Bending analysis of double viscoelastic nanoplates based on the modified couple stress theory and relaxation theory

Based on the modified couple stress theory and stress relaxation phenomenon, the governing equation of motion for a double viscoelastic nanoplate system is established, and the bending analysis of the system is performed. Using Navier's method, an analytical solution of the transverse relative deflection for two nanoplates is obtained. The effects of geometrical and physical factors on the bending behavior of the system are discussed. It is concluded that the transverse relative deflection of two nanoplates depends upon the relaxation time, ratio of the delayed to initial extensional elastic moduli, and damping parameters.