Three-dimensional formulation of a strain-based geometrically nonlinear piezoelectric beam for energy harvesting

2021 ◽  
pp. 1045389X2098879
Author(s):  
Emmanuel Beltramo ◽  
Balakumar Balachandran ◽  
Sergio Preidikman
Keyword(s):  
Finite Element ◽  
Electromechanical Coupling ◽  
Strain Tensor ◽  
Additional Term ◽  
External Loading ◽  
Geometrically Nonlinear ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Piezoelectric Beam ◽  
Highly Nonlinear

In this paper, the authors introduce a model of a strain-based geometrically nonlinear piezoelectric beam for modeling energy harvesters. A nonlinear shear-underfomable 3-D Rayleigh’s beam theory is used to model the displacement fields and can be considered as an interesting alternative to linear and highly nonlinear models commonly presented in the literature. The nonlinearities are introduced to reproduce the behavior of the flexible structure, since moderate to large displacements can occur in response of external loading conditions. The finite element method is used to model the piezolaminated bimorph configuration. Each finite element consists of two piezoelectric energy harvesters embedded or perfectly bonded to an elastic substrate. The electromechanical coupling includes axial and flexural effects as well as additional term that comes from the nonlinearity incorporated into the strain tensor. Additionally, the authors explore briefly two topics for linear harvesters: the influence of the electric domain on the structural properties and, the performance of the harvester near resonance in term of electric power output of a purely resistive network. As a validation case, a cantilevered piezoelectric energy harvester under base excitation is modeled. Alongside, the response to gust of a harvester embedded in a wing structure is analyzed.

A Coupled Finite Element—Circuit Simulation Model for Analyzing Piezoelectric Energy Generators

2008 ◽  
Vol 20 (5) ◽  
pp. 587-595 ◽  
Author(s):  
Niell G. Elvin ◽  
Alex A. Elvin
Keyword(s):  
Finite Element ◽  
Electromechanical Coupling ◽  
Circuit Simulation ◽  
Mechanical Analysis ◽  
Simulation Software ◽  
Solution Technique ◽  
Resistive Load ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Non Linear

A coupled finite element method (FEM) and circuit simulation approach for analyzing piezoelectric energy harvesters is presented. The advantage of the proposed method is that the mechanical analysis of the generator can be done using available FEM packages, while the circuit analysis can be performed using standard circuit simulation software (e.g., SPICE). The electromechanical coupling between the two physical domains is achieved by applying equivalent piezoelectric loads in the mechanical model, and equivalent electrical voltages in the electric model. This approach allows for the modeling of complex mechanical geometries and sophisticated, non-linear circuits. The solutions of two example problems are presented: (1) a beam generator with a resistive load, which is compared to an existing analytical solution, and (2) a plate generator with a non-linear diode bridge circuit. Though relatively easy to implement, the explicit solution technique presented in this article can be computationally expensive for complicated models with long simulation time-histories.

Heartbeat Energy Harvesting Using the Fan-Folded Piezoelectric Beam Geometry

2015 ◽  
Author(s):  
M. H. Ansari ◽  
M. Amin Karami
Keyword(s):  
Natural Frequency ◽  
Energy Harvester ◽  
Low Frequency ◽  
Mode Shapes ◽  
Vibration Energy ◽  
Vibration Energy Harvester ◽  
Mechanical Coupling ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Piezoelectric Beam

A three dimensional piezoelectric vibration energy harvester is designed to generate electricity from heartbeat vibrations. The device consists of several bimorph piezoelectric beams stacked on top of each other. These horizontal bimorph beams are connected to each other by rigid vertical beams making a fan-folded geometry. One end of the design is clamped and the other end is free. One major problem in micro-scale piezoelectric energy harvesters is their high natural frequency. The same challenge is faced in development of a compact vibration energy harvester for the low frequency heartbeat vibrations. One way to decrease the natural frequency is to increase the length of the bimorph beam. This approach is not usually practical due to size limitations. By utilizing the fan-folded geometry, the natural frequency is decreased while the size constraints are observed. The required size limit of the energy harvester is 1 cm by 1 cm by 1 cm. In this paper, the natural frequencies and mode shapes of fan-folded energy harvesters are analytically derived. The electro-mechanical coupling has been included in the model for the piezoelectric beam. The design criteria for the device are discussed.

scholarly journals Performance Assessment and Comparison of Two Piezoelectric Energy Harvesters Developed for Pavement Application: Case Study

2022 ◽  
Vol 14 (2) ◽  
pp. 863
Author(s):  
Chenchen Li ◽  
Shifu Liu ◽  
Hongduo Zhao ◽  
Yu Tian
Keyword(s):  
Elastic Modulus ◽  
Electromechanical Coupling ◽  
Electrical Performance ◽  
Scale Model ◽  
Bridge Structure ◽  
Wheel Load ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Conversion Coefficients ◽  
Electromechanical Conversion

To advance the development of piezoelectric energy harvesters, this study designed and manufactured bridge-unit-based and pile-unit-based piezoelectric devices. An indoor material testing system and accelerated pavement test equipment were used to test the electrical performance, mechanical performance, and electromechanical coupling performance of the devices. The results showed that the elastic modulus of the pile structure device was relatively higher than that of the bridge structure device. However, the elastic modulus of the two devices should be improved to avoid attenuation in the service performance and fatigue life caused by the stiffness difference. Furthermore, the electromechanical conversion coefficients of the two devices were smaller than 10% and insensitive to the load magnitude and load frequency. Moreover, the two devices can harvest 3.4 mW and 2.6 mW under the wheel load simulated by the one-third scale model mobile load simulator, thus meeting the supply requirements of low-power sensors. The elastic modulus, electromechanical conversion coefficients, and electric performance of the pile structure device were more reliable than those of the bridge structure device, indicating a better application prospect in road engineering.

