Technical Briefs

Nonlinear Amplitude-Frequency Response of a Helmholtz Resonator

[+] Author and Article Information
G. K. Yu

Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, Chinaygaokun@yahoo.com.cn

Y. D. Zhang, Y. Shen

Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China

J. Vib. Acoust 133(2), 024502 (Mar 03, 2011) (3 pages) doi:10.1115/1.4002958 History: Received September 18, 2009; Revised July 28, 2010; Published March 03, 2011; Online March 03, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Amplitude-frequency response curve with parameters δ2=0.5044, γ3=0.4, and μ1=0.45. The point in the curve denotes the maximal response amplitude.

Grahic Jump Location
Figure 2

Dependence of the maximal response amplitude |rmax| and corresponding frequency detuning β2 on phase ϕ. The parameters are δ2=0.5044, γ2=0.2, γ3=0.05, and μ1=0. The point in this figure denotes the maximal response of the first case.



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