Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro/nanolaminated composite Euler–Bernoulli beam under thermal loading

Abstract

In this paper, the effect of finite strain on the nonlinear free vibration and bending of the symmetrically micro/nanolaminated composite beam under thermal environment within the framework of the Euler–Bernoulli and modified couple stress theory is studied. The governing equation of motion and boundary conditions are obtained using Hamilton’s principle, and then they are solved by generalized differential quadrature method. The bending and free vibration of the beam are investigated for both carbon/epoxy and glass/epoxy materials based on the finite strain and von Karman assumptions subjected to different boundary conditions. Also, two different fiber orientations including unidirectional and cross-ply are considered in this research. Comparison of the bending results show that there is a significant difference between the finite strain and von Karman particularly for [Formula: see text]. Furthermore, it is found that the natural frequencies predicted by the finite strain are more than the von Karman. Also, when the microbeam is inserted under thermal loading, the natural frequencies increase.