A theoretical solution of resonant circular diaphragm-type piezoactuators with added mass loads

A theoretical solution is formulated to analyze the vibration behaviors of circular diaphragm-type piezoactuators based on the Hamilton's principle and Rayleigh-Ritz method, which are particular suitable for modeling the deflection of multilayer structures. Each of the actuator three layers is considered as an individual layer in the modeling. The energy associated with the solution includes the kinetic energy of the actuator, the elastic potential energy of the various layers, the electric potential energy in the piezodisc, and the work done by the force of electric filed. The transverse displacement is separated into a time dependence term and a mode shape term, then the vibrational governing equation is derived using the functional variation, and is approximately solved through the method of multiple scales. Moreover, added mass loads are introduced to the diaphragm center for the sake of decreasing the resonant frequency, where many MEMS devices, such as gas micropumps and ejectors, have a higher working efficiency. The proposed analytical solution is validated numerically via the finite element method (FEM) and experimentally via measurements; the theoretical results are found to be in good agreement with the FEM results as well as with the experimental results. Furthermore, the effects of mass loads, geometric dimensions and material properties of the piezoactuator on the resonant frequency are discussed.