JP2008101769A - Vibration reduction mechanism and specification method thereof - Google Patents

Abstract

The present invention provides a vibration reduction mechanism capable of obtaining a sufficient stress reduction effect with a small mass using a rotary inertia mass, and a specification setting method thereof.
An additional spring that elastically supports the structure with respect to the support between the structure and the support that supports the structure, and a rotary inertia mass damper that generates a rotational inertial mass by the rotation of the rotating body. (Second rotational inertial mass damper) 10 is interposed in series, and the natural frequency determined by the rotational inertial mass and the additional spring is synchronized with the natural frequency of the structure. The additional damping 6 is installed in parallel with the rotary inertia mass damper or the additional spring. A first rotary inertia mass damper is added between the structure and the support to increase the period, and then the second rotary inertia mass damper is installed.
[Selection] Figure 1

Description

  The present invention relates to a vibration reduction mechanism for reducing vibration of a structure and a specification setting method thereof.

As a mechanism for reducing the vibration of a base-isolated building or equipment installation stand, for example, a so-called tuned mass damper (TMD) as shown in Patent Document 1 is known.
As shown in FIG. 10 as an outline of the vibration model, this is a structure 4 (supported to generate relative vibration via a spring 2 and a damping 3 with respect to a support 1 (ground, floor, etc.). An additional mass 7 is installed via an additional spring 5 and an additional damping 6 on a base-isolated building or equipment installation stand, and the natural (angular) frequency composed of the additional mass 7 and the additional spring 5 is set to the structure 4. The response in the vicinity of the resonance point of the structure 4 is reduced by tuning to the natural (angular) frequency.
According to this, not only vibration due to acceleration excitation input from the support 1 to the structure 4 such as an earthquake or traffic vibration, but also vibration due to an excitation force such as wind or mechanical vibration acting on the structure 4. Can also be effectively reduced.
JP-A 63-156171

In the conventional general TMD, it is necessary to increase the mass m ₂ of the additional mass 7 in order to obtain a large vibration reduction effect, but it is not realistic to add a very large mass m ₂ to the structure 4. Therefore, it is usually only about ₁ to 2% of the mass m ₁ of the structure 4, and therefore the vibration reducing effect is naturally limited.

  In view of the above circumstances, the present invention functions in principle in the same way as TMD, but a vibration reduction mechanism capable of obtaining a sufficient vibration reduction effect without requiring an excessive additional mass like conventional TMD, and its The purpose is to provide a specification setting method.

  The vibration reduction mechanism of the present invention includes an additional spring that elastically supports the structure with respect to the support between the structure and the support that supports the structure, and a rotation inertia mass that generates a rotation inertia mass by the rotation of the rotating body. A damper is interposed in series, and the natural frequency determined by the rotary inertia mass and the additional spring is synchronized with the natural frequency of the structure. The additional damping may be installed in parallel with the rotary inertia mass damper or the additional spring.

  The specification setting method of the vibration reduction mechanism of the present invention includes an additional spring that elastically supports the structure with respect to the support, and a rotating inertial mass by rotation of the rotating body between the structure and the support that supports the structure. The rotational inertial mass damper and the additional spring are connected in series, and the specifications of the rotational inertial mass damper and the additional spring are adjusted so that the natural frequency determined by the rotational inertial mass and the additional spring is synchronized with the natural frequency of the structure. It is characterized by setting.

  In another vibration reduction mechanism of the present invention, the first rotation inertia mass damper that generates a rotation inertia mass by the rotation of the rotating body is provided for the vibration system that supports the structure body by the support through the spring and the damping. By adding the vibration system in parallel with the spring, the vibration system is lengthened, and between the structure and the support, an additional spring that elastically supports the structure with respect to the support, and rotation of the rotating body A second rotational inertial mass damper that generates rotational inertial mass is interposed in series, and the natural frequency determined by the rotational inertial mass of the second rotational inertial mass damper and the additional spring is determined as the first rotational inertial mass damper. It is characterized in that it is tuned to the natural frequency of the vibration system that has been lengthened by the addition of. The additional damping may be installed in parallel with the second rotary inertia mass damper or the additional spring.

