Selection of size dependency theory effects on the wave's dispersions of magneto-electro-thermo-elastic nano-beam resting on visco-elastic foundation

Current research develops a comprehensive wave propagation analysis of a magneto-electro-thermo-elastic (METE) nano-beam (NB) resting on the visco-elastic medium. To model the size dependency effects, modified couple stress (MCS) and Eringen's nonlocal (ENL) theories are employed to analyze and describe the wave propagation behaviors for those nano-beams. These theories were the most used in the literature due to the inclusion of one additional size-dependent length scale parameter. Those theories are compared side by side in this investigation and their impacts/differences on the wave propagation of specific materials are explored. Sinusoidal shear deformation beam model with Hamilton's principle is adopted to develop the governing equations of motion. Then, an analytical solution is executed to extract numerical results for transverse wave propagation in both elastic and METE configurations of the nano-beam. The effects of size-dependent length scale of both theories, thickness of NB, Winkler-Pasternak coefficients, thermal gradient, and magnetic potential and external electric voltage are illustrated and discussed in details. It is concluded that wave frequency decreases with increment of nonlocal parameter for ENL model. On the other hand, a stiffening effect takes place for the wave frequency when the MCS model is considered. Hence, the results indicate that there is a significant difference between ENL and MCS theories in the estimation of the behavior of wave propagation in small-scale structures. One of the main results of this investigation indicates that the MCS theory has similar nonlocal effects as the Eringen's theory for specific conditions.

Automated summary

This study presents a comprehensive analysis of wave propagation in magneto-electro-thermo-elastic nano-beams resting on visco-elastic media. The wave propagation behavior of nano-beams is analyzed using modified couple stress (MCS) and Eringen's nonlocal (ENL) theories, which include size-dependent length scale parameters. The study compares the two theories and explores their impacts and differences on wave propagation. The results reveal that the wave frequency decreases with the increase of the nonlocal parameter in the ENL model, while a stiffening effect occurs when considering the MCS model. The study concludes that there is a significant difference between the ENL and MCS theories in estimating the behavior of wave propagation in small-scale structures.