JP4392700B2 - Method for suppressing vibration of plate-like body - Google Patents

Description

【００１１】
図４の拡大系の最悪ゲインは、下記数２を満たすαの最大値α_ｍａｘを用いて、数３で与えられる。なお、数２におけるμ_Δ（Ｍ_α（ｊω））は、図５におけるＭ_α，Δによって定まる構造化特異値である。
【００１２】
【数２】

【００１３】
【数３】

【００１４】
この最悪ゲインを最小化するという概念を、図１に示す本発明の振動抑制系に適用することにより、各回路素子の適正な値を決定することが可能になる。
図１の振動抑制装置についての拡大系を導く手順は、以下の通りである。板のｍ次モードの運動方程式は下記数４で表される。
【００１５】
【数４】

【００１６】
ここで、η_ｍ（ｔ）はモード振幅を、ｖ_ａ（ｔ）は圧電素子に加わる電圧を、ｆ（ｔ）は集中外力の大きさを、ｉ_ｐ（ｔ）は圧電素子の発生電流を表す。なお、Ｗ_ｃδ_ｃは減衰項の変動を表し、Ｗ_ωδ_ωは固有振動数の変動を表す。また、圧電素子の回路方程式は、下記数５で表される。
【００１７】
【数５】

【００１８】
ここで、ｉ_ｓｕ（ｔ）はシャント回路に流れる電流である。なお、Ｗ_ｃｐδ_ｃｐは圧電素子のキャパシタンスＣ_ｐ ^ｓの変動を表す。シャント回路に流れる電流は、下記数６で表される。
【００１９】
【数６】

【００２０】
数４，数５，数６の信号の結合関係を表すと図６となる。ここで、Σ_{ｐｌａｔｅ}は、数４の［ｆ，ｖ_ａ，Ｗ_ω，Ｗ_ｃ］から［η_ｍ，ｉ_ｐ，ｚ_ω，ｚ_ｃ］までの伝達関数、Σ_ｃｐは、数５の［ｉ_ｐ，Ｗ_ｃｐ］から［ｖ_ａ，ｚ_ｃｐ］までの伝達関数、Σ_ｓｕは数６のｖ_ａからｉ_ｐまでの伝達関数を表す。なお、ｚ_ω，ｚ_ｃ，ｚ_ｃｐの関係式は、下記数７で表される。
【００２１】
【数７】

図６より、本発明の振動抑制系の拡大系図４が定まる。
【００２２】
【発明の実施の形態】
以下、本発明の一実施形態について説明する。図１は、実施形態に板に振動抑制装置を装着した状態を斜視図により示し、図２は振動抑制装置の等価回路を回路図により示したものである。振動抑制装置１０は、振動入力される板１に貼り付けられた板状の圧電素子１１と、圧電素子１１に直列接続されたシャント回路１３とにより構成されている。
【００２３】
圧電素子１１は、ＰＺＴ（ジルコン酸チタン酸鉛），ＰＬＺＴ（ジルコン酸チタン酸ランタン鉛）等の圧電セラミックスや、ＰＶＤＦ（ポリフッ化ビニリデン）等の圧電材料の薄板である。シャント回路１３は、第１抵抗素子Ｒ_１と第１インダクタンス素子Ｌ_１を直列接続した第１回路と、第２抵抗素子Ｒ_２と第２インダクタンス素子Ｌ_２とコンデンサ素子Ｃ_２とを直列接続した第２回路とを並列接続したものである。第１及び第２インダクタンス素子Ｌ_１，Ｌ_２については、チューニングが容易で軽量である電子インダクタンスが用いることが好ましい。例えば、図３に示すような電子インダクタンスが用いられる。
【００２４】
つぎに、具体的な振動抑制装置の振動減衰特性の測定結果について説明する。
圧電素子１１は、形状が７５ｍｍ×７５ｍｍ×０．５ｍｍ、固有振動数ω_１＝４３３ｒａｄ／ｓ、モード減衰率ζ_１＝０．００４、キャパシタンスＣ_ｐ ^ｓ＝１５２ｎＦである。この圧電素子１１が、５００ｍｍ×４００ｍｍ×１．６ｍｍの鋼板１の中央に貼り付けられる。シャント回路１３の各素子の調整は、最悪ゲイン最小化法（以下、μによるチューニングと記す）により行われる。
【００２５】
振動抑制装置１０の特性測定については、鋼板１の圧電素子１１を挟んだ一方側にインパルスハンマで打撃を与え、圧電素子１１を挟んだ反対側でレーザセンサにより振動変化を検出し、検出結果を高速フーリエ変換解析装置（ＦＦＴアナライザ）で解析することにより、振動の振幅及び位相の周波数特性を求めることにより行われる。振動入力モードの変動のない場合とある場合の回路素子Ｌ_１，Ｒ_１，Ｌ_２，Ｒ_２のチューニング値について、下記表１に示す。なお、Ｃ_２＝２２．４ｎＦとした。
【００２６】
【表１】

