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 stresse s is investigated. A finite element formulation is presented for the analys is of laminated Timoshenko beams with an arbitrary number of piezoelectric actuators and/or sensors placed along the length of the beam. Von Karman no nlinear strain-displacement relations are used and ideal linear behavior is assumed for the piezoelectric actuation. It is shown that if the beam is l ongitudinally restrained at both ends the piezolectric actuators induce in- plane stresses that significantly affect the mechanical behavior of the bea m. It is also shown that stress stiffening is more pronounced for slender b eams. 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 negle cting the stress stiffening effects may lead to large errors in both the st atic and dynamic analyses of this widely used configuration for slender bea ms. Further, the stiffness of the beam can be piezoelectrically tuned to si gnificantly change the natural frequency; this has interesting applications in active vibration and acoustics control or smart structures.