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

Cylindrical shells are widely applied in the fields of manufacturing, shipbuilding, aerospace and so on, which are subjected to different types of dynamic loads inevitably. As typical dynamic behaviors of cylindrical shells, axisymmetric vibrations have drawn extensive attention in many engineering fields [1?5] . Rubber pipelines are usually used for energy transportation applications, which are modeled with hyperelastic cylindrical shells [6 , 7] . Moreover, hyperelastic shells also have many advantages to model the finite dynamic deformations of arteries [8] . Undoubtedly, an in-depth understanding on the axisymmetric nonlinear vibration characteristics of hyperelastic cylindrical shells are essential to the design and manufacture. The primary difficulty in modeling the nonlinear vibrations of hyperelastic cylindrical shells lies in incorporating the 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. (c) 2021 Elsevier Inc. All rights reserved.