Shape Control of Flexible Structures using Piezo-Electric Actuator/Sensors

In this paper active damping of a beam as an example of shape control of flexible structures is studied. The purpose is to stabilize significant modes of motion with piezoelectric actuator-sensor. Using a one dimensional partial differential equation model, a variational method is used to find a dissipative energy function. A criteria for the design of the shape of the piezoelectric material or electrode, which can accomplish damping of significant modes, is derived. Unlike previous efforts, which could find electrode shape for dissipativity of one mode, it is proved that the suggested shape guarantees the dissipativity of energy function for all modes of the system.