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, 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.