【００２７】
なお、参考例として、圧電素子に抵抗素子Ｒとインダクタンス素子Ｌを直列接続したＬＲ振動抑制装置を用い、かつ抵抗素子Ｒとインダクタンス素子Ｌの調整を、μによるチューニングと、定点理論によるチューニングにより行った場合についても示す。振動入力モードの変動のない場合とある場合の回路素子Ｌ_１，Ｒ_１に対して、μによるチューニングと、定点理論によるチューニングのチューニング値について、それぞれ下記表２に示す。
【００２８】
【表２】

【００２９】
上記振動抑制装置１０について、振動モードの変動のない場合と変動がある場合のゲイン及び位相特性は、図７及び図８に示すようになる。図において、点線は非制御状態での特性を表し、実線がμによるチューニングが行われた後の特性を表す。これによれば、７０Ｈｚ近辺におけるゲインの減衰が、振動モードの変動のない場合には、μによるチューニング前後で１３．４ｄＢであるのに対して、振動モードの変動のある場合は、μによるチューニング前後で１０．９ｄＢと、その差が２．５ｄＢ程度と非常に小さい。
【００３０】
これに対して、ＬＲ振動抑制装置についてμによるチューニングを適用した場合の、振動モードの変動のない場合と変動がある場合のゲイン及び位相特性は、図９及び図１０に示すようになる。これによれば、７０Ｈｚ近辺におけるゲインの減衰が、振動モードの変動のない場合には、μによるチューニング前後で１４．７ｄＢであるのに対して、振動モードの変動のある場合は、μによるチューニング前後で１０．２ｄＢと、その差が４．５ｄＢ程度と大きくなっている。
【００３１】
また、ＬＲ振動抑制装置について定点理論を適用した場合の、振動モードの変動のない場合と変動がある場合のゲイン及び位相特性は、図１１及び図１２に示すようになる。これによれば、７０Ｈｚ近辺におけるゲインの減衰が、振動モードの変動のない場合には、μによるチューニング前後で１８．９ｄＢであるのに対して、振動モードの変動のある場合は、μによるチューニング前後で約５．７ｄＢと、その差が１３ｄＢ程度と非常に大きくなっている。
【００３２】
以上の結果から明らかなように、本発明にかかる振動抑制装置１０に対してμによるチューニングを行う方法は、ＬＲ振動抑制装置にμによるチューニングを行う方法に比べて、振動モードの変動の有無によるゲインの変動が小さい良好な結果が得られている。さらに、本発明にかかる方法は、ＬＲ振動抑制装置に定点理論によるチューニングを行う方法に比べて、振動モードの変動の有無によるゲインの変動が格段に改善された結果が得られている。
【００３３】
【発明の効果】
上記請求項１の発明によれば、板状体に貼り付けられた板状の圧電素子に、第１回路と第２回路とを並列接続してなるシャント回路を直列接続し、さらにシャント回路を構成する各素子について最悪ゲイン最小化法により適正値に調整することにより、振動モードが変動した場合でも、変動後の振動減衰の変化の程度が低く抑えられる。その結果、請求項１の発明においては、モードパラメータや圧電素子のキャパシタンスなどの変動に対してロバスト性を有する。
【図面の簡単な説明】
【図１】本発明の一実施形態である振動抑制装置の使用状態を概略的に示す斜視図である。
【図２】振動抑制装置の等価回路を示す回路図である。
【図３】インダクタンス素子を構成する電子インダクタンスの一例を示す回路図である。
【図４】振動抑制装置について、最悪ゲイン最小化法を適用するための拡大系を示すブロック線図である。
【図５】図４に示す拡大系を最悪ゲイン最小化法を適用するために変更したブロック線図である。
【図６】図２の振動抑制装置について、最悪ゲイン最小化法を適用するための拡大系を示すブロック線図である。
【図７】図２の振動抑制装置について、振動モードの変動のない場合のゲイン及び位相特性を示すグラフである。
【図８】図２の振動抑制装置について、振動モードの変動がある場合のゲイン及び位相特性を示すグラフである。
【図９】ＬＲ振動抑制装置についてμによるチューニングを適用した場合の、振動モードの変動のない場合のゲイン及び位相特性を示すグラフである。
【図１０】ＬＲ振動抑制装置についてμによるチューニングを適用した場合の、振動モードの変動がある場合のゲイン及び位相特性を示すグラフである。
【図１１】ＬＲ振動抑制装置について定点理論を適用した場合の、振動モードの変動のない場合のゲイン及び位相特性を示すグラフである。
【図１２】ＬＲ振動抑制装置について定点理論を適用した場合の、振動モードの変動がある場合のゲイン及び位相特性を示すグラフである。
【符号の説明】
１０…振動抑制装置、１１…圧電素子、１３…シャント回路。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for suppressing vibration propagating to a plate-like body such as a windshield of an automobile, and in particular, a plate-like piezoelectric element is attached to a plate-like body and the vibration is suppressed by using the piezoelectric element. The present invention relates to a method for suppressing body vibration.
[0002]
[Prior art]
Conventionally, as a method for suppressing vibration of this type of plate-like body, for example, as shown in Patent Document 1, a piezoelectric conversion element is disposed in close contact with an outer peripheral portion of an automotive window glass, and the amount of distortion of the piezoelectric conversion element is determined. There is known a method in which control means for controlling the vibration is provided, and inward internal stress that restrains strain caused by elastic vibration generated in the window glass is generated in the piezoelectric transducer to attenuate the vibration. However, this vibration suppression method for the plate-like body requires an acceleration sensor and a control circuit for controlling the amount of strain of the piezoelectric transducer, and there is a problem that the control cost is expensive.
[0003]
On the other hand, for example, as shown in Non-Patent Document 1, a shunt circuit formed by attaching a plate-like piezoelectric element to a plate-like body that is a vibration control target and connecting a resistance element and an inductance element in series is used as the piezoelectric element. There is known a vibration suppression method for a plate-like body that is connected in series and further adjusted to an appropriate value by fixed point theory for each element constituting a shunt circuit. That is, vibration energy is converted into electric energy by the piezoelectric effect of the piezoelectric element, and the vibration can be attenuated by dissipating the electric energy by the resistance. The inductance increases the efficiency of electric energy dissipation by matching the phase of current and voltage (eliminating the phase difference). Here, the fixed point theory is used to obtain the optimum spring constant and damping coefficient of the vibration damper for a one-degree-of-freedom spring mass system. The optimum is the gain of the transfer function from the external force to the amplitude. It means that the maximum value is minimized.