  Further, according to another specification setting method of the vibration reduction mechanism of the present invention, a first rotation that generates a rotational inertial mass by rotation of a rotating body is performed with respect to a vibration system in which a structure is supported by a support through a spring and damping. An additional spring that elastically supports the structure with respect to the support body between the structure body and the support body, while adding a inertial mass damper in parallel with the spring to lengthen the vibration system; A second rotational inertial mass damper that generates a rotational inertial mass by rotation of the rotating body is interposed in series, and the natural frequency determined by the rotational inertial mass of the second rotational inertial mass damper and the additional spring is set to the first frequency. The specifications of the first and second rotary inertia mass dampers and the additional spring are set so as to synchronize with the natural frequency of the vibration system that has been made long by adding the rotary inertia mass damper. .

  According to the present invention, a small lightweight rotary inertia mass damper (second rotary inertia mass damper) having a small mass rotating body instead of the additional mass in the conventional general TMD is installed between the structure and the support. This is equivalent to adding a large additional mass, and a large vibration reduction effect can be obtained. In particular, in the conventional TMD, the size of the additional mass is limited to about 1 to 2% of the mass of the structure, and the vibration reduction effect is naturally limited. Thus, a rotational inertial mass of 10 to 50% or more can be easily obtained without hindrance, and thereby a vibration reduction effect that is remarkably superior to that of the conventional general TMD can be obtained.

  In addition, by adding the first rotary inertia mass damper and installing the second rotary inertia mass damper as described above, the first rotary inertia mass damper can increase the period and reduce the response. The effect of reducing vibrations by the rotary inertia mass damper is synergistically obtained.

FIG. 1 is a diagram showing an outline of a vibration reduction mechanism according to a first embodiment of the present invention as a vibration model. This functions in principle in the same manner as in the case of the conventional TMD shown in FIG. 10, but the conventional general TMD adds an additional mass to the structure 4 via an additional spring 5 and an additional damping 6. 7 is added, in the present embodiment, the additional spring 5 and the rotary inertia mass damper 10 are interposed in series between the structure 4 and the support 1 supporting the structure 4. The main focus.
In addition, said rotary inertia mass damper 10 functions as a 2nd rotary mass damper in 2nd Embodiment mentioned later.

The rotary inertia mass damper 10 generates a large rotary inertia mass Ψ ₂ by operating when the structure 4 is relatively vibrated with respect to the support 1 and rotating a small mass rotary body (rotational inertia moment I _θ ). In this embodiment, the rotational inertial mass Ψ ₂ is replaced with the mass m ₂ of the additional mass 7 in the case of the conventional general TMD to reduce the vibration of the structure 4. It is used so as to be a control force.

となる。 That is, in this embodiment, the rotational inertial mass Ψ ₂ by the rotational inertial mass damper 10 is the relative displacement in the vibration direction when the rotational inertial mass damper 10 is actuated by the vibration of the structure 4, and the rotational body at that time The rotation angle is θ, and between those x and θ, x = αθ
When there is a relationship
Ψ ₂ = I _θ / α ²
The control force (displacement direction burden force) P for obtaining the vibration reduction effect is expressed as

It becomes.

である。 This means that the general spring multiplies the relative displacement by the spring constant to obtain the burden force, and in this embodiment, the relative acceleration is multiplied by the rotational inertia mass to obtain the burden force. This is very different from the case of using a normal spring in that it is multiplied by relative acceleration instead of displacement.
And since the magnitude | size of this rotational inertia mass (PSI) ₂ will be 10 to 1000 times with respect to the actual mass of a rotary body, it can obtain a very big rotational inertia mass only by rotating a small mass rotary body. Therefore, even with a small mass rotating body, a sufficient vibration reducing effect can be obtained.
Of course, the magnitude of the rotational inertia mass Ψ ₂ is determined by the mass of the rotating body, its radial dimension and the mass distribution in the radial direction. The larger the rotating body mass, the larger the radial dimension, Since the rotational inertial mass becomes larger as it is distributed in the outer peripheral portion than in the inner peripheral portion, a desired rotational inertial mass can be obtained by appropriately setting them.
For example, the rotational inertia moment I _θ of a disk with a radius r and a mass m is

It is.

As the rotary inertia mass damper 10, those used as a seismic isolation device in, for example, Japanese Patent No. 3250795 and Japanese Patent Application Laid-Open No. 2004-44748 are well known, and in this embodiment, as shown in them. A ball screw type rotary inertia mass damper can be suitably used, but the configuration of the rotary inertia mass damper is not particularly limited, and a desired type and characteristics may be arbitrarily adopted.
In the present embodiment, in addition to the rotary inertia mass damper 10, it is sufficient if it has an additional spring 5 and an additional damping 6 as in the conventional TMD. Generally, as in the model shown in FIG. These may be installed individually, but some general-purpose rotary inertia mass dampers 10 include a rotation mechanism and a damping mechanism incorporated in parallel as a model corresponding to the model shown in FIG. When adopting, it is sufficient to install an additional spring 5 in addition.

