Extraction of dispersion curves for lamb waves in an aluminium nitride (AlN) micro plate using consistent couple stress theory

The equations of Lamb wave propagation in an infinite isotropic micro plate with finite thickness on the basis of consistent coupled stress theory is presented in this study. By employing the characteristic length scale parameter, the effect of micro-plate size is considered, and thereby the effects of different plate dimensions on the dispersion of Lamb waves is illustrated. Lamb wave propagation velocity in aluminum nitride micro-plates has received many interests due to its applications in surface acoustic resonators. In the current work, at first, the dimensionless relations are developed through the definition of dimensionless parameters where the extracted curves can be applied to all thicknesses, propagation wavelengths and characteristic length scale parameters of a micro-plate. In addition, using the quasi-static approximation, the Lamb wave dispersion curves in both symmetric and asymmetric modes for an aluminum nitride micro plate are plotted and compared with the results from the classical theory. The integrity of the present formulation is verified by comparing the obtained results with the experimental data in the literature. Finally, by employing the dispersion curves and the reported experimental data, a novel method has been proposed to determine the size of characteristic length parameter in the consistent coupled stress theory.