Stress Stiffening Effects in Laminated Beams with Piezoelectric Actuators

The effectiveness of using piezoelectric elements to enhance the mechanical performance of laminated structures by inducing favorable in-plane stresses is investigated. A finite element formulation is presented for the analysis of laminated Timoshenko beams with an arbitrary number of piezoelectric actuators and/or sensors placed along the length of the beam. Von Kdrman nonlinear strain-displacement relations are used and ideal linear behavior is assumed for the piezoelectric actuation. It is shown that if the beam is longitudinally restrained at both ends the piezolectric actuators induce in-plane stresses that significantly affect the mechanical behavior of the beam. It is also shown that stress stiffening is more pronounced for slender beams. A configuration with a piezoelectric actuator at the top of a slender beam and a sensor at the bottom is analyzed. It is demonstrated that neglecting the stress stiffening effects may lead to large errors in both the static and dynamic analyses of this widely used configuration for slender beams. Further, the stiffness of the beam can be piezoelectrically tuned to significantly change the natural frequency; this has interesting applications in active vibration and acoustics control or smart structures.