Nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) beams subjected to aero-thermal loads

This paper studies the nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) cantilever beams subjected to aero-thermal loads. The nonlinear partial differential equations governing the problem are determined based on the Euler-Bernoulli beam theory using the von K ' arm ' an-type geometrical nonlinearities. The Galerkin method is then applied to discretize the differential equations and to transform them into a nonlinear ordinary differential equation. The coupled ordinary differential equations are solved analytically using the method of multiple time scales (MTS) to study the nonlinear forced vibration time response of the selected FG-FRCL structures, where a large parametric study checks for the effect of power-index, uniform temperature rise, velocity of the free stream air and Mach number on their axial and lateral response, with interesting insights from a scientific and design purposes.