frequency tuning can be performed reliably and accurately.

One embodiment of the vibration reducing mechanism of the present invention is shown in FIG.
The present embodiment is an application example to a tower-like high-rise building where bending deformation is dominant, and FIG. 1A is an overall schematic diagram, and FIG. 1B is a vibration model thereof.
A high-rise building as a vibration reduction target structure in the present embodiment is structurally provided integrally with the main structure 1 in a form in which the main structure 1 that constitutes the core portion and the top part of the structure jump out to the periphery. A rigid member 2 and an axial force member 3 that stands up structurally independently around the main structure 1 and constitutes an outer peripheral frame. The upper end portion of the axial force member 3 and the rigid member The main purpose is that a rotary inertia mass damper 4 is interposed between the two tip portions.
This is basically the same structure as the bending deformation control type damping structure shown in Patent Document 2, and the main structure 1, the rigid member 2, the axial force member 3, and the rotation in this embodiment. The inertia mass damper 4 corresponds to the core, the top girder, the outer peripheral frame (or outer peripheral wall), and the vibration control device in the vibration control structure disclosed in Patent Document 2, respectively.

  However, the vibration control device in the conventional vibration control structure is a simple damper such as an oil damper, whereas the rotary inertia mass damper 4 in the present embodiment is a member whose bending deformation of the main structure 1 is a rigid member. By being transmitted as an axial force through the rotation of 2, the weight rotates to generate a desired rotational inertial mass.

上式は、一般的なバネが相対変位にバネ定数を乗じて負担力とするのと同様に、相対加速度に回転慣性質量を乗じて負担力とすることを意味しており、相対変位ではなく相対加速度を乗じる点で通常のバネによる場合と大きく異なるものである。 That is, the rotary inertia mass damper 4 used in the present embodiment receives a force that is deformed in the axial direction (vertical direction) by the rotation of the rigid member 2 in the vertical plane accompanying the bending deformation of the main structure 1. A configuration in which a mass with a small mass rotates in a horizontal plane, and a vibration reducing effect is obtained by using the moment of inertia generated in the weight due to the rotational moment of inertia and angular acceleration of the weight as a control force. belongs to.
Specifically, the relative displacement in the force (vibration) direction generated in the rotary inertia mass damper 4 is x, and the rotation angle of the weight at that time is φ, and between these relative displacement x and the rotation angle φ, x = When there is a relationship of αφ, ignoring the rotation loss due to friction or the like, the inertia force (control force) P in the displacement direction of the rotary inertia mass damper 4 is expressed by the following equation.

The above equation means that the general spring multiplies the relative displacement by the spring constant to make the burden force, which means that the relative acceleration is multiplied by the rotational inertia mass to make the burden force. This is very different from the case of using a normal spring in that it is multiplied by relative acceleration.

The magnitude of the rotational inertia mass Ψ generated by the rotary inertia mass damper 4 as described above is 10 to 500 times as large as the actual mass of the rotating weight. Therefore, only by rotating the small mass weight. An extremely large inertial rotating mass Ψ can be obtained. Therefore, even if the weight is small, a sufficient control force, that is, a sufficient vibration reducing effect can be obtained.
Moreover, the magnitude of the rotational inertia mass Ψ is determined not only by the mass of the weight but also by its diameter and radial mass distribution. The larger the weight, the larger the diameter, Since the rotational inertial mass Ψ increases as it is distributed in the outer peripheral part rather than the peripheral part, the rotational inertial mass Ψ can be set to a desired size by appropriately setting them, and the desired vibration reduction effect Can be obtained.

  In addition, as this kind of rotary inertia mass damper, what is used as a seismic isolation device is known, for example in patent 3250795 and Unexamined-Japanese-Patent No. 2004-44748, and is shown in them in this embodiment. Such a ball screw type rotational inertial mass damper can be suitably employed, but the configuration of the rotational inertial mass damper 4 is not particularly limited, and a desired type and characteristics can be arbitrarily employed.

