### A Theoretical Analysis for the SH Wave in a Thin Plate

Tomonori WATANABE, Ning HU
2011 Journal of Environment and Engineering
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
more » ... calar 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. we adopt the novel idea that we achieve a proper balance between the nonlinearity and the dispersion by choosing an appropriate space-time scale for observation. To realize this, we apply some mathematical techniques which have been greatly developed recently (5), (6) . As the second point, we conduct the mathematical analysis of the SH wave. The mathematical analysis would lead us to the rigorous results. Thus, by the analysis, we intend to obtain the highly accurate and reliable results. We believe that we would be able to contribute to the better interpretation and application of the wave. This paper is organized as follows. Section 2 is devoted to derivation of the governing equation which describes the behaviors of the SH wave in the thin plate from a microscopic scalar model. In Sec.3, we apply some mathematical techniques to the governing equation in order to obtain the SH wave which can propagate through the thin plate without the dissipation. In Sec.4, we discuss the behaviors of the stable SH wave and the conditions to obtain the wave. Section 5 concludes this paper.