Finite element modeling of stiffened piezolaminated plates and shells with piezoelectric layers for active vibration control

摘要

In this paper, a piezolaminated stiffened shell element is formulated. This piezoelectric shell element is a 9-noded, isoparametric, shear flexible and field-consistent element with five elastic degrees of freedom at each node and one electric degree of freedom per element per piezoelectric layer. The stiffener element is a three-noded isoparametric beam element with three degrees of freedom at each node. The effect of the stiffener is incorporated by internally constraining the stiffener displacement fields to the relevant shell displacement fields and hence this formulation allows the positioning of the stiffener element anywhere within the shell element along lines of natural coordinates, which gives a great flexibility in the choice of the mesh size. This stiffened shell element is validated for static deflection and dynamic response with the results available in literature. The active control performance of the stiffened composite plate and shell structures with distributed piezoelectric sensors and actuators are studied using a number of examples. The active vibration control is carried out using the LQR optimal control.