3:1 internal resonance behavior of thermo-hyperelastic moderately thick-walled cylindrical shells subjected to a steady-state temperature field

In practical engineering applications, hyperelastic cylindrical shells are frequently subjected to complex environmental and mechanical loadings, which can induce intricate nonlinear dynamic behaviors. This study investigates the nonlinear dynamic responses of thermo-hyperelastic Mooney-Rivlin cylindrical shells under radial harmonic excitation in a steady-state temperature field. By incorporating thermal effects, the governing differential equations are derived using the temperature-dependent thermo-hyperelastic Mooney-Rivlin constitutive model, higher-order shear deformation theory, and Lagrange's equations. The accuracy of the proposed model is validated, and the influences of temperature and structural parameters on natural frequencies are systematically examined. Furthermore, the critical conditions for 3:1 internal resonance are identified. Approximate analytical solutions are obtained using the harmonic balance method combined with a modified arc-length continuation technique, whereas numerical solutions are derived via the fourth-order Runge-Kutta method. An extensive parametric study is conducted to reveal the effects of key parameters on the resonant and chaotic dynamic responses of the shell structures. The results show that the mean temperature governs both the global stiffness of the thermo-hyperelastic Mooney-Rivlin material and the evolution of the system response state. An increase in mean temperature significantly raises the probability of chaotic responses. In contrast, the temperature gradient mainly regulates the modal energy distribution and selectively affects individual vibration modes, with a relatively weaker influence on the overall response evolution. These findings provide theoretical guidance and engineering references for the dynamic design, vibration control, and safety assessment of hyperelastic cylindrical shell components serving in steady-state high-temperature environments, such as aerospace thermal protection systems, high-temperature pressure vessels, deep-sea high-temperature pipelines, and nuclear engineering facilities.