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弯曲振动压电陶瓷薄圆板的等效电路和剪应力

THE EQUIVALENT CIRCUIT AND THE SHEAR STRESS OF THE THIN PIEZOCERAMIC COMPOSITE CIRCULAR PLATE

  • 摘要: 本文讨论了压电陶瓷和金属构成的三层复合薄圆板的等效电路和粘接面上的剪应力分布。利用电压策动下强迫振动的稳态解求出系统的纯弹性能,纯电能和机电耦合能。再用推导等效电路的能量法求得系统的四端等效电路。在无损耗的情况下,该等效电路在所有的频率上都是正确的。然后利用等效电路求出共振频率附近的有损耗存在的位移函数。再由运动微分方程就可得到动态剪应力的分布。剪应力与策动电压和机械品质因数的乘积成正比。圆板中心处的剪应力为零。随着半径的增加剪应力迅速增加。当r/a=0.85时,剪应力有极大值,边缘上的应力略有下降。

     

    Abstract: This paper reports the electromechanical equivalent circuit and the shear stress of metal-piezoceramic thin composite circular plate of radius a for simply supported edge. The parameters and the equations of the equivalent circuit are obtained with internal energy of system and energy method to derive equivalent circuit. Provided there is not dissipation in the system, preceding equivalent circuit is always correct at all the frequencies.
    The displacement function of damped system at resonance is obtained with the equivalent circuit. Using the displacement function and the dynamic equation, distribution of amplitude of dynamic shear stress is obtained. The amplitude of dynamic shear stress is directly proportional to the product of excited voltage and mechanical quality factor. The shear stress at center of plate is equal to zero. Increases along the radius until to 0.85 a, where the maximum value of shear stress occurs.
    The approximate curve of dynamic deformation is in good agreement with the exact curve. However there is considerably more deviation of the approximate distribution of shear stress from exact distribution.

     

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