[0004]
As a procedure for determining the resistance and inductance value by this method, a closed loop transfer function is obtained, the square of the gain of the transfer function is obtained, and a fixed point (a point that always passes through the gain diagram even if the resistance R is changed) is obtained. Further, optimum tuning is performed to obtain an optimum inductance L so that the heights of the fixed points are the same, and optimum attenuation is performed to determine an optimum resistance R so that the gain is maximized at the fixed points. This vibration suppression method has a simple configuration that does not require a control circuit or the like. By determining the optimum resistance R and inductance L in advance, an effect of easily and appropriately attenuating the vibration input component can be obtained. However, in the case of the vibration suppression method based on this fixed point theory, an appropriate vibration damping effect can be obtained when there is no uncertainty or fluctuation in the vibration mode, but the vibration damping effect is deteriorated when there is uncertainty or fluctuation in the vibration mode. There is a problem that the so-called robustness is inferior.
[0005]
[Patent Document 1]
JP-A-10-287127 (second page, FIG. 8)
[Non-Patent Document 1]
NWHagood and AVFlotow, Journal of Sound and Vibration, Vol.142, No.6, 1991, pp.243-268
[0006]
[Problems to be solved by the invention]
The present invention is intended to solve the above-described problems, and uses a piezoelectric element and a simple configuration that does not require a control circuit, and appropriately attenuates vibration of a plate-like body regardless of uncertainty or fluctuation in vibration mode. It is an object of the present invention to provide a vibration suppressing method for a plate-like body having good robustness.
[0007]
[Means for Solving the Problems]
In order to achieve the above object, the structural feature of the first aspect of the present invention is that a plate-like piezoelectric element is attached to a plate-like body that is the object of vibration suppression, and the first resistance element and the first resistance element. A shunt circuit formed by connecting in parallel a first circuit in which inductance elements are connected in series, and a second circuit in which a second resistance element, a second inductance element, and a capacitor element are connected in series is connected in series to the piezoelectric element, and further shunted By using the worst gain minimization method for each element constituting the circuit, the worst value of the peak gain when the vibration mode of the plate-like body fluctuates in advance is adjusted to an appropriate value so as to reduce the worst value using the robustness index. Thus, the vibration of the plate-like body is appropriately damped regardless of the uncertainty or fluctuation of the vibration mode.
[0008]
In the invention of claim 1 configured as described above, a shunt circuit in which a first circuit and a second circuit are connected in parallel to a plate-like piezoelectric element affixed to a plate-like body that is subject to vibration suppression. Are connected in series, and each element constituting the shunt circuit is adjusted to an appropriate value by the worst gain minimization method, so that even when the vibration mode fluctuates, the degree of deterioration of vibration attenuation after fluctuation can be kept low.
[0009]
The worst gain minimization method is to tune the elements of the shunt circuit so as to reduce the worst gain by using the worst value (worst gain) of the peak gain when the vibration parameter fluctuates as an index of robustness. . The worst gain can be calculated using a structured singular value used in robust control theory. The worst gain of the enlargement system shown in FIG. Here, ω represents an angular frequency, and j represents an imaginary unit. Further, F ₁ (M (jω), Δ ₂ (jω)) represents a linear fractional transformation related to Δ ₂ (jω) of the transfer function M (jω), and is a transfer function from f to η _m in FIG. . σ (Δ ₂ (jω)) (excluding the horizontal bar above σ) is the maximum singular value of Δ ₂ (jω).
[0010]
[Expression 1]

