The constituent equations of piezoelectric cantilevered three-layer actuators with various external loads and geometry

This paper presents test results for deformation conditions of three-layer, piezoelectric cantilever converters subjected to various electrical and mechanical boundary conditions. A general solution has been developed based on implementation of piezoelectric triple segments (PTS) to the beam. A working mechanism and conditions for strain of the PTS segment have been determined. Basing on the general solution, for the cantilever actuator subjected to an external force (of single and dual PTS segments) and a uniform load (of single PTS segment), particular solutions have also been developed. Moreover, dimensionless frequencies of the oscillating motion for the analyzed converters have been determined. In the next step, the influence of such factors as length, quantity and position of PTS segments, their relative stiffness and unit weight on values of the obtained frequencies of vibration have been defined. The resulting analytical solutions have been compared with the developed FEM solution.