Asymptotic analytical solution for horizontal shear waves in a piezoelectric elliptic cylinder shell

Abstract

In this study, an asymptotic analytical solution for horizontal shear waves in a confocal piezoelectric elliptic cylinder shell, with poling direction parallel to the axis, is obtained. On the basis of tensor analysis and elastodynamic equations, the field-governing equation in elliptic cylinder coordinates, which is expressed by displacement and electric potential, is deduced. By the separation of variables, the partial differential equations are translated into ordinary differential equations. Considering electrically open boundary conditions, the ordinary differential equations are solved, and the wave functions of horizontal shear waves (SH waves) in a piezoelectric elliptic cylinder are obtained by the Wentzel–Kramers–Brillouin and power series methods. In a numerical example, the relation between the correction coefficient of the wave number and frequency of SH waves in different piezoelectric elliptic cylinder shells is discussed. The waves’ structures for the first three modes are also illustrated. The results reveal that one or more mode SH waves can propagate along the circumference in a confocal piezoelectric elliptic cylinder shell. The correction coefficient of the wave number of the first mode, which depends on the size of the piezoelectric elliptic cylinder shell, is approximately a constant. The number of modes increases with the frequency and thickness of the shell. For the first mode, the wave energy should concentrate on the convex surface at high frequency. These results should provide theoretical guidance not only for non-destructive evaluation of curved structures but also for the design of novel acoustic devices based on curved structures.