Nonlinear vibrations of a shallow arch subject to resonant and low harmonic frequency excitations under 1:1 internal resonance

Abstract

In the present work the nonlinear dynamics of a two degree of freedom shallow arch model, excited by resonant external harmonic forcing and subject to an imposed slow harmonic motion of its support, are investigated. The case of 1:1 internal resonance between the first and the second bending modes is studied. The charts of behaviors are obtained analytically using the multiple scales method, both in the presence and the absence of the slow excitation, and they are validated numerically. It is shown that the low parametric frequency excitation triggers the existence of periodic bursters in vicinity of the boundaries between the different dynamics of the arch.