Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory

Vibration of orthotropic double-layered graphene sheets under hygrothermal conditions is investigated in this paper using the trigonometric shear deformation plate theory. This theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional shear deformation theory, the present trigonometric theory contains only two unknowns. The two layers are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundations. The equations of motion are derived based on the nonlocal theory. The motion equations contain the small scale effect as will as hygrothermal effect. The present solution is examined by comparing the present results with those being in the open literature. The effects played by small scale parameter, temperature rise, the degree of moisture concentration, plate aspect ratio and side-to-thickness ratio are studied.