Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber

In order to apply the nonlinear energy sink (NES) to reduce the low-frequency noise inside a 3D acoustic cavity with an impedance boundary, a two degrees-of-freedom (DOF) dynamic model of the coupled system of one damped acoustic mode of a regular 3D acoustic cavity and a nonlinear membrane absorber as the NES is established. The damping coefficient of the acoustic mode is obtained based on the finite element analysis method and the relationship of the boundary impedance and the absorption coefficient of the cavity. Based on the set-up of the system, the damping coefficient of the acoustic mode is determined. The frequency responses and the targeted energy transfer (TET) phenomenon of the coupled system are analyzed, and the theoretical and numerical results of the frequency responses of the system are in good agreement with the experimental ones. The effects of the wall impedance of the cavity on the optimal TET are discussed. With the increase in the impedance ratio of the wall, the amplitude of the acoustic displacement plateau decreases, and the frequency bandwidth of the plateau and the two thresholds of the optimal TET interval of the excitation increase. It provides a comprehensive theoretical model and experimental basis for the application of NES in the actual complex structure and provides a reliable design method and control strategy for controlling vehicle interior low-frequency broadband noise