Feasibility of parametric excitation of acoustic resonators
Varnadore, Larry P.
Bruce C. Denardo, Thomas J. Hofler.
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This thesis examines the feasibility of parametrically exciting a mode of an acoustic resonator. Such excitation may result in substantially larger amplitudes than by direct excitation, and would thus be useful in acoustic devices that require high-amplitude standing waves. Parametric excitation of a mode occurs if the natural frequency is modulated at twice its value, and if the drive amplitude is above a threshold value due to dissipation. It is theoretically shown to be possible to excite the fundamental longitudinal mode of a pipe of any length filled with sulfur hexafluoride if the length is modulated with an Electrovoice EVX-150A driver. For carbon dioxide, excitation is predicted to occur if the pipe is longer than 1.2 meters. Also investigated is parametric excitation of the fundamental radial mode of a cylindrical cavity by modulating the height and thus the temperature. In this case, no driver was found to be capable of exceeding the threshold, regardless of the gas. Use of an electromagnetic wave source to modulate the temperature was also considered as a means of parametrically exciting the fundamental radial mode. Preliminary investigations show that sufficient heat conduction cannot occur over an acoustic cycle, indicating that this method is infeasible.
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