Primary and Secondary Resonance Analyses of Hyperelastic Thin Cylindrical Shells Under Radial Harmonic Excitation

This paper studies the primary and secondary resonance responses of a hyperelastic thin cylindrical shell to a mono-frequency radial excitation under simply supported boundary conditions. First, for an incompressible Mooney–Rivlin material, the motion equations are derived based on Donnell’s theory for shallow shells and the Lagrange equation. By applying the static condensation method to eliminate the effect of small membrane displacements, one generalized Duffing equation is obtained to illustrate the system’s large radial deflection. Initially, the weak nonlinearity of the problem is examined to validate the multiple-scale method as an effective analytical technique. The novelty of this work lies in performing a multiple-scale analysis of superharmonic and subharmonic resonances in a thin hyperelastic cylindrical shell. The system’s response is analyzed by examining the impact of load and geometric parameters. Moreover, the influence of excitation frequency on the amplitude-excitation load behavior of the structure is explored across 1/3 subharmonic, primary and third-order superharmonic resonances. The results show that for primary resonance, there is a strong hardening behavior and a slight softening. Additionally, the frequency response curve for superharmonic resonance consistently shifts to the right. The system’s response in both primary and secondary resonances is profoundly affected by geometric parameters.