Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations

Abstract

A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented in this paper. The new contributions for modelling the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretization, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations and orthonormalized global matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously by other researchers. There are also benefits to presenting the numerical techniques proposed in this paper. First, the proposed numerical techniques can be used for applications in many different geometrical models, including micro-electro-mechanical system power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can result in a very practical design, which avoids direct contact with piezoelectric material because of its brittle nature. Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating single voltage, we introduce the new electromechanical discretization, consisting of the mechanical and electrical discretized elements. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions of the displacement, velocity, voltage, current and power, including optimal power harvesting. The normalized numerical strain node and eigenmode shapes are also further formulated using numerical discretization. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under a resistive shunt circuit show good agreement with the experimental studies.