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中文核心期刊

压电陶瓷和金属构成的复合薄圆板的强迫振动——A电压策动

FORCED VIBRATIONS OF METAL-PIEZOCERAMIC THIN COMPOSITE CIRCULAR PLATE EXCITED WITH VOLTAGE

  • 摘要: 本文报告了电压策动下的复合薄圆板的强迫弯曲振动的严格解和近似解。复合薄圆板是由两片半径为b的压电陶瓷片和半径为aab)的金属薄圆板构成的。我们把它称作一般复合薄圆板,因为它可简化为各种特殊薄圆板.在压电陶瓷的极性做适当的安排后,交流策动电压将使一般复合薄圆板产生弯曲振动。从哈密顿原理出发推导了该系统的运动微分方程,连接条件和边界条件。并给出了一般解和严格共振频率方程。对于b=a的特殊复合薄圆板作了特殊的讨论。在简支边界情况下,策动电压的作用相当于在边界上加一个策动弯矩。当边界固定时,b=a的复合薄圆板表现为纯弹性,电压策动不能使之发生振动。本文还用里兹方法求出了一般复合圆板在电压策动下的强迫振动的近似解和近似共振频率方程。共振频率的近似值与实验值进行了比较,结果表明近似结果在工程上是可以使用的。

     

    Abstract: This paper reports the exact solution and the approximate solution of forced vibration of general metal-piezoceramic thin composite circular plate excited with voltage. The general thin composite circular plate are constructed using two piezoceramic diskes of radius b and one metal thin circular plate of radius a. After correctly arranged polarity of piezoelectric ceramics, flexural vibration of general thin composite circular plate can be excited with alternating voltage. The equations of motion, continuous conditions and boundary conditions of the system are derived from Hamilton's principle. The exact solution and the equation of resonant frequency for simply supported edge and clamped edge are obtained. Under simply supported boundary condition, the effect of excited voltage is just like a excited bending moment on the edge for thin composite circular plate for b=a. Under clamped boundary condition, the thin composite circular plate for b=a exhibit pure elasticity, hence flexural vibration can not be excited with voltage.
    The approximate solution of forced vibration, excited with voltage, and the equation of resonant frequency of general thin composite, circular plate are obtained with Rayleigh-Ritz method. The approximate resonant fre quencies are in good agreement with the experimentation.

     

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