An implicitly coupled finite element-electronic circuit simulator method for efficient system simulations of piezoelectric energy harvesters - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Intelligent Material Systems and Structures, 2023)
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.
CRIS-Team Scopus Importer:2023-04-07
Keywords: coupled problem; electronic circuit simulator; finite element method; multiphysics simulation; numerical simulation; Piezoelectric energy harvesting

Investigation of a nonlinear piezoelectric energy harvester with advanced electric circuits with the finite element method - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (SN Applied Sciences, 2022)
Abstract: 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.
CRIS-Team Scopus Importer:2022-04-15
Keywords: Coupled problem; Finite element method; Multiphysics simulation; Numerical simulation; Piezoelectric energy harvesting

Nonlinear finite element system simulation of piezoelectric vibration-based energy harvesters - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Intelligent Material Systems and Structures, 2021)
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.
CRIS-Team Scopus Importer:2021-10-22
Keywords: coupled problem; finite element method; multiphysics simulation; nonlinear analysis; numerical simulation; Piezoelectric energy harvesting

Numerical investigation of the transient charging behavior of a piezoelectric vibration-based energy harvester for different base excitations - Hegendörfer, Andreas; Mergheim, Julia (Proceedings of SPIE - The International Society for Optical Engineering, 2022)
A piezoelectric vibration-based energy harvester (PVEH) is a combined device, which consists of an electromechanical structure and an electric circuit. Typically, the energy output of a PVEH is too low to continuously supply electrical devices, thus, the harvested energy must be accumulated and stored. In the case of a strongly coupled PVEH, the electrical and mechanical behavior significantly influence each other resulting in complex coupling phenomena. Therefore, system simulations that accurately account for electromechanical coupling are valuable tools for understanding the behavior of PVEHs. In the present work a system simulation method based on the finite-element method (FEM) is applied to investigate the transient charging process of a storage capacitor. A strongly coupled bimorph PVEH with a standard and a synchronized switch harvesting on inductor (SSHI) circuit is considered and a harmonic and a shock-like triangular pulse excitation are applied. The FEM solves the complete set of piezoelectric equations while the electric circuit is considered via the boundary conditions. Therefore, all coupling effects between the mechanical and electrical behavior are precisely taken into account in the simulations. The simulation results show that the standard circuit is more efficient for the harmonic excitation, while the SSHI circuit is more efficient than the standard circuit for the shock-like triangular pulse excitation. Furthermore, the influence of different capacitors on the charging behavior of the standard and SSHI circuit for the harmonic and the shock-like triangular pulse excitation is discussed.
CRIS-Team Scopus Importer:2022-06-24
Keywords: energy harvesting; finite element method; storage capacitor; System simulation; transient charging process

Numerical Optimization of a Nonlinear Nonideal Piezoelectric Energy Harvester Using Deep Learning - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Low Power Electronics and Applications, 2023)
This contribution addresses the numerical optimization of the harvested energy of a mechanically and electrically nonlinear and nonideal piezoelectric energy harvester (PEH) under triangular shock-like excitation, taking into account a nonlinear stress constraint. In the optimization problem, a bimorph electromechanical structure equipped with the Greinacher circuit or the standard circuit is considered and different electrical and mechanical design variables are introduced. Using a very accurate coupled finite element-electronic circuit simulator method, deep neural network (DNN) training data are generated, allowing for a computationally efficient evaluation of the objective function. Subsequently, a genetic algorithm using the DNNs is applied to find the electrical and mechanical design variables that optimize the harvested energy. It is found that the maximum harvested energy is obtained at the maximum possible mechanical stresses and that the optimum storage capacitor for the Greinacher circuit is much smaller than that for the standard circuit, while the total harvested energy by both configurations is similar.
CRIS-Team Scopus Importer:2023-04-07
Keywords: coupled optimization; electronic circuit simulator; finite element method; multiphysics optimization; numerical optimization; piezoelectric energy harvesting

Temperature-dependent vibration energy harvesting performance of polyimide/(Na,K)NbO3 piezoelectric composites - Yamamoto, Ryota; Hegendörfer, Andreas; Mergheim, Julia; Kakimoto, Ken-Ichi (Japanese Journal of Applied Physics, 2022)
A composite structure of piezoelectric particles and soft polymer composite material is one of the candidates that converts environmental vibration energy into electrical energy. Presently, expanding the usage of applications is needed in terms of the working environment at harsh temperatures. Polyimide is flexible and temperature-stable polymer. In this research, we report a synthesis of polyimide/(Na,K)NbO3 (PI/NKN) flexible composites. We constructed a setup, where vibration and heat are simultaneously applied to the PI/NKN composites. The frequency and temperature dependence of the output voltage were investigated at room temperature up to 200 °C. Relative permittivity, piezoelectric constant, and output voltage of the PI/NKN showed temperature stability. Flexibility and glass transition temperature of a polymer matrix are important factors. PI/NKN composites are potential energy harvesting materials with flexibility and excellent high-temperature stability.
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Keywords: piezoelectric; polymer/ceramic composite; thermal stability; vibration energy harvesting

Vibration energy harvesting and internal electric potential of (Na,K)NbO3/polyimide piezoelectric composites - Yamamoto, Ryota; Hegendörfer, Andreas; Mergheim, Julia; Kakimoto, Ken-Ichi (Japanese Journal of Applied Physics, 2021)
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)NbO3/polyimide composites sheets with NKN fraction of 0-40 vol% were fabricated and open-circuit voltage was measured. The open-circuit 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.
CRIS-Team WoS Importer:2021-09-10