Investigations of nonlinear waves and parametric excitation

• Main Author: Jones, William P.
• Other Authors: Denardo, Bruce C.
• Format: Others
• Published: Monterey California. Naval Postgraduate School 2012
• Subjects: Gravity waves; Education; Mechanics; Mathematics; Physics
• Online Access: http://hdl.handle.net/10945/1963

Nonlinearity in oscillations and waves can lead to dramatic and useful behavior. The course PH4459 at the Naval Postgraduate School was recently redesigned to extend its original subject of nonlinear acoustics to nonlinear oscillations and waves in general, with minimal prerequisites so that non-acoustics-tracked students can enroll in the course. Due to the unusual behavior and mathematical difficulty of nonlinear systems, lecture demonstrations are vital to the teaching of the course. The purpose of this thesis is to develop two new demonstrations for the course, and to improve an existing demonstration. In one of the new demonstrations, we investigate the generation and detection of high-amplitude waves on water to demonstrate the dependence of the wave speed upon amplitude. The experimental data agree with the theory. In the other new demonstration, we investigate a compression driver that exhibits a strong response at half the frequency of the drive. Data and the current scientific literature indicate that this behavior is due to parametric excitation of the deformation modes of the diaphragm assembly. Finally, we describe improvements to a torsional oscillator that is parametrically excited by modulation of its length. The improvements include a new motor, sturdier construction, and a new torsional strip.