抄録
This paper examines the validity of Galerkin's procedure for analyzing continuous systems with a cubic geometric nonlinearity. As an example, we treat a simply supported beam and consider the effect of the midplane stretching. The near-resonant response of two lateral directions is investigated for the case in which the natural frequencies of the lateral modes are commensurate in a near one-to-one ratio. For this purpose, we discretize the nonlinear governing equation by using Galerkin's procedure where the displacement of the beam is approximated by the linear mode shapes, and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions, they are compared with the solutions obtained by the finite difference method. Furthermore, not only periodic but also quasi-periodic and chaotic responses are presented.
