Computation of axisymmetric nonlinear low-frequency resonances of hyperelastic thin-walled cylindrical shells

Abstract

Abstract A mathematical modeling is employed to investigate the axisymmetric nonlinear low-frequency vibrations of a class of hyperelastic thin-walled cylindrical shells subjected to axial harmonic excitations. A modified frequency domain method is presented to determine the stability of periodic solutions. Based on the variational method, the system of nonlinear governing differential equations describing the coupled axial-radial vibrations of simply supported shells is derived. Then, the harmonic balance method and the arc length method with two-point prediction are adopted to obtain the complicated steady-state solutions effectively, and the stability is discussed with the modified sorting method. Significantly, numerical results manifest that the length-diameter ratio serves a critical role in the nonlinear low-frequency vibrations, its variation should give rise to abundant nonlinear phenomena, such as the typical softening and hardening, the resonance peak shift and the isolated bubble shaped response.