In the present invention, after using such a rotary inertia mass damper 4, the rotary inertia mass Ψ generated by the rotary inertia mass damper 4 and the axial rigidity k _v of the axial force member 3 (addition spring 5 as will be described later). The gist is to set the specifications so that the natural frequency determined by the natural rigidity of the main structure 1 is synchronized with the natural frequency of the main structure 1 when the spring is installed.
That is, in general, the natural angular frequency ω in the vibration system with the mass m and the spring k is ω ² = k / m
In the vibration system composed of the rotary inertia mass damper 4 and the axial force member 3 as in the present invention, the natural angular frequency ω ₀ is equal to the rotational inertia mass Ψ and the axial rigidity of the axial force member. From k _v ω ₀ ² = k _v / Ψ
It is determined by the relationship. Therefore, if the natural angular frequency ω ₀ is substantially matched with the natural primary angular frequency ω ₁ of the main structure 1, that is, ω ₀ ² = k _v / Ψ≈ω ₁ ^2.
If the values of Ψ and k _v are set so that the relationship of is established, the response of the main structure 1 to the vibration of the natural first mode can be greatly reduced.

The shaft stiffness k _v The above may be used as it is axial stiffness k _c of the axial force member 3 itself, axial force member as shown in FIG. 1 (b) in order to adjust its axial stiffness k _v may an appropriate additional spring 5 to 3 strategic points so as to incorporate in series, whereby the axial force member 3 can set the overall axial stiffness k _v a whole more easily and reliably. Overall axial stiffness k _v axial force member 3 in case of adding such an additional spring 5 is given by the following equation.

Further, as shown in FIG. 1B, this vibration reduction mechanism also requires an additional damping 6, and the additional damping 6 may be installed in parallel with the rotary inertia mass damper 4 as in the illustrated example. Alternatively, when the additional spring 5 is installed, it may be installed in parallel therewith. Alternatively, a rotary inertia mass damper 4 may be used in which additional damping is incorporated in parallel and integrated, and in that case, it is not necessary to install any other additional damping. In any case, the natural angular frequency ω of the vibration reducing mechanism does not exactly match the natural primary angular frequency ω ₁ of the main structure 1 due to such additional damping 6, but substantially. Can be almost equivalent.

  In addition, although it is preferable to provide the rigid member 2 in this embodiment so that it may protrude horizontally from the top part of the main structure 1, it is not restricted to it, and it may also be protruded from the intermediate part of the main structure 1. It is good, and it is not limited to the horizontal, but may be slanted upward or obliquely downward. Further, the fixed end of the axial force member 3 may not be a fixed point such as a foundation, and may be a place where deformation is small, such as a low-layer part of a structure. Further, the rigid member 2 may be provided in multiple stages in the intermediate portion of the main structure 1, and in that case, the axial force member 3 and the rotary inertia mass damper 4 are provided between the fixed end and the rigid member 2 at each stage. Just do it.

As described above, the vibration reduction mechanism of the present embodiment has an additional vibration system including the axial force member 3 and the rotary inertia mass damper 4 with respect to the main vibration system including the tower-like main structure 1 and the rigid member 2. In addition, the axial rigidity k _v of the axial force member 3 is made to tune the rotational inertia mass of the rotary inertia mass damper 4 in order to synchronize the natural angular frequency ω of the additional vibration system with the natural primary angular frequency ω ₁ of the main vibration system. By making the value divided by Ψ substantially equal to the square of the natural primary frequency ω ₁ of the main structure, the resonance characteristics and response to bending vibration of the main vibration system (ie, main structure 1) can be effectively improved. A great vibration reduction effect can be obtained.

In this regard, in contrast to the conventional bending deformation control type damping structure shown in Patent Document 2, the conventional damping structure is resistant to bending deformation of the core by the additional vibration system by the outer peripheral frame and the damping device. Although it is the same as the present invention in that the vibration reduction effect is obtained, the vibration control device is merely a simple damper such as an oil damper. Therefore, the vibration control device is merely operated in the entire frequency range. Thus, neither tuning with the main vibration system as in the present invention is possible, nor is it possible to obtain excellent resonance characteristic improvement effect or response reduction effect as in the present invention.
In addition, in the above conventional vibration control structure, the axial deformation of the outer peripheral frame or the outer peripheral wall corresponding to the axial force member 3 in the present invention is only a loss that reduces the vibration control effect, so that they have sufficiently high axial rigidity. it is necessary to, but to in the present invention is to effectively use the overall shaft stiffness k _v properly set to the frequency tuning of the axial force member 3, the axial force member 3 optionally itself the additional spring 5 installed so as to complement the axial stiffness k _c of can adjust the overall axial stiffness k _v optimally, thereby structurally quite reasonable because the optimum can easily be performed frequency tuning It is.

