Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations
Smart materials and structures (Print)
A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented. The new contributions for modelling of the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretisation, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations and orthonormalised
... matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously from other researchers. There are also benefits in presenting the proposed numerical techniques. First, the proposed numerical techniques can be used for applications in many different geometrical models including MEMS power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can give a very practical design in order to avoid the direct contact of piezoelectric material because of its brittle nature. Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating the single voltage, the new electromechanical discretisation consisting of the mechanical and electrical discretised elements is introduced. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions (FRFs) of the displacement, velocity, voltage, current and power including optimal power harvesting. The normalised numerical strain node and eigenmode shapes are also further formulated using numerical discretisation. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under resistive shunt circuit show good agreement with the experimental studies.