Dynamic Modeling of a Piggybacked Cantilever Beam System

Typically, 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 torque and translational force to the base structure attachment point; this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). In this paper, Hamilton’s Principle is used to develop the equations of motion for a continuous two-beam system composed of a cantilevered, primary base beam with a secondary piezoelectric bender mounted to its surface. A disturbance force is applied near the fixture location of the base beam and the system response is estimated using a sufficient quantity of assumed eigenfunctions that satisfy the geometric boundary conditions. A theoretical study is performed to compared the continuous system eigenfunctions to a finite element model (FEM) of the two-beam structure and the required number of eigenfunctions required to yield a convergent solution for an impulse excitation is explored. In addition, the frequency response function for the dynamic system is presented and compared to that of a FEM.