Modeling and analysis of power harvesting by a piezoelectric layer coated on an electrostatically actuated microcantilever

The present study models and analyzes energy harvesting by a piezoelectric layer from the induced vibration of an electrostatically actuated microcantilever. In this structure, a layer of radioisotope materials is placed across from the microcantilever which emits electrons. An electrostatic force is created between the microcantilever and the plate across from it by charging the microcantilever. With further increase of charging, the pull-in instability occurs and microbeam is attracted to the electrode layer. Then discharge occurs, and the microcantilever is released. The piezoelectric layer converts the vibration of the released microcantilever into electricity. For extracting the equation of motion, the terms of energy are first calculated and then are discretized using the assumed method. Discretization is performed using the exact mode shape of linear vibration of the non-uniform microcantilever (i.e., the mode shape of the microcantilever with considering the geometrical effect of the piezoelectric layer). Subsequently, the Lagrange equation is applied, and discretized equations of motion are derived. In contrast to previous works, the linear and nonlinear effect of the electrostatic force and also geometrical effect of the piezoelectric layer are considered. Equations of motions are solved using the Runge–Kutta method for two conditions, one time with considering the effects of electrostatic force and other one ignoring it, and then the results are compared. By calculating the equations governing the system, output voltage and, therefore, the level of harvested electrical energy are examined based on various parameters, including material, thickness, length, location of piezoelectric layer, and resistive load, and maximum output power is obtained based on the geometry and conditions of the problem.