Complete guided wave modes in piezoelectric cylindrical structures with fan-shaped cross section using the modified double orthogonal polynomial series method

Abstract

The complete guided wave modes are made up of propagative wave modes and evanescent wave modes whose amplitudes exhibit an exponential or damped attenuation with propagation distance. The solutions for evanescent modes are complex and very difficult to be solved. The conventional method usually needs an iterative search procedure to find the complex roots. Accordingly, the modified double orthogonal polynomial series method, an analytical treatment, is proposed to investigate the complex guided waves in piezoelectric cylindrical structures with fan-shaped cross section. By the present method, the real, imaginary and complex solutions are simultaneously obtained without iterative process. Compared with available reference results, the correctness of the proposed method is confirmed. The displacement and electric potential distributions are illustrated, and the piezoelectric effect is detailed. Results reveal that there are some evanescent wave modes, which have much higher velocities than the propagative modes and simultaneously have very low attenuation. The piezoelectric effect can be adjusted by changing the geometric size of the cross section.