であるから、これを構造体４の固有角振動数ω_０

に同調するように設定することとする。 In the conventional general TMD, the natural (angular) frequency composed of the additional mass 7 and the additional spring 5 is tuned to the natural (angular) frequency of the structure 4. In this embodiment, the rotational inertia mass 10 And the natural (angular) frequency determined by the additional spring 5 are synchronized with the natural (angular) frequency of the structure 4.
That is, natural angular frequency omega ₂ defined by the rotational inertia mass [psi ₂ and the additional spring k ₂ is

Therefore, this is the natural angular frequency ω ₀ of the structure 4.

It shall be set to tune to.

Further, the additional damping 6 between the structure 4 and the support 1 is arranged in parallel to the rotary inertia mass damper 10 as shown in FIG. 1A, or as shown in FIG. 6 in parallel. In any case, substantially the same effect can be obtained as shown in the analysis result described later, but the optimum value of the additional spring k ₂ is slightly different even when the rotational inertia mass Ψ ₂ is the same. This is a ω ₂ ≠ ω ₀ is strictly an optimal design of a vibration system imparted with attenuation, general [psi ₂ is ω ₂ ≒ ω ₀ is much smaller range than m _1.

According to the vibration reduction mechanism of the present embodiment, a large additional mass (rotational inertia mass Ψ ₂ ) is added only by installing a small and lightweight rotary inertia mass damper 10 as compared with the additional mass 7 in the conventional general TMD. It is equivalent to this, and thereby a large vibration reduction effect can be obtained.
For example, in the conventional TMD, the limit is that the mass m ₂ of the additional mass 7 should be about ₁ to 2% of the mass m ₁ of the structure 4. In the embodiment, if necessary, a rotational inertia mass Ψ ₂ of 10 to 50% or more of the mass m ₁ of the structure 4 is given, and thereby a vibration reduction effect that is remarkably superior to that of the conventional general TMD. Obtainable.

In addition, since the response reduction effect does not depend on the amplitude in the vibration reduction mechanism of this embodiment, it can handle a wide range from fine vibration to large amplitude vibration, and tuning of the frequency is performed by adjusting the value of the spring constant k ₂ of the additional spring 5. It can be done easily.
Of course, as with conventional TMD, it is effective not only for vibrations caused by acceleration excitation input from the ground, such as earthquakes and traffic vibrations, but also for vibrations caused by the application of excitation forces such as wind and mechanical vibrations. Therefore, it is effective as a mechanism for supporting the entire building in isolation, and also as a vertical or horizontal vibration reducing mechanism applied to an isolation frame for installing a vibration isolator or the like. However, since the optimal spring and damping amount differ between acceleration (displacement) input due to earthquakes and the like and excitation force input due to winds, etc., it is necessary to set so that the desired damping can be obtained for the dominant external force. is there.

In the present embodiment, the load force of the rotary inertia mass damper 10 is equivalent to the inertia force of the additional mass 7 in the conventional TMD, and even if the substantial amount of the rotating body is small, it becomes a large inertia force. In designing the rotary inertia mass damper 10 and a joining member for installing the rotary inertia mass damper 10, it is necessary to allow for sufficient strength in consideration thereof.
Therefore, if necessary, a limiter may be applied to the load force of the additional spring 5 in order to prevent the excessive inertial force from acting on the rotary inertia mass damper 10 and damaging it. As a limiter mechanism for that purpose, for example, when the additional spring 5 receives a burden force exceeding an allowable limit, it is possible to yield, or to arrange a sliding mechanism in series with the additional spring 5. Further, when the relative acceleration acting on the rotary inertia mass damper 10 exceeds the allowable limit, the same limiter effect can be obtained even if the rotary inertia does not become excessive and the rotary inertia mass does not become excessive.

  The vibration reduction principle by the rotary inertia mass damper, the analysis method and the analysis result are shown below.

