Accession Number:

ADA435509

Title:

Investigations of Parametric Excitation in Physical Systems

Descriptive Note:

Master's thesis

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA

Personal Author(s):

• Janssen, Michael T.

Report Date:

2005-06-01

Pagination or Media Count:

79.0

Abstract:

Parametric excitation can occur when the value of a parameter of an oscillator is modulated at twice the natural frequency of the oscillator. The response grows exponentially and is only limited by a nonlinearity of the system, so large response amplitudes typically occur. However, there is no response unless the parametric drive amplitude is above a threshold value that is dictated by the damping. We investigate parametric excitation in three physical systems. The first involves an acoustic standing wave in a pipe that is driven by a piston at one end. An analysis shows that parametric excitation is not feasible in this system unless one uses a very large-excursion piston for example, from an aircraft engine. The second system is an inductor-capacitor circuit which can undergo oscillations of the current. An analysis of capacitance modulation with a bank of alternate rotating and stationary parallel plates shows that parametric excitation would be very difficult to achieve. Finally, we describe the construction of a torsional oscillator whose length is modulated. Parametric excitation is successfully demonstrated in this system. A comparison of data to predictions of the standard theory of parametric excitation reveals significant deviations.

Descriptors:

• *ACOUSTIC WAVES
• *PARAMETRIC DEVICES
• OSCILLATORS
• PHYSICAL PROPERTIES
• THRESHOLD EFFECTS
• EXCITATION
• DAMPING
• NONLINEAR SYSTEMS
• OSCILLATION
• TORSION
• STANDING WAVES

Subject Categories:

• Electrical and Electronic Equipment
• Acoustics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE