Dynamic Modeling and Experimental Study of a Hyperelastic Cylindrical Shell for Vibration Reduction Using a History-Driven Incremental Iteration Method

This paper presents an equivalent mechanical model for hyperelastic cylindrical shell (HCS) structures, developed using a history-driven incremental iteration method to clarify the influence of external excitation on their frequency response function under dynamic loading. The approach, grounded in the conventional linear vibration mechanics framework, iteratively integrates dynamic characteristic changes resulting from unit deformations along their historical evolution, thereby transforming continuous nonlinear variations into discrete linear increments. In combination with a sine-sweep vibration experiment, the variation trends of equivalent dynamic stiffness and damping with displacement amplitude at different excitation levels were determined, clarifying the excitation-induced mechanisms affecting the frequency response of HCS structures. The results showed that, under resonance conditions, increasing the excitation amplitude from 1.5[Formula: see text]g to 3.5[Formula: see text]g raised the displacement amplitude from 0.84[Formula: see text]mm to 3.08[Formula: see text]mm. Concurrently, the equivalent dynamic stiffness decreased from 4.38[Formula: see text]kN/m to 2.86[Formula: see text]kN/m, while the equivalent dynamic damping decreased from [Formula: see text] to [Formula: see text]. This reduction in stiffness and damping caused the HCS structure to enter resonance and vibration–isolation states earlier, completing the phase transition within a narrower frequency range in the sharp phase-transition region. Clarifying these mechanisms promotes a shift in hyperelastic shell design from empirical trial-and-error methods to model-driven approaches, thereby supporting the broader application of hyperelastic shell structures in vibration engineering.