Nonlinear vibrations of a shallow arch under a low frequency and a resonant harmonic excitations

In the present work we investigate analytically and numerically nonlinear dynamics of a two degrees of freedom model of a shallow arch subject to a resonant external harmonic forcing and to a very slow harmonic imposed displacement of one of its supports. Charts of behaviors are determined, especially the zones of existence of periodic bursters and chaos. Periodic bursters are found to exist in the boundaries of the instability regions. Various bursters involving fixed points, quasi-periodic and chaotic solutions are found. More importantly, it is shown that small amplitudes of the slow parametric excitation may suppress chaos from wide regions of control parameters.

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