非均匀压电薄板面内自由振动的精确解

由于板面内振动频率一般远高于通常的激励频率,所以一百多年来面内振动的研究一直处于停滞状态。随着高速飞行器和高速舰船的快速发展,以及直线型压电超声电机的研制,板的面内振动问题逐渐成为当前工程领域研究的热点。假设压电材料参数沿厚度方向以同一指数形式变化,给出了非均匀压电薄板面内自由振动的基本方程。应用分离变量方法,对四边简支非均匀压电薄板的面内自由振动的精确解进行了研究,给出了不均匀系数与振动频率之间变化规律。通过算例讨论了相关问题。

Exact solution to in-plane free vibration of an inhomogeneous rectangular piezoelectric plate

As natural frequencies of in-plane vibration of a rectangular plate are much higher than usual excitation frequencies, study on plates’ in-plane vibration has been in a state of stagnation for more than one hundred years. With the rapid development of high-speed aircrafts and warships, and the development of linear piezoelectric ultrasonic motors, in-plane vibration problems of plates gradually become hot topics in engineering. Here, parameters of inhomogeneous piezoelectric material were assumed to vary with the same exponent form along its thickness direction. Basic dynamic equations for in-plane free vibration of an inhomogeneous rectangular piezoelectric plate were derived. Using the variables separation method, the exact solution to in-plane free vibration of the inhomogeneous rectangular piezoelectric plate with 4-side simply supported was studied in detail. The variation laws between non-uniform coefficient and the plate’s natural frequencies were deduced. Finally, the corresponding problems were discussed with examples.