Internal resonance induced nonlinear vibration and acoustic radiation of a hyperelastic cantilever structure immersed in fluid

Hyperelastic structures can exhibit peculiar nonlinear vibration and acoustic behavior due to the existence of geometric and material nonlinearities. In order to comprehend the nonlinear vibro-acoustic responses of a hyperelastic cantilever structure configured with internal resonances, a finite element model that considers both the geometric and material nonlinearities in the structure and the finite-amplitude acoustic waves has been developed. The vibro-acoustic problem is described in an arbitrary Lagrangian-Eulerian frame with perfectly matched layers. Based on the finite element model, a loosely coupled serially staggered procedure is applied to solve the nonlinear governing equations. It is found that with large harmonic axial excitation applied to the hyperelastic cantilever structure, the structural vibration undergoes an axial-to-bending transition due to the 2:1 internal resonance, resulting in the variation of acoustic directivity and frequency characteristics. This transition of vibration form occurs quickly when the excitation amplitude is larger or the excitation frequency is closer to the frequency of the axial mode. A threshold of dissipation energy is proposed to determine the transition of the structural and acoustic responses due to nonlinear internal resonance. Saturation of the structural vibration and acoustic responses is observed in the frequency components associated with the first axial mode of the hyperelastic structure, which only exists in the case of the occurrence of the axial-to-bending transition.