Escape, crossing and cut-off frequencies of SH waves in nonlocal piezoelectric nanoplates

An improved Legendre polynomial series approach (I-LPSA) is proposed to investigate the SH wave in nonlocal piezoelectric nanoplates. Different from the open LPSA only for classical structures, the I-LPSA can be used both for nonlocal nano and classical ones. Meanwhile, the boundary conditions are realized quickly by the iterative calculation of integral containing nonlocal factor and Legendre polynomial. The comparative study shows the correctness of the I-LPSA. Moreover, the solution formula of escape frequency with nonlocal parameter and piezoelectric constant is deduced, and indicates that escape frequency is independent of the boundary conditions. Besides, the novel modal compression can be predicted by the proposed cut-off frequency formula. More meaningfully, several dispersion curves cross at one point under the nonlocal effect, which does not appear in classical theory. And the formula of crossing frequency is presented to predict the dispersion laws.