となる。
ここで、変位ｘが角振動数ωの正弦波振動であるとして
ｘ_ｊ＝ｘ_ｊｅ^ｉωｔ （ｊ＝０，１）
とし、構造体の固有角振動数をω_０とすると
ω_０ ^２＝ｋ_１／ｍ_１
であり、さらに減衰定数ｈ_１は
ｈ_１＝ｃ_１／（２ｍ_１ω_０）
であるから、

さらに、ξ＝ω／ω_０とおくと

となる。
この式で求まる｜ｘ_１／ｘ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率（変位、速度、加速度とも同じ）を示すものとなる。
図２（ｂ）はこのモデルにおいて減衰定数ｈ_１＝０．０２の場合の応答倍率を示すもので、これは加振振動数ωが構造体の固有振動数ω_０と一致する場合（ξ＝ω／ω_０＝１）に応答倍率が最大となる一般的な共振曲線を示すものである。この場合の応答倍率の最大値は１／（２ｈ_１）＝２５となる。 (I) When acceleration excitation is input (earthquake, traffic vibration, etc.)
(I) Basic model (see Fig. 2)
FIG. 2 (a) shows a vibration model of only a structure without a rotary inertia damper. In this model, the displacement excitation input x (t) at the fixed end is expressed as x (t) = x ₀ · e ^iωt
Assume, when viewed in the balance equation of the mass point of the stationary coordinate system (absolute displacement), as the excitation point displacement x ₀

It becomes.
Here, assuming that the displacement x is a sinusoidal vibration having an angular frequency ω, x _j = x _j e ^iωt (j = 0, 1)
And the natural angular frequency of the structure is ω ₀ , ω ₀ ² = k ₁ / m ₁
Further, the attenuation constant h ₁ is h ₁ = c ₁ / (2m ₁ ω ₀ ).
Because

Furthermore, if ξ = ω / ω ₀ ,

It becomes.
| X ₁ / x ₀ | (absolute value of complex number) obtained by this equation indicates the response magnification (same for displacement, velocity, and acceleration) of the structure with respect to the excitation input.
FIG. 2B shows the response magnification in the case of the damping constant h ₁ = 0.02 in this model. This is the case where the excitation frequency ω matches the natural frequency ω _{0 of the} structure (ξ = ω / ω ₀ = 1) shows a general resonance curve with a maximum response magnification. In this case, the maximum value of the response magnification is 1 / (2h ₁ ) = 25.

(Ii) When a rotary inertia mass damper is installed (1) (see Fig. 3)
A model shown in FIG. 3A is assumed as a model corresponding to FIG. This is obtained by adding a rotary inertia mass damper and an additional spring in series to the basic model of FIG. 2A and adding an additional damping in parallel to the rotary inertia mass damper.
Here, assuming that the rotational moment of inertia is I _θ , the displacement amount in the x direction relative to the unit rotation angle is α, the displacement of the structure is x ₁ , the displacement at the junction between the damper and the additional spring is x ₂ , and the mass balance equation When displayed with

上式で求まる｜ｘ_１／ｘ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率（変位、速度、加速度とも同じ）を示す。 ω ₀ ² = k ₁ / m ₁
h ₁ = c ₁ / (2m ₁ ω ₀ )
Ψ ₂ = I _θ / α ²
ω ₂ ² = k ₂ / Ψ ₂
h ₂ = c ₂ / (2Ψ ₂ ω ₂ )
ξ = ω / ω ₀
η = ω ₂ / ω ₀
After all,

| X ₁ / x ₀ | (absolute value of complex number) obtained by the above equation indicates the response magnification (same for displacement, velocity, and acceleration) of the structure with respect to the excitation input.

FIG. 3B shows that the rotational inertial mass is 0.01 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.01, and k ₂ / k ₁ = 0.0102, h ₂ = 0.07. In this case, the maximum response can be reduced by 62% in the vicinity of the resonance point. The actual mass of the rotating body is 1/100 or less of the rotational inertial mass, and therefore is 1/10000 or less with respect to the mass of the structure, and a large vibration reducing effect can be obtained with such a small mass of the rotating body. I understand that
FIG. 3C shows that the rotational inertial mass is 0.1 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.1, and k ₂ / k ₁ = 0.12, h ₂ = 0.2. In this case, the maximum response can be reduced by 85% in the vicinity of the resonance point. If the actual mass of the rotating body is 1/100 or less of the rotational inertial mass, the mass is 1/1000 or less with respect to the mass of the structure.
FIG. 3D shows a case where the rotational inertial mass is half of the mass of the structure, that is, Ψ ₂ / m ₁ = 0.5, and k ₂ / k ₁ = 2.5 and h ₂ = 1.0. In this case, the resonance phenomenon disappears and the response of the structure can be reduced by 94%. However, the amplitude is slightly increased in the high frequency range as compared with the case without the rotational inertial mass. Even in this case, the actual mass of the rotating body is 1/100 or less of the rotational inertial mass (less than 1/200 of the mass of the structure).