  In contrast to the conventional general TMD, the conventional general TMD is common to the present invention in that the frequency tuning is performed by the additional vibration system. However, as described above, the conventional general TMD has sufficient vibration. In order to obtain a reduction effect, there is a difficulty in that a large additional mass is required, but in the present invention, by using the rotary inertia mass damper 4 configured to rotate a small mass weight, the weight is 10 to 500. Since a rotational inertia mass as much as twice as large can be obtained, a vibration inertia effect equivalent to or higher than that of a rotational inertia mass damper 4 that is much smaller and lighter than that of a conventional general TMD can be obtained. In other words, if an effect equivalent to that of the present invention is to be obtained by a conventional general TMD, the additional mass required for it becomes extremely large, which is not realistic.

Hereinafter, an analysis method for confirming the effect of the vibration reduction mechanism of the present embodiment and the result thereof will be described in detail with reference to FIG.
In the vibration model shown in FIG. 1B, the bending rigidity EI of the main structure 1, its equivalent mass m, the rotational moment of inertia I _θ , the total axial rigidity k _{v of} the axial force member 3, the axial force member 3 itself The axial stiffness k _c , the additional spring k ₀ , the rotational inertia mass Ψ by the rotary inertia mass damper 4, and the additional damping c ₀ (installed in parallel with the rotary inertia mass damper 4). Further, the total height H of the structure is a distance b between the main structure 1 and the axial force member 3. The main structure 1 (specifically, the core portion) bears all the shearing force, and the axial force member 3 (specifically, the outer peripheral frame) bears only the axial force.

The horizontal displacement of the top mass x, as the rotation angle theta, the shear forces acting on the structure Q, the following equation holds when the bending moment and M ₁ to bear at the top of the main structure 1.

When the horizontal displacement x ₀ of the fixed end of the leg portion of the main structure 1 and the damping coefficient of the main structure 1 are C, the vibration equation is expressed by the following equation (1). Here, Z _k is a series spring of the axial rigidity k _v of the rotary inertia mass damper 4 and the axial force member 3.

Assuming that the displacement x and the rotation angle θ are sinusoidal vibrations at an angular frequency ω, the top response displacement with respect to the excitation point displacement x ₀ using x _j = x _j e ^iωt and θ = θe ^iωt (j = 0, 1). The ratio of x (response magnification) is expressed by the following equation (2).

From equation (2) above

By substituting this into equation (1), equation (3) is obtained.

Therefore, the response magnification (￣x) = x / x ₀ is obtained by the following equation (4). In addition, (を x) represents that a ￣ (bar) is added to the upper part of x (hereinafter, the same applies to other symbols).

とすると、応答倍率は次の（５）式あるいは（６）式により求められる。なお、これらの式は複素数表示しているので、（￣ｘ）の絶対値が応答倍率となる。 Here, to simplify the study, the rotational moment of inertia of the structure is ignored, and I _θ = 0,
Let ω ₁ ² = 3EI / (mH ³ ). Note that ω ₁ is the natural primary angular frequency of the structure when the bending back effect of the rigid member 2 is ignored.
The damping constant h = c / (2 mω ₁ ) of the structure against this. Also, for the additional vibration system

Then, the response magnification is obtained by the following equation (5) or (6). Since these expressions are expressed in complex numbers, the absolute value of (￣x) is the response magnification.

Next, for comparison, a case where only the additional attenuation is added without installing the rotary inertia mass damper 4 will be considered. In order to simplify the examination, ignoring the axial expansion and contraction of the axial force member 3 and the bending deformation of the rigid member 2, in equation (5), Ψ = 0, k _v → ∞, and addition to the primary mode of the structure When the attenuation constant of attenuation is set to h ₀₁ = c ₀ / (2 mω ₁ ), the response magnification when the rotary inertia mass damper 4 is not used is obtained by the following equation.

On the other hand, the burden force P of the rotational inertia mass damper 4 is determined by the following equation from the theta top rotation angle ignoring I _theta.

Further, assuming that (￣b) = b / H, the damper reaction force magnification with respect to the excitation force mx ₀ ω ₁ ² is obtained by the equation (7).

となる。 Since this expression is expressed as a complex number, this absolute value is the reaction force magnification.
In addition, when only the additional damping is not used without using the rotary inertia mass damper 4, Ψ = 0, k _v → ∞ in the equation (7)

It becomes.

