Nonlinear Amplitude-Frequency Response of a Helmholtz Resonator

Abstract

Nonlinear amplitude-frequency response of an acoustic Helmholtz resonator is investigated by incorporating linear damping, nonlinear damping, and nonlinear restoration. Method of multiple time scale is used for theoretical analysis, and a reasonable explanation of an experiment observation, i.e., the downward shift of resonance frequency, is given. We also discuss the response of two-frequency driving, and find that amplitude-frequency response depends on the phase difference of the driving. In addition, the response amplitude of two-frequency driving can increase approximately 10% as compared with the single frequency driving at a certain phase difference for the parameters we choose to simulate.