[0011]
The worst gain of the expansion system in FIG. 4 is given by Equation 3 using the maximum value α _max of α satisfying Equation 2 below. Note that μ _Δ (M _α (jω)) in Equation 2 is a structured singular value determined by M _α , Δ in FIG.
[0012]
[Expression 2]

[0013]
[Equation 3]

[0014]
By applying the concept of minimizing the worst gain to the vibration suppression system of the present invention shown in FIG. 1, it is possible to determine an appropriate value for each circuit element.
The procedure for deriving the expansion system for the vibration suppression device of FIG. 1 is as follows. The equation of motion of the m-th order mode of the plate is expressed by the following equation (4).
[0015]
[Expression 4]

[0016]
Here, η _m (t) is the mode amplitude, v _a (t) is the voltage applied to the piezoelectric element, f (t) is the magnitude of the concentrated external force, and i _p (t) is the current generated by the piezoelectric element. To express. W _c δ _c represents the variation of the attenuation term, and W _ω δ _ω represents the variation of the natural frequency. The circuit equation of the piezoelectric element is expressed by the following formula 5.
[0017]
[Equation 5]

[0018]
Here, i _su (t) is a current flowing through the shunt circuit. Note that W _cp δ _cp represents the fluctuation of the capacitance C _p ^s of the piezoelectric element. The current flowing in the shunt circuit is expressed by the following formula 6.
[0019]
[Formula 6]

