Parametric design-based modal damped vibrational piezoelectric energy harvesters with arbitrary proof mass offset: Numerical and analytical validations

Abstract

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.

A unified electromechanical finite element dynamic analysis of multiple segmented smart plate energy harvesters: circuit connection patterns

“…Note that although the expression given in Eq. 21shows a similar form to that of given in [31], the smart plate structure shows more complex physical system compared with the smart beam structure giving different normalized modal matrix with increasing degrees of freedom. At this point, the normalized eigenvector or modal matrix can simply be formulated as φ=U/…”

“…The various analytical studies of the piezoelectric power harvesting devices have been investigated using the lumped parameter models with electrical equivalent systems [19] and extensive circuit technique combinations [20]- [23], Rayleigh-Ritz methods [24]- [25] modal analysis method [26], assumed-mode method [27], and the weak-form techniques [28]- [29]. Other theoretical methods of piezoelectric power harvesting with different studies have also been investigated using random vibration analysis [30], fully closed-form boundary value methods [31]- [32], and analytical voltage-and charge-type Hamiltonian formulations [33]. For segmented piezoelectric structure, a few published works focusing on the structural discontinuity of piezoelectric components including beam orientation have investigated the use of the transfer matrix method [34] and analytical solutions [35].…”

“…The finite element model of the cantilevered piezoelectric bimorph beam structure with negligible electrode effects has also been investigated in [54]. Moreover, the numerical techniques in application to vibration energy harvester using the distributed piezoelectric beam with the electrode and damping effects were introduced into the derivations of coupled system [31], [55]. The technical concept underlies on formulating the set of the series multimode frequency response functions using the electromechanical discretization into the finite element equations.…”

Finite-element modeling of piezoelectric energy harvesters using lead-based and lead-free materials for voltage generation

“…Many researchers have investigated different piezoelectric materials and their application in cantilever structures for capturing ambient vibrations [5,6]. These designs provide good power output but are quite bulky in size and hence cannot be used for microscale applications.…”

Contribución al estudio de la generación de energía eléctrica a partir de materiales piezoeléctricos

“…Debido al reducido tamaño de estas estructuras su frecuencia de resonancia mecánica es mucho más alta que la predominante en el ambiente en las aplicaciones prácticas, por lo que se justifica la necesidad de suplementar en el extremo del cantilever una masa adicional con el objetivo de reducir la frecuencia de resonancia y amplificar la generación de tensión en el piezoeléctrico [20]. Desde los inicios del siglo XXI se suscitó un notable interés por esta técnica reflejándose en el incremento en el número de publicaciones indexadas en la Web of Science.…”