Effective Placement of a Cantilever Resonator on Flexible Primary Structure for Vibration Control Applications: Part 1: Mathematical Modeling and Analysis

In this first part of a two-part series, the theoretical modeling and optimization are presented. More specifically, the effect of attachment location on the dynamics of a flexible beam system is studied using a theoretical model. Typically, passive/active resonators for vibration suppression of flexible systems are uniaxial and can only affect structure response in the direction of the applied force. The application of piezoelectric bender actuators as active resonators may prove to be advantageous over typical, uniaxial actuators as they can dynamically apply both a localized moment and translational force to the base structure attachment point. Assuming unit impulse force disturbance, potential actuator/sensor performance for the secondary beam can be quantifiedby looking at fractional root mean square (RMS) strain energy in the actuator relative to the total system.