Active vibration control of intelligent stiffened laminates using smart piezoelectric materials by the finite element method

Abstract

The advent of high strength and light weight composite materials and newly developed smart materials (piezoelectric materials like polyvinylidene fluoride) have radically changed the concepts of advanced space structures and mechanical systems. Advanced structures with integrated self-monitoring and control capabilities are becoming very important due to the rapid development of intelligent mechanical systems and space structures. Since the structures are distributed and flexible in nature, distributed vibration measurement and active vibration suppression are of importance to their performance. A generalised finite element formulation of a consistent plate model for active vibration control of stiffened laminates integrated with piezoelectric polymer layers acting as distributed sensors and actuators is presented in this study. Total charge developed on the sensor layer is calculated from the direct piezoelectric equations. The equation of motion is discretized with a 9-noded Langrangian quadratic shear deformable isoparametric element. The piezoelectric sensor is not only distributed, but also integrated to the substrate since the output charge and so also the voltage is dependent on the sensor area. Also, the piezoelectric actuator induces the control moments at the ends of the actuators, Therefore, the number, size and location of the sensors and the actuators are very important in the control system design. By selective assembling of the element matrices for each electrode, responses of various sensor/actuator geometries can be investigated. For vibration control in the time domain, Newmark's direct integration method is used in the present investigation.