となり、応答倍率は

となる。
上式で求まる｜ｘ_１／ｘ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率を示す。 (Iii) When a rotary inertia mass damper is installed (2) (see FIG. 4)
A model shown in FIG. 4A is assumed as a model corresponding to FIG. This is obtained by adding an inertial inertia mass damper and an additional spring in series to the basic model of FIG. 2A and adding an additional damping in parallel to the additional spring.
In this case, the mass balance formula is

And the response magnification is

It becomes.
| X ₁ / x ₀ | (absolute value of complex number) obtained by the above equation indicates the response magnification of the structure with respect to the excitation input.

FIG. 4B shows that the rotational inertial mass is 0.01 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.01, and k ₂ / k ₁ = 0.0098, h ₂ = 0.07. In this case, the response magnification is shown, and the maximum response can be reduced by 62% in the vicinity of the resonance point.
FIG. 4 (c) shows that the rotational inertial mass is 0.1 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.1, and k ₂ / k ₁ = 0.085 and h2 = 0.2. The response magnification in the case is shown, and the maximum response can be reduced by 84% in the vicinity of the resonance point.
FIG. 4D shows a case where the rotational inertial mass is half the mass of the structure, that is, Ψ ₂ / m ₁ = 0.5, and k ₂ / k ₁ = 0.25 and h ₂ = 0.3. In this case, the resonance phenomenon no longer occurs and the response of the structure can be reduced by 92%. Also, unlike FIG. 3, the response in the high frequency range gradually decreases with the increase in the frequency.

となる。ここで、変位ｘが角振動数ωの正弦波振動であるとして
ｘ_ｊ＝ｘ_ｊｅ^ｉωｔ
とし、構造体の固有角振動数をω_０とすると
ω_０ ^２＝ｋ_１／ｍ_１
であり、さらに減衰定数ｈ_１は
ｈ_１＝ｃ_１／（２ｍ_１ω_０）
であるから、

さらに、ξ＝ω／ω_０とおくと

となる。
この式のｆ_０／ｋ_１は加振力の絶対値をバネで除した静的変位を意味している。
この式で求まる｜ｋ_１ｘ_１／ｆ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率（加振入力が静的に作用したときの変位に対する比）を示すものとなる。
図５（ｂ）はこのモデルにおいて減衰定数ｈ_１＝０．０２の場合の応答倍率を示すもので、これは加振振動数ωが構造体の固有振動数ω_０と一致する場合（ξ＝ω／ω_０＝１）に応答倍率が最大となる一般的な共振曲線を示すものである。この場合の応答倍率の最大値は１／（２ｈ_１）＝２５となる。 (II) When vibration input is applied to the structure (wind load, etc.)
(I) Basic model (see Fig. 5)
FIG. 5 shows a vibration model of the structure itself without the rotary inertia mass damper. In this model, the excitation input f (t) is expressed as f (t) = f ₀ · e ^iωt
Assuming that the balance point of the mass coordinate system (absolute displacement) is displayed,

It becomes. Here, assuming that the displacement x is a sinusoidal vibration with an angular frequency ω, x _j = x _j e ^iωt
And the natural angular frequency of the structure is ω ₀ , ω ₀ ² = k ₁ / m ₁
Further, the attenuation constant h ₁ is h ₁ = c ₁ / (2m ₁ ω ₀ ).
Because

Furthermore, if ξ = ω / ω ₀ ,

It becomes.
In this equation, f ₀ / k ₁ means a static displacement obtained by dividing the absolute value of the excitation force by a spring.
| K ₁ x ₁ / f ₀ | (absolute value of complex number) obtained by this equation indicates the response magnification of the structure with respect to the vibration input (ratio to displacement when the vibration input is applied statically). .
FIG. 5B shows the response magnification when the damping constant h ₁ = 0.02 in this model. This is the case where the excitation frequency ω matches the natural frequency ω _{0 of the} structure (ξ = ω / ω ₀ = 1) shows a general resonance curve with a maximum response magnification. In this case, the maximum value of the response magnification is 1 / (2h ₁ ) = 25.

