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

Abstract

The vibration modes of an elastic plate are usually divided into propagating and non-propagating (evanescent) kinds. Nonpropagating 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 threedimensional 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.