Vibrational behavior of thermally pre-/post-buckled FG-CNTRC beams on a nonlinear elastic foundation: a two-step perturbation technique

Abstract

The current research is concerned with the small- and large-amplitude free vibrations of a composite beam made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) media. It is assumed that the beam is operating in a uniform temperature field, which results in thermally pre-buckled or post-buckled configurations. It is further assumed that a three-parameter nonlinear elastic foundation is in contact with the beam during deformation which acts in compression as well as in tension. The elastic material properties of the beam are evaluated by using a modified rule of mixtures scheme which contains efficiency parameters. The thermomechanical properties of the beam are assumed as temperature dependent. The motion equations of the beam are established using three different beam models, namely first-order, third-order, and sinusoidal beam theories. The obtained equations are reformulated using the fact that both ends of the beam are immovable in axial direction. The established equations are transformed into dimensionless presentation. After that, suitable for beams with both ends pinned, with the aid of the two-step perturbation technique, closed-form expressions are provided for small- and large-amplitude free vibrations of FG-CNTRC beams in thermally pre-buckled or post-buckled states. Results of this study are first validated with the available data in the open literature. After that, novel numerical results are provided to explore the effects of geometrical parameters of the beam, foundation stiffness, temperature variation, and different beam theories.