Wave propagation analysis of magneto-electro-thermo-elastic nanobeams using sinusoidal shear deformation beam model and nonlocal strain gradient theory

The main goal of this research is to provide a more detailed investigation of the size-dependent response of magneto-electro-thermo-elastic (METE) nanobeams subjected to propagating wave, employing sinusoidal shear deformation beam theory (SSDBT). With the aim to consider the size influences of the structure, the nonlocal strain gradient theory (NSGT) is utilized. Hamilton’s principle within constitutive relations of METE materials is incorporated to derive thegoverning equations. Utilizing Maxwell’s relation and magnet-electric boundary conditions, proper distributions for magnetic and electric potentials along the nanobeam are obtained. Thereafter an exact analysis is used to obtain the axial and flexural dispersion relations of METE nanobeams. In numerical results, detailed investigations of wave dispersion behavior related to three modes are addressed. In addition, a relation is introduced to determine the cut-off frequency of the system. Moreover, the effectiveness of various parametersincluding length scale and nonlocal parameters, nanobeam thickness, and theloadings due to imposed thermo-electro-magnetic field on the response ofpropagating wave in METE nanobeams are examined.