In the above description, b / H = 0.1 for the main system, structural damping h = 0.02, Ψ / m = 0.2 for the additional damping system, (￣ω ₀ ) = ω ₀ / ω ₁ = 1. 01, additional attenuation h ₀ = c ₀ / (2Ψω ₀ ) = 0.07 (this corresponds to h ₀₁ = c ₀ / (2mω ₁ ) = (￣Ψ) (￣ω ₀ ) h ₀ = 0.014 2), the top response magnification (ratio of the top response to the excitation amplitude) in that case is shown in FIG. 2, and the damper reaction force magnification (which is also a burden force of the axial force member 3) is shown in FIG. .
In addition, FIGS. 2 to 3 also show a case in which only a damping is used without using a rotary inertia mass damper for comparison, but this uses a rotary inertia mass damper 4 with a top response magnification. This is a case where attenuation h ₀₁ = 0.7 so as to be equivalent to the above case.

From the above examination, it can be seen that the top response can be reduced by about 60% by using the rotary inertia mass damper 4 as shown in FIG. 2 as compared with the case where it is not used. In order to obtain a response reduction effect equivalent to this only by attenuation, it is necessary to increase the attenuation h ₀₁ by 50 times (= 0.7 / 0.014). For that purpose, an extremely large capacity oil damper is required. I understand that I need it.
Further, as shown in FIG. 3, the damper reaction force (the sum of the rotational inertial mass and the damping) at the resonance frequency is equivalent to the case where only the damping is applied even when the rotating inertial mass damper 4 is used. However, the damper hardly bears the reaction force except in the vicinity of the resonance point, whereas in the latter, the burden force of the damper increases as the vibration frequency increases. Therefore, in the case of excitation having various frequency components such as an earthquake, the reaction force acting on the damper and the axial force member becomes smaller in the present invention, and a more rational design can be achieved.

It is the conceptual diagram and vibration model of the vibration reduction mechanism which are embodiment of this invention. It is a figure which shows the analysis result about a response magnification similarly. It is a figure which shows the analysis result about reaction force magnification.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Main structure 2 Rigid member 3 Axial force member 4 Rotary inertia mass damper 5 Additional spring 6 Additional damping

Claims (4)

A vibration reduction mechanism for structures such as high-rise buildings where bending deformation is outstanding,
A rigid member that jumps out around the main structure in the vibration reduction target structure is provided integrally with the main structure,
Around the main structure, an axial force member independent of the main structure is juxtaposed to fix one end thereof, and between the other end of the axial force member and the rigid member. In addition, a rotation inertia mass damper that generates a rotation inertia mass by rotating the weight by transmitting the bending deformation of the main structure through the rigid member,
In order to synchronize the natural frequency determined by the rotational inertial mass generated by the rotational inertial mass damper and the axial stiffness of the axial force member with the natural frequency of the main structure, the axial stiffness of the axial force member is set to the rotational inertial mass. A vibration reduction mechanism characterized in that a value obtained by dividing a damper's rotational inertial mass substantially coincides with the square of the natural primary angular frequency of the main structure . The vibration reduction mechanism according to claim 1,
A vibration reduction mechanism characterized in that an additional spring for adjusting the axial rigidity of the axial force member is installed in series with the axial force member. A specification setting method of a vibration reduction mechanism for a structure such as a high-rise building where bending deformation is outstanding,
A rigid member that jumps out around the main structure in the vibration reduction target structure is provided integrally with the main structure,
Around the main structure, an axial force member independent of the main structure is juxtaposed to fix one end thereof, and between the other end of the axial force member and the rigid member. In addition, a rotation inertia mass damper that generates a rotation inertia mass by rotating the weight by transmitting the bending deformation of the main structure through the rigid member,
In order to synchronize the natural frequency determined by the rotational inertial mass generated by the rotational inertial mass damper and the axial stiffness of the axial force member with the natural frequency of the main structure, the axial stiffness of the axial force member is set to the rotational inertial mass. Vibrations characterized by setting the specifications of the rotary inertia mass damper and the axial force member so that the value divided by the rotary inertia mass of the damper substantially matches the square of the natural primary angular frequency of the main structure. Specification method for reduction mechanism. A specification setting method for a vibration reduction mechanism according to claim 3,
A specification setting method for a vibration reduction mechanism, wherein the axial rigidity of the entire axial force member is adjusted by installing an additional spring in series with the axial force member.

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