Wave propagation in double nano-beams in thermal environments using the Reddy's high-order shear deformation theory

We study the bending wave, shear wave and longitudinal wave characteristics in the double nanobeams in this paper for the first time, in the process of research, based on the Reddy's higher-order shear deformation theory and considering shear layer stiffness, linear stiffness, inter-laminar stiffness, the pore volume fraction, temperature variation, functionally graded index influence on wave propagation, based on the nonlocal strain gradient theory and Hamilton variational principle, the wave equation of the double-nanometer beams are derived. Since there are three different motion states for the double nanobeams, which includes the cases of "in phase", "out of phase" and "one nanobeam fixed", the propagation characteristics of shear-, bending-, and longitudinal- waves in these three cases are discussed respectively, and some valuable conclusions are obtained.