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 global 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.

This paper presents the multifrequency responses of multielectromechanical piezoelectric bimorph beams using a novel analytical model based on the closed-form boundary value method reduced from the strong form of Hamiltonian¿s principle. The reduced constitutive multielectromechanical dynamic equations for the multiple bimorph beams connected in series, parallel, and mixed series-parallel connections can be further formulated using Laplace transformation to give new formulas for power harvesting multifrequency response functions. The parametric case studies based on the change in geometrical structures of the multiple bimorphs with and without tip masses are discussed to analyze the trend of multifrequency power harvesting optimization under resistive load. Nyquist responses based on varying geometrical structures and load resistances were used to analyze the multifrequency power amplitudes in the complex domain. Overall, the trend of system response using multiple tiers consisting of multiple bimorphs was found to significantly widen the multifrequency band followed by increasing the power amplitudes.

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical

The primary contribution of this paper focuses on the development of novel numerical and analytical studies of the modal damped vibration energy harvester using the cantilevered piezoelectric unimorph beam with arbitrary proof mass offset under input base transverse motion. The key equations of electromechanical finite element discretisation for the piezoelectric element with thin electrode layers are revealed and simplified, indicating the most relevant numerical technique in the application for the power harvester research. Full derivations of the electromechanical vibration with damping effects using the extended Lagrangian principle have been developed to give matrix and scalar forms of the coupled system equations. To evaluate the performance of the numerical studies, the analytical closed-form boundary value equations of the physical system have also been developed using the extended Hamiltonian principle. The results from the electromechanical frequency response functions (EFRFs) derived from numerical and analytical studies show excellent agreement with experimental studies. The benefit of numerical techniques is that they can give effective and quick predictions in analysing parametric design optimisation and physical properties for various piezoelectric materials whereas the analytical techniques can provide a very challenging process for developing the derivations and for analysing the complex smart structure. However, the new analytical method presented here shows complete equations of the electromechanical vibration of the piezoelectric structure with dynamical proof mass offset and damping effects providing complementary study for validating the numerical technique. Moreover, the parametric studies using the optimal power harvesting responses enable the identification of the performance for the piezoelectric materials and the particular piezoelectric and proof mass geometries before conducting the micro-fabrication process for emerging micro-sensor power harvesting applications.

Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment, vehicles, aircraft, piping systems, fluid flow, and even external movement of the human body. A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology. The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions, simultaneously or singularly. This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian's principle and space-and time-dependent eigenfunction series which were further formulated using orthonormalization. The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions (FRFs). The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.