Stiffening effects on the natural frequencies of laminated plates with piezoelectric actuators

Piezoelectric actuators are usually mounted to the top and bottom surfaces of plates and may induce in-plane extension, bending and localized shear deformations at the structural element. The in-plane stresses may have a significant influence on the mechanical behavior of thin plates as initial and/or residual stresses affect the flexural stiffness and in turn the dynamic and stability characteristics of plates. In this work, the effect of the in-plane piezoelectric induced stresses on the natural frequencies of composite plates is numerically and experimentally investigated. A finite element formulation is presented for the analysis of laminated plates with an arbitrary number of piezoelectric actuators and/or sensors. Von Kàrmàn non-linear strain–displacement relations are used and ideal linear behavior is assumed for the piezoelectric actuation. The problem is decomposed into an in-plane problem where the strain field induced by the piezoelectric actuators is computed. The natural frequencies and vibration modes are then computed taking the stress stiffening effects of these piezoelectric stresses into account. A number of different configurations are numerically and experimentally analyzed to verify the proposed theory. The configurations use eight PZT actuators bonded to three layer glass fiber/epoxy plates. The plates are square and clamped along two opposing edges and free along the other two. Good agreement is obtained between the predicted and measured natural frequencies.