A Theoretical Analysis for the SH Wave in a Thin Plate

Abstract

A theoretical analysis for the shear horizontal (SH) wave in a thin plate with the material nonlinearity has been conducted by using a microscopic scalar model. In the present study, the effects of the material nonlinearity and dispersion of the wave are taken into account. Especially, the influence of the material nonlinearity of second order is also considered in addition to that of third order. A governing equation which describes the behaviors of the SH wave is derived from the microscopic scalar model. Since the governing equation is complicated, some mathematical techniques are applied in order to analyze the behaviors of the SH wave. As a result, it is shown that the SH wave which can propagate through the thin plate without dissipation exists theoretically. The factors which have the effects on the propagation of the SH wave are revealed clearly. Moreover, the conditions which make the SH wave exist without the dissipation are shown analytically.