Dynamic modeling and analysis of circumferential and spiral waves in piezoelectric cylinders

Abstract

Understanding the dynamic characteristics of ultrasonic guided wave in structures is important, as it is one of the methods that are widely used in many different areas of industrial sectors and inspections, such as Non-Destructive Testing (QNDT). The ultrasonic guided wave is transmitted and reflected at the surface of the wave materials. A detailed study and interpretation of mode conversion in guided wave is required. The current research presents a theoretical study of guided wave in piezoelectric cylinders based on the theory of elasticity. Two different methods were employed to study dispersion relations in piezoelectric cylinders. One of them is a finite element method and the other is an analytical method. In the analytical method, three displacement potentials are introduced to obtain dispersion relation of guided wave modes. This method is developed primarily to cross check finite element results. In the finite element method, the dispersion equation has been formulated as a generalized eigenvalue problem by treating mechanical displacements and electric potential with one dimensional (quadratic) finite element model through the thickness of the cylinder. Computer codes have been developed and verified by comparing with limited published results. The numerical results are presented for different cylinders and electric boundary conditions. In the numerical studies, three dimensional wave spectrum surfaces were generated. Discussion of guided wave propagating in different direction in cylinders was given as well.