Nonlinear Vibrations of Thermo-Hyperelastic Moderately Thick Cylindrical Shells with 2:1 Internal Resonance

Abstract

The nonlinear vibration of a hyperelastic moderately thick cylindrical shell with 2:1 internal resonance in a temperature field is investigated based on the third-order shear deformation theory. A radial harmonic excitation is applied to the shell. First, by employing the higher-order approximation for the curvature-related expansion, the displacement field of the moderately thick cylindrical shell with improved coefficients is derived. For the temperature field with gradient, the shear modulus of the shell is thickness dependent because of the temperature-dependent nature of the hyperelastic materials used. The graphical results manifest that the temperature gradient has a significant impact on the nonlinear vibration of the shell. In addition, the separation of the resonance peak caused by the variations of the structural parameter and temperature will result in a bubble shaped response curve for the shell.