A nonlinear oscillator model for an acoustic resonance chamber.

The exact nonlinear acoustic wave equation, derived from conservation of momentum, mass, and the equation of state, was used to average out the spatial dependence and obtain a forced anharmonic oscillator equation for the time-dependent part. The non-linearity is expressed by a resistive-restoring coupling term [open_aye]xx, rather than the restoring term αx2 + βx3 in the modified Duffing equation. A solution is sought in the form of a Fourier series, including all harmonics, and the equation is solved by a perturbation technique, retaining the dominant term in each harmonic. This results in an infinite system of coupled, nonlinear algebraic equations and leads to non-Lorentzian response curves for a sinusoidally driven resonator. These response curves are evaluated numerically and compared with predictions of the Duffing equation and with recent measurements of response curves and harmonic generation in an acoustic resonance chamber (M. Barmatz, N. Jacobi, and J. Stoneburner, 10th International Congress on Acoustics, Sydney, 1980). [Work supported by NASA.] [ABSTRACT FROM AUTHOR]