Parametric excitation of a Helmholtz resonator
Wayne E. Prather, Bruce C. Denardo, Richard Raspet · The Journal of the Acoustical Society of America · 1998
Parametric excitation of an oscillator results from the modulation of a parameter upon which the natural frequency of the oscillator depends. If the drive amplitude exceeds a threshold determined by dissipation, the response amplitude grows exponentially until it is saturated by a nonlinearity of the system. Hence, large amplitudes may be possible. An unsuccessful attempt to parametrically excite the fundamental mode of a Helmholtz resonator is reported. The apparatus consists of two equal-volume cavities connected by a U-shaped neck similar to a trombone slide, where the neck length is modulated at twice the Helmholtz frequency. In model systems, the effective quality factor diverges as the parametric drive amplitude approaches threshold from below. the extent to which a parametric drive amplitude is below threshold can thus be probed by performing a frequency sweep with a small-amplitude direct drive. However, the effective quality factor in our system is found to decrease as the parametric drive amplitude is increased, as a result of turbulence caused by the parametric drive. This indicates that parametric excitation by neck length modulation may not be possible. Current work on a Helmholtz resonator in which the cavity volume is modulated is also reported on. [Work sponsored by ONR.]