The Application of a Finite Shell Element for Composites Containing Piezo-Electric Polymers in Vibration Control

Kurzfassung

Advanced composite structures with integrated sensors and actuators are becoming increasingly important due to the demand for very large, lowmass space structures. This paper focuses on the finite element analysis of shell structures with thin piezo-electric layers bonded to the surfaces. A finite element formulation taking the piezo-electric effect into account is given and a finite shell element is presented, allowing for the computation of these advanced composite structures. The dynamic matrix equation accounting for the piezo-electric material response is formulated and found to have the same form as the well-known equation of structural dynamics. By using the second or direct method of Lyapunov, a control law is derived, which is used in vibration control and ensures asymptotic stability. A numerical example is given to show the accuracy of the finite element, as well as the efficiency of the algorithm.