(Ii) When a rotary inertia mass damper is installed (1) (see FIG. 6)
A model shown in FIG. 6A is assumed as a model corresponding to FIG. This is obtained by adding a rotary inertia mass damper and an additional spring in series to the basic model of FIG. 5A and adding an additional damping in parallel to the rotary inertia mass damper.
Here, assuming that the rotational moment of inertia is I _θ , the displacement amount in the x direction relative to the unit rotation angle is α, the displacement of the structure is x ₁ , the displacement at the junction between the damper and the additional spring is x ₂ , and the mass balance equation When displayed with

上式で求まる｜ｋ_１ｘ_１／ｆ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率を示す。 ω ₀ ² = k ₁ / m ₁
h ₁ = c ₁ / (2m ₁ ω ₀ )
Ψ ₂ = I _θ / α ²
ω ₂ ² = k ₂ / Ψ ₂
h ₂ = c ₂ / (2Ψ ₂ ω ₂ )
ξ = ω / ω ₀
η = ω ₂ / ω ₀
After all,

| K ₁ x ₁ / f ₀ | (absolute value of complex number) obtained by the above equation indicates the response magnification of the structure with respect to the vibration input.

FIG. 6B shows that the rotational inertial mass is 0.01 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.01, and k ₂ / k ₁ = 0.0101, h ₂ = 0.07. In this case, the response magnification is shown, and the maximum response can be reduced by 62% in the vicinity of the resonance point.
FIG. 6 (c) shows that the rotational inertial mass is 0.1 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.1, and k ₂ / k ₁ = 0.11 and h ₂ = 0.2. In this case, the response magnification is shown, and the maximum response can be reduced by 85% in the vicinity of the resonance point.
FIG. 6D shows a case where the rotational inertial mass is equal to the structure mass, that is, Ψ ₂ / m ₁ = 1.0, and k ₂ / k ₁ = 2.0 and h ₂ = 1.0. In this case, the resonance phenomenon disappears and the response of the structure can be reduced by 96%. This means that the displacement amplitude is less than or equal to the static displacement in all frequency regions. Even in this case, the substantial amount of the rotating body is 1/100 or less of the structure.

となり、応答倍率は

となる。 (Iii) When a rotary inertia mass damper is installed (2) (see FIG. 7)
A model shown in FIG. 7A is assumed as a model corresponding to FIG. This is obtained by adding an inertial inertia mass damper and an additional spring in series to the basic model of FIG. 5A and adding an additional damping in parallel to the additional spring.
In this case, the mass balance formula is

And the response magnification is

It becomes.

FIG. 7B shows that the rotational inertial mass is 0.01 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.01, and k ₂ / k ₁ = 0.0097, h ₂ = 0.07. In this case, the response magnification is shown, and the maximum response can be reduced by 62% in the vicinity of the resonance point.
FIG. 7 (c) shows that the rotational inertial mass is 0.1 times the mass of the structure, that is, Ψ ₂ / m ₁ = 0.1, and k ₂ / k ₁ = 0.081, h ₂ = 0.2. In this case, the response magnification is shown, and the maximum response can be reduced by 84% in the vicinity of the resonance point.
FIG. 7D shows a case where the rotational inertial mass is equal to the structure mass, that is, Ψ ₂ / m ₁ = 1.0, and k ₂ / k ₁ = 0.25 and h ₂ = 0.25. In this case, the resonance phenomenon disappears and the response of the structure can be reduced by 93%. In addition, there is a remarkable effect that the response does not become larger than the case where the rotational frequency is less than the resonance frequency.

であり、これはΨ_２＝ｍ_２とおくと上述した図７（ａ）に示したモデルの場合の釣り合い式（[数１７]）と同じであり、このことから図７（ａ）に示す振動低減機構は振動理論上から従来のＴＭＤ機構と全く同じものといえる。すなわち、図１０のｍ_２，ｋ_２，ｃ_２を図７のΨ_２，ｋ_２，ｃ_２とすれば同じ効果が得られるということで、従来のＴＭＤのように重い質量を構造物上に載せなくても、軽量な回転慣性質量ダンパーを支持体と構造物との間に付加バネと直列に設置するだけで良い。 In addition, when an excitation input acts on the conventional general TMD shown in FIG.

This is the same as the balance equation ([Equation 17]) in the case of the model shown in FIG. 7A described above when Ψ ₂ = m ₂ , and from this, it is shown in FIG. 7A. The vibration reduction mechanism can be said to be exactly the same as the conventional TMD mechanism in terms of vibration theory. In other words, that it to _{m 2,} k _{2, c} 2 in FIG. 10 is Ψ _{2, k 2, c 2} Tosureba same effect in Figure 7 is obtained, on the heavy weight structures like the conventional TMD Even if it is not mounted, it is only necessary to install a lightweight rotary inertia mass damper in series with the additional spring between the support and the structure.

