Nonlinear Dynamic Characteristics of Incompressible Hyperelastic Plates with Different Constitutive Relations

Hyperelastic plates have excellent mechanical properties and are widely used in fields such as engineering and machinery. In practical working conditions, the plates are inevitably affected by external forces. Therefore, research on the nonlinear dynamics of hyperelastic plates is of significant importance. Considering the Mooney–Rivlin, Yeoh and neo-Hookean models, the nonlinear dynamic characteristics are analyzed for the incompressible hyperelastic plates. Utilizing the plate theory, hyperelastic theory and energy variational method, the governing equations of the hyperelastic plates are derived. The relations between the vibration amplitudes and the excitation frequencies are presented, and the effects of different parameters on the nonlinear dynamic behaviors of hyperelastic plates are analyzed. From the numerical results, it can be observed that the hardening behavior is more pronounced under an external excitation and structural parameters. The strange attractor exhibits stretching and twisting under different parameters, further demonstrating the chaotic vibrations of the plate under different constitutive relationships. Compared with those of the other two hyperelastic models, the Yeoh plate exhibits the largest vibration amplitude and the neo-Hookean plates are more likely to generate chaotic vibrations. The research presented in this paper contributes to the theoretical framework for both chaotic system regulation and the identification of resonance thresholds, thereby enabling proactive prevention of resonance-related failures.