A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Civil Engineering

Thesis (M.Eng.) - Asian Institute of Technology, 1993

In this study the governing equation of motion for beam structure with integrated piezoelectric actuator was formulated from the virtual work principle. The resulting governing equations are expressed in the form of ordinary differential equations in modal coordinates, where the effect of the electrically-induced strain in the actuator is shown in term of modal force. In the formulation, transverse motion as well as axial motion of the beam structure were considered. A simple beam with a direct feedback control was then studied. The feedback signal is proportional to the time rate of change in the dynamic strain at the extreme fiber of the beam nearest the actuator. This feedback introduces not only active damping to every vibrational mode, but also coupling between modes; these effects were represented in terms of a non-proportional active damping matrix. Therefore, complex modal analysis is needed to compute complex modes and complex eigenfrequencies of the system. The complex eigenfrequencies are then transformed into the equivalent modal dampings and modal frequencies. It was found that the relation between modal dampings and feedback gain is not linear; the damping increases, reaches its maximum, and then decreases when the gain is monotonically increased. Such a nonlinear phenomenon can not be identified if the coupling between modes is neglected. The phenomenon also implies that there is a physical limitation on the effectiveness of the active control scheme.