Nonlinear dynamic response of shallow arches

Abstract

Buckled beams and shallow arches exhibit nonlinear force-deflection curves as a result of their geometric shape. These structural components share the common characteristic of nonlinear loaddeflection curves, exhibiting both stable and unstable equilibrium states. Previous work has shown that with the application of sufficiently large static or dynamic loads, snap-buckling can occur, in which the structure suddenly jumps from one stable equilibrium configuration to another. The dynamic response due to harmonic forcing has been shown to contain orbits encompassing either of the stable equilibrium positions, or orbits encompassing both the stable and unstable equilibrium positions. The investigation of the dynamic response of a shallow arch is undertaken using a two rigid-link, singledegree-of-freedom model. The method of harmonic balance, coupled with a continuation scheme, is used to find the solutions for an entire range of externally applied loading. Floquet analysis provides the requisite stability information, as well as information about the bifurcation points encountered in the solution. The dynamic response of the arch to harmonic forcing is shown to exhibit both symmetric Ph. D. Candidate Mcmbcr AIAA