Power-generation prediction for piezoelectric composite plates by modal analysis

When the thickness of a plane structure is much smaller than its other characteristic lengths, a plate model is more realistic than a beam model. For a thin piezoelectric layer fully coated with metal electrodes on its top and bottom surfaces, the internal electric field is simple and easy to model. Therefore, it is advantageous to derive a piezoelectric composite plate model based on e-form constitutive equations. This approach is adopted to develop a mathematical model of Kirchhoff–Love type for a plate composed of a piezoelectric layer and a metal layer. To develop a method for calculating the loaded-circuit voltage between the top and bottom electrodes is one of the major tasks of this paper. The electric power generated from piezoelectric layer is found by modal analysis. Top and bottom electrodes of the piezoelectric layer are shorted for calculating resonant frequencies and mode shapes. Once these two electrodes are connected to an external circuit load, boundary conditions of top and bottom surfaces become nonhomogeneous. Superposition of short-circuit modes and one particular field constitutes the nonhomogeneous solution. A composite plate composed of a 0.3mm thick copper layer and a 0.2mm thick PZT-5A layer is investigated. The cantilever plate of 25mm in length is base-excited near the first resonant frequency. When connected to a circuit with certain load impedance, more than 80% efficiency of power generation can be achieved.