[0020]
FIG. 6 shows the coupling relationship of the signals of Equation 4, Equation 5, and Equation 6. Here, Σ _plate is a transfer function from [f, v _a , W _ω , W _c ] in Equation 4 to [η _m , i _p , z _ω , z _c ], and Σ _cp is [i in [5] _p, the transfer function from _{W cp]} to _{[v a, z cp],} Σ su represents the transfer function from the number 6 of _{v a} to _{i p.} The relational expression of z _ω , z _c , and z _cp is expressed by the following formula 7.
[0021]
[Expression 7]

From FIG. 6, an enlarged system diagram 4 of the vibration suppression system of the present invention is determined.
[0022]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an embodiment of the present invention will be described. FIG. 1 is a perspective view showing a state in which a vibration suppression device is mounted on a plate in the embodiment, and FIG. 2 is a circuit diagram showing an equivalent circuit of the vibration suppression device. The vibration suppression device 10 includes a plate-like piezoelectric element 11 attached to a plate 1 to which vibration is input, and a shunt circuit 13 connected in series to the piezoelectric element 11.
[0023]
The piezoelectric element 11 is a thin plate of piezoelectric ceramics such as PZT (lead zirconate titanate) or PLZT (lead lanthanum zirconate titanate), or piezoelectric materials such as PVDF (polyvinylidene fluoride). Shunt circuit 13 has a first circuit first resistance element R ₁ and the first inductance element L ₁ connected in series, a second resistance element R ₂ and the second inductance element L ₂ and the capacitor element C ₂ connected in series The second circuit is connected in parallel. For the first and second inductance elements L ₁ and L ₂ , it is preferable to use electronic inductance that is easy to tune and lightweight. For example, an electronic inductance as shown in FIG. 3 is used.
[0024]
Next, measurement results of vibration damping characteristics of a specific vibration suppressing device will be described.
The piezoelectric element 11 has a shape of 75 mm × 75 mm × 0.5 mm, natural frequency ω ₁ = 433 rad / s, mode damping rate ζ ₁ = 0.004, and capacitance C _p ^s = 152 nF. The piezoelectric element 11 is attached to the center of a steel plate 1 having a size of 500 mm × 400 mm × 1.6 mm. Adjustment of each element of the shunt circuit 13 is performed by the worst gain minimization method (hereinafter referred to as tuning by μ).
[0025]
With respect to the characteristic measurement of the vibration suppression device 10, an impact hammer is applied to one side of the steel plate 1 across the piezoelectric element 11, and a vibration change is detected with a laser sensor on the opposite side across the piezoelectric element 11. The analysis is performed by obtaining frequency characteristics of vibration amplitude and phase by analyzing with a fast Fourier transform analyzer (FFT analyzer). Table 1 below shows tuning values of the circuit elements L ₁ , R ₁ , L ₂ , and R ₂ when the vibration input mode does not vary. Note that C ₂ = 22.4 nF.
[0026]
[Table 1]

[0027]
As a reference example, an LR vibration suppression device in which a resistance element R and an inductance element L are connected in series to a piezoelectric element is used, and the resistance element R and the inductance element L are adjusted by tuning by μ and tuning by a fixed point theory. The case is also shown. Table 2 below shows the tuning values for tuning by μ and tuning by the fixed point theory for the circuit elements L ₁ and R ₁ when there is no fluctuation in the vibration input mode.
[0028]
[Table 2]

