Limit cycles and acoustic radiation analysis of a van der Pol oscillator-plate-medium system

Abstract

The approximate analytical solution of the limit cycle and the acoustic radiation characteristics of a nonlinear vibro-acoustic coupling system consisting of a non-autonomous van der Pol oscillator, a plate, and the surrounding acoustic medium are investigated. The nonlinear coupling equations of the vibro-acoustic coupling system under external excitation are derived using variational theory. The modal expression method and the incoherent superposition assumption are employed to discretize the displacements and the surface acoustic pressure of the plate, and then the incremental harmonic balance (IHB) method is used to drive the approximate analytical expressions for the limit cycles of the coupling system. The acoustic radiation power level and the surface average velocity under multi-frequency excitation are defined to describe the response of the plate. The results are that there are limit cycle motions in the vibration of the vibro-acoustic coupling system due to the van der Pol oscillator’s excitation, and there are more harmonic components in the system when the parameters are increased. The vibro-acoustic characteristics of the plate present nonlinear variation because of the oscillator’s nonlinear damping force. The method combining the IHB method and the modal expression method can be used to investigate the nonlinear vibro-acoustic coupling characteristics of a structure under external and self-excited excitation.