Modeling and vibro-acoustic behavior analysis of a plate-cavity coupling system equipped with a nonlinear energy sink

This study establishes a three-dimensional model of a local NES-plate-acoustic cavity coupling system and investigates the nonlinear vibro-acoustic response of the NES-equipped plate coupled with the acoustic cavity and the control effect of the NES on the plate-cavity coupling system. Using the energy method to construct the governing equation of the coupled system, the vibro-acoustic behavior of the system is solved by the harmonic average approach and numerical integration method. The correctness of the results is proved through the comparison with the reference and mutual verification between different methods. On this basis, the control effect of NES on the vibration response and sound pressure response of the plate-cavity coupling system is investigated. It is found that NES exhibits a good control effect on the higher plate-controlled (PC) modal response peak, while showing a limited control effect on the lower PC modal response peak and the cavity-controlled (CC) modal peak. Due to the installation of the NES, various complex dynamic behaviors are generated in the unstable response area of the plate and cavity. At this time, the vibration state of sound pressure in the cavity is consistent with the vibration state of the plate, but the frequency distribution is different. The targeted energy transfer (TET) phenomenon between the NES and plate occurs at some frequencies. Furthermore, the nonlinear stiffness and concentrated mass of NES have a great influence on the response of the coupled system, and the damping effect of NES plays a major role in higher-order resonance response. When the damping and nonlinear stiffness are constant, an optimal value for the mass of NES exists to minimize the peak response. Finally, the comparison of vibro-acoustic characteristics of the plate-cavity coupling system equipped with the NES and TMD are investigated.