Formulation of SH wave characteristics in nonlocal nanoplates

Abstract

The scale effect of mechanical properties is one of the most critical issues in application of the nanostructures. In order to study the scale effect on SH waves in nanoplates, a Legendre polynomial series method combined with the nonlocal theory (N-LPSA) is developed in this paper. The presented method enables the boundary condition achieved quickly by the derived iterative solution formula of the integral, which contains nonlocal factors and Legendre polynomials.Besides, the formula of escape frequency is deduced analytically to facilitate the study of wave propagation law. Numerical comparisons show the correctness of the N-LPSA. The results indicate that cut-off frequencies of some higher-order modes are higher than their escape frequencies. The anisotropy with the nonlocal effects can lead to the intersection of the modal curves, which does not appear in classical structures. Moreover, the fitting formulas of cut-off and crossing frequencies are developed to predict the compression and the intersection of the modal curves, respectively.