Complex dispersion solutions for guided waves and properties of non-propagating waves in a piezoelectric spherical plate

Xiaoming Zhang,Jiangong Yu,Zhi Li

doi:10.1177/1687814018820693

Xiaoming Zhang, Jiangong Yu + Show 1 more

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https://doi.org/10.1177/1687814018820693

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Abstract

The vibration modes of an elastic plate are usually divided into propagating and non-propagating (evanescent) kinds. Non-propagating wave modes are very important for guided wave inspection of defect size and shape. But it is difficult to obtain the complex solutions of the transcendental dispersion equation, corresponding to the non-propagating wave. In this article, we present an improved Legendre polynomial method to calculate the complex-valued dispersion and study properties of the non-propagating wave in a piezoelectric spherical plate. Comparisons with other related studies are conducted to validate the correctness of the presented method. The complete dispersion and attenuation curves are plotted in three-dimensional frequency-complex wave number space. The influences of material piezoelectricity and radius–thickness ratio on non-propagating waves in piezoelectric spherical plates are investigated. The amplitude distributions of the electric potential and displacement are also discussed in detail. All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation and are promising to be applied to improve the resolution of piezoelectric transducers.

Highlights

Due to the unique properties of coupling between mechanical and electrical properties, piezoelectric materials are widely used in several industry fields, such as vibration control devices, electromechanical transducers, measuring instruments, actuators, and filters.[1]
Dimensionless phase velocity and attenuation and frequpenfficffiffiyffiffiffiffiffiffiaffiffiffire respectively adopted aps ffiffiffiffiffiVffiffiffipffiffiffi=ffi v=(Re(k) Á C55=r), Im(kh) and fh = vh=(2p C55=r). These curves reveal that the phase velocity of propagating modes decreases and gradually tends to a stable value with increasing frequency, but that of non-propagating modes with complex wave number increases with increasing frequency
To reveal the characteristics of non-propagating waves, we calculate the distributions of the displacement and electric potential for a piezoelectric spherical plate with h = 10, which can be obtained by equations (5) and (7)

Summary

Introduction

Due to the unique properties of coupling between mechanical and electrical properties, piezoelectric materials are widely used in several industry fields, such as vibration control devices, electromechanical transducers, measuring instruments, actuators, and filters.[1]. Keywords Non-propagating, piezoelectric spherical plate, Legendre polynomial method, complex dispersion, attenuation, radius– thickness ratio Yu et al.[8] investigated the guided propagating wave in piezoelectric spherical plates using polynomial approach.

Results

Conclusion