The first embodiment has been described above. Next, the second embodiment will be described with reference to FIGS. In the second embodiment, a rotary inertia mass damper 20 is added between the support 1 and the structure 4 based on the first embodiment shown in FIG.
In the following description, the rotary inertia mass damper 20 added in the second embodiment is referred to as a “first rotary inertia mass damper”, and the rotary inertia mass damper installed in the same manner as in the first embodiment. 10 is distinguished as a “second rotational inertial mass damper”.

That is, in the present embodiment, the first rotary inertia mass damper 20 is added in parallel with the spring 2 to the vibration system in which the structure 4 is supported by the support 1 via the spring 2 and the damping 3. Thus, after the vibration system is lengthened, the second rotary inertia mass damper 10 and the additional spring 5 are installed in series as in the first embodiment. Then, the natural vibration of the vibration system in which the natural frequency determined by the rotational inertia mass Ψ ₂ by the second rotational inertia mass damper 10 and the additional spring 5 is lengthened by adding the first rotational inertia mass damper 20. Each item is set to be synchronized with the number.
Also in this embodiment, the additional damping 6 is installed in parallel with the second rotary inertia mass damper 10 as shown in FIG. 8 (a), or in parallel with the additional spring 5 as shown in (b). Just install it.

In this case, if the rotational inertia mass added by the first rotary inertia mass damper 20 to the mass m ₁ of the structure 4 is ψ ₁ , the natural frequency of the vibration system is (m ₁ by adding it. / (M ₁ + Ψ ₁ )) The period is increased by a factor of ^1/2, and an excellent response reduction effect can be obtained in the peripheral region of the natural frequency thus increased as in the first embodiment. Become.
Further, when the vibration is applied at the angular frequency ω = (k ₁ / Ψ ₁ ) ^1/2 determined by the spring 2 supporting the structure 4 and the first rotary inertia mass damper 20, the response is almost all. The vibration isolating effect of zero (transfer function becomes close to zero) can also be obtained.

Assuming that the model shown in FIG. 9A is a model corresponding to FIG. 8A, the structure displacement is x ₁ , the displacement at the joint between the damper and the additional spring is x ₂ , and the excitation point displacement x0. , When displaying the balance of mass points,

上式で求まる｜ｘ_１／ｘ_０｜（複素数の絶対値）が加振入力に対する構造体の応答倍率（変位、速度、加速度とも同じ）を示す。 ω ₀ ² = k ₁ / m ₁
h ₁ = c ₁ / (2m ₁ ω ₀ )
ω ₂ ² = k ₂ / Ψ ₂
h ₂ = c ₂ / (2Ψ ₂ ω ₂ )
ξ = ω / ω ₀
η = ω ₂ / ω ₀
After all,

| X ₁ / x ₀ | (absolute value of complex number) obtained by the above equation indicates the response magnification (same for displacement, velocity, and acceleration) of the structure with respect to the excitation input.

9 (b) is 0.5 times the rotational inertial mass [psi ₁ to the structure mass _{m 1} (i.e. _{Ψ 1 / m 1 = 0.5)} , 0.1 times the rotational inertial mass [psi ₂ (i.e. Ψ ₂ / m ₁ = 0.1), the damping constant h ₁ of the structure is 0.02, and the additional spring 5 indicates the response magnification in the case of 0.073 times that of the structure spring 2.
In this case, only by installing the first rotary inertia mass damper 20, the vibration reduction effect can be obtained only by about 20% at the frequency that is increased by adding the first rotary inertia mass damper 20. By installing the inertial mass damper 10 and synchronizing the frequency of the additional vibration system by the additional spring 5 and the rotational inertial mass Ψ ₂ with the natural frequency having a long period, the response in the solid frequency region is increased. It can be seen that the maximum response value can be reduced by 87%.
In this case, as shown in FIG. 9 (c) in which the vertical axis of FIG. 9 (b) is enlarged, the frequency region in which the response can be reduced is sufficiently wide. It can be seen that the response can be reduced, and in particular, at the above-mentioned cutoff frequency determined by the spring 2 and the first rotary inertia mass damper 20, the response magnification becomes almost zero. Although there is a region where the response increases, the range is narrow and the increase rate is small, so this is not a problem in practice.

