Nonlinear propagation of multi-frequency acoustic waves induced by vibration of hyperelastic structures under internal resonance

Nonlinear acoustic propagation plays a crucial role in many practical applications, such as medical therapy and underwater communications. However, the nonlinear propagation behavior of multi-frequency acoustic waves radiated from nonlinear vibrating structures remains insufficiently understood. This study develops a coupled structural-acoustic model to numerically investigate the nonlinear acoustic radiation and propagation from a hyperelastic structure undergoing nonlinear vibration. Both geometric and material nonlinearities are incorporated into the finite element model of the structure, while nonlinear acoustic propagation in the surrounding fluid is solved using a high-order finite-difference time-domain scheme. The fluid-structure coupling is achieved through an improved immersed boundary method, which ensures the implicit satisfaction of compatibility conditions at the interface. Based on this framework, the nonlinear transient acoustic responses of the hyperelastic structure are examined, and the effects of the fluid nonlinearity parameter B/A and excitation amplitude on multi-frequency wave interactions are systematically analyzed. The numerical results demonstrate that the multi-frequency response induced by structural nonlinearity provides the necessary foundation for nonlinear wave-wave interactions, which, in turn, redistribute energy in different frequency components and modify the spatial patterns of high-order acoustic harmonics.