Abstract
The frequency response and nonlinear resonance frequency shift for an acoustical resonator with losses and having a varying cross section were investigated previously using Lagrangian mechanics for resonator shapes that are close to cylindrical [J. Acoust. Soc. Am. 110, 109 (2001)]. The same approach is extended to include resonators having any shape for which a one-dimensional Webster-type equation is a valid model in the linear approximation. Admissible shapes include cones and bulbs proposed for acoustical compressors. The approach is appropriate for approximate but rapid parameter estimations for resonators with complicated shapes, requiring 100 times less computer time than for direct numerical solution of the one-dimensional model equation ordinarily used for these resonators [Ilinskii et al., J. Acoust. Soc. Am. 104, 2664 (1998)]. Results for cone and bulb shaped resonators with losses are compared with results from the previous one-dimensional theory and with experimental data. It is shown that the direction of the resonance frequency shift is determined by the efficiency of second-harmonic generation in modes having natural frequencies below versus above the frequency of the second harmonic, and how the net effect of this coupling compares with the frequency shifts due to cubic nonlinearity and static deformation.
Published Version
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