Non-linear dynamic response of shallow arches to harmonic forcing

The investigation of the dynamic response of a shallow arch to harmonic forcing is undertaken. The method of harmonic balance, coupled with a continuation scheme, is used to determine 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. Results are presented for a range of loading at three excitation frequencies. In addition, the effect of the excitation frequency on the response for three fixed values of the magnitude of the loading is investigated. The dynamic response of the arch to harmonic forcing is shown to exhibit both symmetric and asymmetric solutions. Additionally, stable solutions are found that have a fundamental period of an integer multiple of the excitation period. Finally, regions of chaotic motion are observed.