As described above, according to the vibration reduction mechanism of the second embodiment, the effect of the long period by the first rotary inertia mass damper 20 and the vibration reduction effect by the second rotary inertia mass damper 10 are synergistic. In particular, the frequency range where response can be reduced is wide, the response and reaction force at each frequency in that range can be greatly reduced, and the mechanism is effective only in the resonance region with a long period of time. The response does not increase in the frequency range, and the response reduction effect does not depend on the amplitude.
Therefore, a sufficient response reduction effect can be obtained even with random vibration inputs such as earthquakes and traffic vibration inputs, and if applied to a base-isolated building, a wind fluctuation reduction effect can be obtained while increasing the period, which is extremely effective.
Of course, the frequency tuning operation for tuning to the desired resonance point can be easily and widely handled by adjusting the value of the additional spring as in the conventional TMD, and the change after installation can be done freely and easily. It can be carried out.

It is a model figure which shows the outline | summary of the vibration reduction mechanism which is 1st Embodiment of this invention. The analysis model and analysis results are shown. The analysis model and analysis results are shown. The analysis model and analysis results are shown. The analysis model and analysis results are shown. The analysis model and analysis results are shown. The analysis model and analysis results are shown. It is a model figure which shows the outline | summary of the vibration reduction mechanism which is 2nd Embodiment of this invention. The analysis model and analysis results are shown. It is a figure which shows the outline | summary of TMD which is a conventional general vibration reduction mechanism.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Support body 2 Spring 3 Damping 4 Structure 5 Additional spring 6 Additional damping 10 Rotation inertia mass damper (2nd rotation inertia mass damper)
20 rotary inertia mass damper (first rotary inertia mass damper)

Claims (8)

A mechanism for reducing vibration of a structure,
Between the structure and the support that supports it, an additional spring that elastically supports the structure with respect to the support and a rotary inertia mass damper that generates a rotational inertial mass due to the rotation of the rotating body are interposed in series. A vibration reduction mechanism characterized in that the natural frequency determined by the rotary inertia mass and the additional spring is synchronized with the natural frequency of the structure. The vibration reduction mechanism according to claim 1,
A vibration reduction mechanism characterized in that additional damping is installed in parallel with the rotary inertia mass damper. The vibration reduction mechanism according to claim 1,
A vibration reduction mechanism characterized in that an additional damping is installed in parallel with the additional spring. A specification setting method for a mechanism for reducing vibration of a structure,
Between the structure and the support that supports it, an additional spring that elastically supports the structure with respect to the support and a rotary inertia mass damper that generates a rotational inertial mass due to the rotation of the rotating body are interposed in series. Various characteristics of the vibration reduction mechanism characterized by setting the specifications of the rotary inertia mass damper and the additional spring so that the natural frequency determined by the rotary inertia mass and the additional spring is synchronized with the natural frequency of the structure. Original setting method. A mechanism for reducing vibration of a structure,
For a vibration system in which a structure is supported by a support through a spring and damping, a first rotation inertia mass damper that generates a rotation inertia mass by the rotation of the rotation body is added in parallel with the spring. With longer period,
Between the structure body and the support body, an additional spring that elastically supports the structure body with respect to the support body and a second rotary inertia mass damper that generates a rotation inertia mass by the rotation of the rotating body are interposed in series. The natural frequency determined by the rotational inertial mass of the second rotational inertial mass damper and the additional spring is tuned to the natural frequency of the vibration system having a long period due to the addition of the first rotational inertial mass damper. The vibration reduction mechanism characterized by becoming. The vibration reduction mechanism according to claim 5,
A vibration reduction mechanism characterized in that an additional damping is installed in parallel with the second rotary inertia mass damper. The vibration reduction mechanism according to claim 5,
A vibration reduction mechanism characterized in that an additional damping is installed in parallel with the additional spring. A specification setting method for a mechanism for reducing vibration of a structure,
For a vibration system in which a structure is supported by a support through a spring and damping, a first rotation inertia mass damper that generates a rotation inertia mass by the rotation of the rotation body is added in parallel with the spring. With longer period,
Between the structure body and the support body, an additional spring that elastically supports the structure body with respect to the support body and a second rotary inertia mass damper that generates a rotation inertia mass by the rotation of the rotating body are interposed in series. The natural frequency determined by the rotary inertia mass by the second rotary inertia mass damper and the additional spring is tuned to the natural frequency of the vibration system having a long period due to the addition of the first rotary inertia mass damper. And setting the specifications of the first and second rotary inertia mass dampers and the additional spring.

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