Abstract： From viewpoint of nonlinear dynamics, the shallow arch under impact can be considered as a continuous dynamic system or dynamic system with infinite dimension. The governing equation for the shallow parabolic arch under impact is derived following the nonlinear shell theory. Then, a new nonlinear Galerkin method, namely, Inertial Manifolds with Time Delay, is developed and applied to the dynamic buckling analysis of shallow arch, which is governed by a set of nonlinear partial differential equations. By this method, the solutions of the governing equations are projected onto the complete space spanned by the eigenfunctions of the linear operator of the governing equations. In comparison with traditional Approximate Inertial Manifolds(AIMs), the relationship between the high and low modes is improved by Approximate Inertial Manifolds with Time Delay (AIMTDs), that is, not only the instantaneous relationship is considered, but also the past behaviors. Finally, the method is applied to the dynamics buckling analysis of the shallow arch under impact, and the comparisons between traditional Galerkin's procedure, traditional AIMs, and AIMTDs are given. It can be concluded that the methods presented are effective for the dynamic buckling analysis of continuous dynamic system.
2009, Vol. 28 
