Thickness-stretched model for thermal vibrational behaviors of graphene origami reinforced doubly curved

Higher-order vibrational behavior of a shear deformable doubly curbed shell is studied in this article based on a thickness-stretched model. The shell is assumed composed of Copper matrix enriched with graphene origami in which the effective modulus of elasticity, Poisson's ratio, density and heat expansion coefficients are estimated through micromechanical model including four modification coefficients. The thickness-stretched model assumes the transverse deflection as summation of three parts named as bending, shear, and stretching ones where the third part simulates thickness-dependent of transverse deflection. The Hamilton's principle is extended for derivation of the governing equations of motion and the numerical results are obtained through the analytical method. A verification study is presented for approving the formulation, solution methodology, and numerical results. The natural frequencies are presented in terms of thermal loading, graphene amount, folding degree, geometric parameters of the shell, and graphene origami. The mentioned results are presented with and without thickness stretching effect. A comment on the difference between them is added to the results. The results show this fact that the results based on without thickness stretching is more than ones based on with thickness stretching. The full numerical results are presented to investigate effect of material and geometric characteristics on the thermal vibration results of the reinforced doubly curved shell.