Ph.D. Thesis Defense by Phillip Nguyen
Thursday, June 15, 2000

(Dr. Jerry Ginsberg, advisor)

"An Exploration of Parametric Excitation as a Tool for Vibration Control"


This thesis explores a novel concept for vibration control of nonautonomous dynamic systems using a technique that is neither passive nor active.  The technique is similar to active control in that a secondary disturbance is supplied to the systems with a goal of reducing vibration.  The difference is that the concept does not use any sensing devices.  The fundamental concept is to generate a secondary harmonic excitation, which appears as time-varying coefficients in the governing equations of motion.  This is known as parametric excitation.  The notion is that adjusting the parametric excitation can counter the direct excitation.  Three types of parametric excitation are considered.  They are parametric excitation appearing as the stiffness coefficient, the damping coefficient, and all coefficients of the equations of motion.

Cases under consideration are vibration control of the pendulum using a sliding pivot, vibration control of one-degree-of-freedom systems using a modulated stiffness or damping constant, and control of flexural vibration of a simply supported beam using a sliding mass or support.  In the case of the beam, the standard/modified Ritz series method is employed in the formulation of the equations of motion.  The responses are obtained through numerical integration of the equations of motion.  In the special cases, the analytical method is applied to validate the numerical work.

An overview leads to a general conclusion that parametric excitation generated by the dynamics of the systems can reduce the forced response amplitude, as in the cases of the pendulum and the simply supported beam.  In contrast, parametric excitation induced by modulating the system parameters does not seem to be effective for vibration control, as shown in one-degree-of-freedom systems with modulated stiffness/damping constants.