Horizontal shear waves in a parabolic cylinder piezoelectric shell

Horizontal shear (SH) waves in parabolic cylinder shells with a polling direction parallel to a generatrix are investigated. Based on the motion equation, electrical displacement equilibrium equations, piezoelectric constitutive equations, geometric equation, and the relation between electrical intensity and electrical potential, the field-governing equation in parabolic cylinder coordinates that is expressed by the displacement and electrical potential is deduced. Based on the Wentzel-Kramers-Brillouin and power series methods, ordinary differential equations are solved and the wave functions of the SH waves in a piezoelectric parabolic cylinder are determined. As a numerical example, the relation between the correction coefficient of the wave number and the frequency of the SH waves is discussed, and the structures of the waves are illustrated. Results reveal that one or more modes of the SH waves can propagate along the circumferential direction in parabolic cylinder shells. The correction coefficient of the wave number of the first modeis approximately a constant. The number of modes increases with the frequency and thickness of the shell. These results should provide theoretical guidance for evaluating curved structures non-destructively and for designing novel acoustic devices based on curved structures.