Rate of surface energy changes on the wave propagation analysis of METE nanoplates based on couple stress small-scale and nonlocal strain gradient theories

The modified couple stress and nonlocal strain gradient small-scale models are manipulated to scrutinize generally the rate of surface energy layer changes on the wave propagation analysis of a rectangular magneto-electro-thermo-elastic (METE) nanoplate. The METE nanoplate is a compound of BiTiO 3 –CoFe 2 O 4 nanomatters. The presented model considers concurrently modified couple stress, nonlocal, strain gradient, and surface energy hypotheses. Using the refined plate theory (RPT), which is a suitable plate theory in comparison with the other models, the nonclassical governing equilibrium equations are derived according to Hamilton's principle. The RPT has been implemented for the first time, based on the authors' knowledge, to derive the presented governing equilibrium equations through the modified couple stress hypothesis. With incorporating the impacts of diverse external in-plane loads, an analytical solution is utilized in order to compute the rate of surface energy variations upon the wave propagation of a rectangular METE nanoplate. For exactness of the anticipated model, the procured results are compared with those formerly mentioned outcomes in the literature. The results of the present study represented that for the wave propagation analysis of the METE nanoplate, the modified couple stress and strain gradient small-scale coefficients would have a reverse influence on the rate of surface layers changes in comparison with that of nonlocal one.