[0029]
Regarding the vibration suppression device 10, the gain and phase characteristics when there is no fluctuation and when there are fluctuations are as shown in FIGS. 7 and 8. In the figure, the dotted line represents the characteristic in the uncontrolled state, and the solid line represents the characteristic after tuning by μ. According to this, when attenuation of the gain in the vicinity of 70 Hz is 13.4 dB before and after tuning by μ when there is no fluctuation in vibration mode, tuning by μ is performed when there is fluctuation in vibration mode. The difference between the front and rear is 10.9 dB and the difference is as small as about 2.5 dB.
[0030]
On the other hand, when the tuning by μ is applied to the LR vibration suppressing device, the gain and phase characteristics when there is no fluctuation and when there are fluctuations are as shown in FIGS. According to this, the attenuation of the gain in the vicinity of 70 Hz is 14.7 dB before and after tuning by μ when there is no fluctuation in the vibration mode, whereas it is tuned by μ when there is fluctuation in the vibration mode. It is 10.2 dB before and after, and the difference is as large as about 4.5 dB.
[0031]
Further, when the fixed point theory is applied to the LR vibration suppression device, the gain and phase characteristics when there is no vibration mode variation and when there is variation are as shown in FIGS. According to this, the attenuation of gain in the vicinity of 70 Hz is 18.9 dB before and after tuning by μ when there is no fluctuation in the vibration mode, while tuning by μ when there is fluctuation in the vibration mode. It is about 5.7 dB before and after, and the difference is as large as about 13 dB.
[0032]
As is clear from the above results, the method of performing the tuning with μ on the vibration suppressing device 10 according to the present invention depends on the presence or absence of fluctuations in the vibration mode as compared with the method of performing the tuning with μ on the LR vibration suppressing device. Good results with small gain fluctuations are obtained. Furthermore, the method according to the present invention has a result that the fluctuation of the gain due to the presence or absence of the fluctuation of the vibration mode is remarkably improved as compared with the method of tuning the LR vibration suppression device by the fixed point theory.
[0033]
【The invention's effect】
According to the first aspect of the present invention, the shunt circuit formed by connecting the first circuit and the second circuit in parallel to the plate-like piezoelectric element attached to the plate-like body is connected in series, and the shunt circuit is further connected. By adjusting each component element to an appropriate value by the worst gain minimization method, even when the vibration mode changes, the degree of change in vibration attenuation after the change can be kept low. As a result, in the first aspect of the invention, it has robustness against fluctuations such as mode parameters and capacitance of the piezoelectric element.
[Brief description of the drawings]
FIG. 1 is a perspective view schematically showing a usage state of a vibration suppression device according to an embodiment of the present invention.
FIG. 2 is a circuit diagram showing an equivalent circuit of the vibration suppressing device.
FIG. 3 is a circuit diagram showing an example of an electronic inductance constituting the inductance element.
FIG. 4 is a block diagram showing an expansion system for applying the worst gain minimization method for the vibration suppressing device.
FIG. 5 is a block diagram obtained by modifying the expansion system shown in FIG. 4 in order to apply the worst gain minimization method.
6 is a block diagram showing an expansion system for applying the worst gain minimization method for the vibration suppressing device of FIG. 2; FIG.
7 is a graph showing gain and phase characteristics when there is no fluctuation in vibration mode for the vibration suppressing device of FIG. 2; FIG.
8 is a graph showing gain and phase characteristics when the vibration mode varies in the vibration suppressing device of FIG. 2; FIG.
FIG. 9 is a graph showing gain and phase characteristics when there is no fluctuation in vibration mode when tuning by μ is applied to the LR vibration suppressing device.
FIG. 10 is a graph showing gain and phase characteristics when there is a fluctuation in vibration mode when tuning by μ is applied to the LR vibration suppression device.
FIG. 11 is a graph showing gain and phase characteristics when there is no fluctuation in vibration mode when the fixed point theory is applied to the LR vibration suppression device.
FIG. 12 is a graph showing gain and phase characteristics when there is a fluctuation in vibration mode when a fixed point theory is applied to the LR vibration suppression device.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 10 ... Vibration suppression apparatus, 11 ... Piezoelectric element, 13 ... Shunt circuit.

Claims (1)

A first circuit in which a plate-like piezoelectric element is attached to a plate-like body that is subject to vibration suppression, and a first resistance element and a first inductance element are connected in series, a second resistance element, a second inductance element, and a capacitor element A shunt circuit formed by connecting a second circuit connected in series with each other in series is connected in series to the piezoelectric element, and each element constituting the shunt circuit is previously subjected to vibration of the plate-like body by the worst gain minimization method. By using the worst value of peak gain when the mode fluctuates as an indicator of robustness, and adjusting the value to an appropriate value to reduce the worst value , the vibration of the plate-shaped body can be made appropriate regardless of the uncertainty or fluctuation of the vibration mode. A method for suppressing vibration of a plate-like body, characterized in that the vibration is attenuated to a low level.

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