Working equations for piezoelectric actuators and sensors

A new solution to the force, displacements, and charges developed in piezoelectric beams is derived. Differing from previous solutions [1]-[3], this development determines the neutral axis where the bending strains are zero and results in a closed form solution (without matrix inversion). With the closed form, simplifications become evident which increase understanding and facilitate calculations. These equations are than expanded to account for axial, built-in strains in the beam. A design example where axial forces exerted by the piezoelectric layer are important is presented. [354].