A general comparison the surface layer degree on the out-of-phase and in-phase vibration behavior of a skew double-layer magneto–electro–thermo-elastic nanoplate

The present study investigates and compares the value of the surface layers on the out-of-phase and in-phase vibration behavior of skew double-layer magneto–electro–thermo-elastic (DLMETE) nanoplates. These two nanoplates are coupled by an elastic medium named van der Waals forces; furthermore, the DLMETE nanoplates are surrounded by Winkler and the shear moduli of elastic foundations. The two nanoplates are moving in the same direction in the out-of-phase case; in contrast, in the in-phase mode, those two nanoplates are moving in the opposite direction. Manipulation of the refined plate, surface energy, and nonlocal hypotheses is done to expand the governing equations; furthermore, Hamilton's principle is utilized to derive the equilibrium equations. Galerkin method is also employed to solve these equations. In addition, for the validation of those equations, the Navier's method is used. The present research is, therefore, concerned with the effect of the main parameters, namely, external electric potential, external magnetic potential, in-plane mechanical force, elastic foundations, skew angle, and temperature change, on the rate of surface layers of the out-of-phase and in-phase vibration behavior of a skew DLMETE nanoplate. By increasing the skew angles, the in-phase and out-of-phase natural frequency ratios are shown to be converged; following a specific value of skew angle Ψ ≥ 70°, they overlap. By raising the skew angles, the effects of the van der Waals modulus on the vibration behavior are undermined. Therefore, the results of the present work could contribute to designing NEMS/MEMS components which make use of smart composite nanostructures.