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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.

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In this study, an improved third order shear deformation theory is used to analyze the thermoelastic buckling of a functionally graded rectangular plate. The plate is assumed to be under two types of thermal loading, namely, uniform temperature rise across the thickness and linear temperature change across the thickness of the plate. Moreover, the material properties of the functionally graded plate vary linearly through the thickness and simply supported are considered for all edges of the plate. First, the nonlinear strain-displacement relations are considered based on improved third order theory and then the equilibrium and stability equations are derived. In continue, displacements and the pre-buckling forces are calculated using the equilibrium equations. The temperature difference relation of buckling is obtained by solving the stability equations. To obtain the critical temperature difference, the recent relation is minimized with respect to the number of half wave parameters. Resulting equations are compared with the literature. The results show that, the values of temperature difference buckling obtained based on improved third order shear deformation theory, are lower compared with the classical plate theory, first and third order shear deformation theories. Moreover, the value of critical temperature difference under linear temperature change is bigger compared with the uniform temperature rise across the thickness, and the difference between the two values will be bigger with increasing the thickness of the plate.