An analytical model and working equations for static deflections of a circular multi-layered diaphragm-type piezoelectric actuator

This paper presents an analytical model based on the classical laminated plate theory for deflections of multi-layered circular diaphragm-type piezoelectric actuators subjected to voltage and uniform pressure loads. Analytical equations are derived from the model and solved in closed form to obtain transverse and lateral deflections of a multi-layered actuator with the diaphragm layer only partially covered by the piezoelectric and other material layers as functions of the actuator geometry, the material properties and the applied voltage and pressure loads. The analytical equations are validated numerically via finite element analysis and experimentally via static deflection measurements on a commercially available piezoelectric actuator. The analytical results are found to be in agreement with the finite element results within 0.5% and with the experimental measurements within 4%. The application of the equations in typical analysis and design optimization of an actuator are elucidated through numerical examples.