Axi-symmetric vibration of piezoelectric disc based on improved double-Legendre polynomial

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (21) : 169-175.

ZHOU Hongmei, HAN Kangle, YU Jiangong, ZHANG Huiduan, WANG Xianhui, ZHANG Xiaoming

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Abstract

With force electric coupling characteristics, piezoelectric ceramics are widely used in structural shape control, vibration and noise control and structural damage monitoring, and the other fields. Double Legendre polynomial method can automatically add to boundary conditions through the rectangular window function for the constitutive equation.Which automatically meet the boundary conditions of piezoelectric structure, successful application in the study of vibration characteristics of piezoelectric disc. But calculating process of the traditional method is slow. Higher-order data need more time to compute, so it limits the double Legendre polynomial method in the application of the vibration control equation of piezoelectric materials. Based on the traditional double Legendre polynomial method about vibration analysis, using nature properties of the Legendre polynomial, the analytical integral expression is deduced, which makes the calculation efficiency by more than 90%. By compared with the existing literature the presented method is correct and valid. At last the relationship between the natural frequency and radius-thickness ratio of the piezoelectric disc are analyzed. The results show that the frequency radius product tends to be stable with the increase of diameter-thickness ratio, and the lower order reaches a stable value faster.

Key words

Piezoelectric disc / Axisymmetric vibration / double Legendre Polynomial;Analytical integral method

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ZHOU Hongmei, HAN Kangle, YU Jiangong, ZHANG Huiduan, WANG Xianhui, ZHANG Xiaoming. Axi-symmetric vibration of piezoelectric disc based on improved double-Legendre polynomial[J]. Journal of Vibration and Shock, 2023, 42(21): 169-175

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