A theoretical investigation of high amplitude standing waves in an acoustical resonator is presented. A one-dimensional model equation for the velocity potential is derived from the fundamental gas dynamic equations for an ideal gas. Since the energy losses in the resonator occur in the acoustic boundary layer, we modified the model equation to include the boundary layer. A second modification is the addition of a turbulence model to account for turbulence dissipation. Both hardening and softening behavior is observed and shown to be geometry dependent.
Hysteresis effects are present in the frequency response curves.
Comparison between measurements and calculations are shown for waveforms and power dissipation. In both cases a good agreement is obtained. Contact Kevin Cunningham for more information about the Acoustics Seminar Series, Spring 1999.