Thermal buckling and post-buckling analyses of rotating Timoshenko microbeams reinforced with graphene platelet

Abstract

A comprehensive study is established to investigate on the thermal buckling instability and the subsequent post-critical deflection of a rotating nanocomposite microbeam reinforced with graphene platelet. The main scope of the current research is shedding light on the effectiveness of reinforcing a rotating microbeam with graphene platelet subjected to a constant temperature development. The Timoshenko beam theory comes along the von-Karman strain displacement relations to extract the governing equations of motion in accordance with the modified couple stress theory. The modified Halpin–Tsai micromechanical model is implemented to determine the practical elasticity modulus of the nanocomposite beam. The Ritz technique is accompanied by the Chebyshev orthonormal polynomial set to discretize the weak form of the nonlinear equations of motion. The Newton–Raphson technique is applied to the discretized static nonlinear equations of motion to compute the static deformation due to the centrifugal force. On the basis of two effective algorithms the nonlinear equations of motion are attacked to find out the critical buckling temperature change as well as the succeeding post-critical deflection. It is observed that adjoining the graphene phase in the form of an X-pattern promotes the static strength of a rotating microbeam against the buckling instability. However, in contrast, for stationary microbeams and microbeams that rotate with a velocity below a threshold speed adjoining the graphene platelet reinforcement in the form of an O-Pattern not only does not strengthen the microbeam but also weakens it against the buckling instability. Moreover, the buckling modeshape of rotating simply-clamped microbeams is more impressed by the graphene phase.