Internal resonance characteristics of hyperelastic thin-walled cylindrical shells composed of Mooney–Rivlin materials

Abstract

The internal resonance characteristics are investigated for a thin-walled cylindrical shell composed of incompressible Mooney–Rivlin material, where the shell is subjected to a radial harmonic excitation. Based on the Kirchhoff–Love hypothesis, Donnell’s nonlinear shallow-shell theory and variational principle of energy, the coupled nonlinear differential equations, describing the radial motion of the shell, are obtained. The existence condition of 2:1 internal resonance is given via examining the natural frequencies of different modes. Then the multiple scale method is applied to derive the amplitude–frequency relations in the presence of 2:1 internal resonance, and the stabilities of steady-state responses are determined. In addition, the accuracy of the model is verified by using a homogeneous cylindrical shell with simply supported boundary conditions, some comparisons are made with the previous published researches and good agreement is found. The effects of excitation amplitudes and the structure parameters on the resonance responses of the system are examined. Numerical results show that the range of resonance increases along with the excitation amplitude; the typical phenomenon of double-jumping appears, and the generation and vanishing of double peaks are related to the values of structure parameters.