Piezoelectric vibration-based energy harvesters consist of an electromechanical structure and an electric circuitry, influencing each other. We propose a novel approach that allows a finite element based system simulation of nonlinear electromechanical structures coupled to nonlinear electric circuitries. In the finite element simulation the influence of the electric circuit on the electromechanical structure is considered via the vector of external forces, using an implicit time integration scheme. To demonstrate the applicability of the new simulation method an active power circuit is considered. Several examples of piezoelectric vibration-based energy harvesters, connected to standard or synchronized switch harvesting on inductor (SSHI) circuits, showing linear or nonlinear mechanical behavior, are studied to validate the proposed simulation method against numerical results reported in the literature. The advocated method allows for consistent and efficient simulations of complete nonlinear energy harvesters using only one software tool.

A composite structure of piezoelectric particles and soft polymer composite materials is a promising component of vibration energy harvesters. However, the energy harvesting behavior which originates from ceramic particles inside the polymer has not been clarified. In this study, (Na,K)NbO 3 /polyimide composites sheets with NKN fraction of 0-40 vol% were fabricated and open-circuit voltage was measured. The opencircuit voltage was increased nonlinearly from 0.72 to 2.21 V with increasing of the particle fraction (10%-30%) The experimental results were confirmed using a microstructure based finite element method and electric potential and electromechanical coupling coefficients were higher value in the content of 30% NKN particles. Analysis indicates that the internal electric potential inside the matrix under strain could be an important factor for macroscopic piezoelectric constant and electrical output.

In this contribution, a system simulation method based on the finite element method (FEM) is applied to simulate a strongly coupled bimorph piezoelectric vibration-based energy harvester (PVEH) with various nonlinear, non-ideal and active circuits: The standard circuit, the synchronized switch harvesting on inductor circuit and the synchronized electric charge extraction circuit are considered. Furthermore, nonlinear elastic behavior of the piezoelectric material is taken into account and harmonic base excitations of different magnitudes at a fixed frequency are applied. The holistic FEM-based system simulation approach solves the complete set of piezoelectric equations together with the equation of the electric circuit such that all electromechanical coupling phenomena are taken into account. This fully coupled numerical analysis enables the detailed evaluation of the influences of the electric circuits on the vibrational behavior and the harvested energy of the PVEH with respect to the magnitude of base excitation. Results from literature on the efficiency of electric circuits are confirmed and interactions between mechanical and electrical nonlinearities of PVEHs are revealed. Article highlights System simulations of a mechanically and electrically nonlinear piezoelectric energy harvester are performed using only one software tool. The infuence of electric circuits on the vibration behavior and the effciency of an energy harvester are investigated in detail. Interactions between mechanical and electrical nonlinearities of an energy harvester are revealed.

A piezoelectric vibration-based energy harvester (PVEH) consists of an electromechanical structure and an electric circuit, influencing each other. The finite element method (FEM) allows for the simulation of arbitrarily shaped and nonlinear electromechanical structures, while an electronic circuit simulator (ECS) can be applied to simulate arbitrary electric circuits. We propose a novel implicit FEM-ECS coupling method, which combines the advantages of the FEM and the flexibility of an ECS. The Newton-Raphson method is applied to achieve rapid convergence at the interface between the FEM and ECS simulations, so that arbitrary PVEHs can be efficiently analyzed. The new implicit FEM-ECS coupling is validated against explicitly and monolithically coupled FEM-ECS simulations of PVEHs from literature. Moreover, an application example consisting of a nonlinear electromechanical structure and a self-powered SSHI circuit is considered and a shock-like base excitation is applied. The examples demonstrate the practical applicability of the novel coupling method for realistic simulations of PVEHs.

A system simulation method based on the Finite-Element Method (FEM) is applied to simulate a bimorph piezoelectric vibration-based energy harvester (PVEH) with different electric circuits: The standard circuit, the synchronized switch harvesting on inductor (SSHI) circuit and the synchronized electric charge extraction (SECE) circuit are considered. Moreover, nonlinear elasticity of the piezoelectric material is taken into account and different magnitudes of base excitations are applied. The holistic FEM-based system simulation approach allows the detailed evaluation of the influences of the considered electric circuits on the vibrational behavior of the PVEH. Furthermore, the harvested energy of the different applied electric circuits with respect to the magnitude of base excitation is compared and results from literature regarding the efficiency of electric circuits are confirmed.