Two-Dimensional Geometrically Nonlinear Finite Element Formulation for Analysis of Straight Pipes

2020 ◽  
Author(s):  
Saher Attia ◽  
Magdi Mohareb ◽  
Michael Martens ◽  
Nader Yoosef Ghodsi ◽  
Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Strain Tensor ◽  
Structural Response ◽  
Small Strain ◽  
Nonlinear Finite Element ◽  
Finite Element Formulation ◽  
Single Element ◽  
Element Formulation ◽  
Geometrically Nonlinear

Abstract The paper presents a new and simple geometrically nonlinear finite element formulation to simulate the structural response of straight pipes under in-plane loading and/or internal pressure. The formulation employs the Green-Lagrange strain tensor to capture finite deformation-small strain effects. Additionally, the First Piola-Kirchhoff stress tensor and Saint Venant-Kirchhoff constitutive model are adopted within the principle of virtual work framework in conjunction with a total Lagrangian approach. The formulation is applied for a cantilever beam under three loading conditions. Results are in good agreement with shell models in ABAQUS. Although the solution is based on a single element, the formulation provides reasonable displacement and stress predictions.

Equivalent impedance and power analysis of monostable piezoelectric energy harvesters

2020 ◽  
Vol 31 (14) ◽  
pp. 1697-1715
Author(s):  
Chunbo Lan ◽  
Yabin Liao ◽  
Guobiao Hu ◽  
Lihua Tang
Keyword(s):  
Equivalent Circuit ◽  
Electromechanical Coupling ◽  
Energy Harvester ◽  
Performance Enhancement ◽  
Damping Ratio ◽  
Power Performance ◽  
Closed Form Solutions ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Power Limit

Nonlinearity has been successfully introduced into piezoelectric energy harvesting for power performance enhancement and bandwidth enlargement. While a great deal of emphasis has been placed by researchers on the structural design and broadband effect, this article is motivated to investigate the maximum power of a representative type of nonlinear piezoelectric energy harvesters, that is, monostable piezoelectric energy harvester. An equivalent circuit is proposed to analytically study and explain system behaviors. The effect of nonlinearity is modeled as a nonlinear stiffness element mechanically and a nonlinear capacitive element electrically. Facilitated by the equivalent circuit, closed-form solutions of power limit and critical electromechanical coupling, that is, minimum coupling to reach the power limit, of monostable piezoelectric energy harvesters are obtained, which are used for a clear explanation of the system behavior. Several important conclusions have been drawn from the analytical analysis and validated by numerical simulations. First, given the same level of external excitation, the monostable piezoelectric energy harvester and its linear counterpart are subjected to the same power limit. Second, while the critical coupling of linear piezoelectric energy harvesters depends on the mechanical damping ratio only, it also depends on the vibration excitation and magnetic field for monostable piezoelectric energy harvesters, which can be used to adjust the power performance of the system.

Modeling and Analysis of Piezoelectric Energy Harvesting With Dynamic Plucking Mechanism

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Xinlei Fu ◽  
Wei-Hsin Liao
Keyword(s):  
Energy Harvesting ◽  
Research Work ◽  
Dynamic Interaction ◽  
Contact Theory ◽  
Vibration Energy ◽  
Piezoelectric Energy Harvesting ◽  
Comprehensive Model ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Piezoelectric Beam

Nonharmonic excitations are widely distributed in the environment. They can work as energy sources of vibration energy harvesters for powering wireless electronics. To overcome the narrow bandwidth of linear vibration energy harvesters, plucking piezoelectric energy harvesters have been designed. Plucking piezoelectric energy harvesters can convert sporadic motions into plucking force to excite vibration energy harvesters and achieve broadband performances. Though different kinds of plucking piezoelectric energy harvesters have been designed, the plucking mechanism is not well understood. The simplified models of plucking piezoelectric energy harvesting neglect the dynamic interaction between the plectrum and the piezoelectric beam. This research work is aimed at investigating the plucking mechanism and developing a comprehensive model of plucking piezoelectric energy harvesting. In this paper, the dynamic plucking mechanism is investigated and the Hertzian contact theory is applied. The developed model of plucking piezoelectric energy harvesting accounts for the dynamic interaction between the plectrum and the piezoelectric beam by considering contact theory. Experimental results show that the developed model well predicts the responses of plucking piezoelectric energy harvesters under different plucking velocities and overlap lengths. Parametric studies are conducted on the dimensionless model after choosing appropriate scaling. The influences of plucking velocity and overlap length on energy harvesting performance and energy conversion efficiency are discussed. The comprehensive model helps investigate the characteristics and guide the design of plucking piezoelectric energy harvesters.

scholarly journals Design and Analysis of a Magnetically Coupled Multi-Frequency Hybrid Energy Harvester

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3203 ◽  
Author(s):  
Zhenlong Xu ◽  
Hong Yang ◽  
Hao Zhang ◽  
Huawei Ci ◽  
Maoying Zhou ◽  
...  
Keyword(s):  
Output Power ◽  
Electromechanical Coupling ◽  
Energy Harvester ◽  
Hybrid Energy ◽  
Energy Harvesters ◽  
Peak Output Power ◽  
Piezoelectric Energy ◽  
Operating Bandwidth ◽  
Frequency Sweep Test ◽  
Hybrid Energy Harvesting

The approach to improve the output power of piezoelectric energy harvester is one of the current research hotspots. In the case where some sources have two or more discrete vibration frequencies, this paper proposed three types of magnetically coupled multi-frequency hybrid energy harvesters (MHEHs) to capture vibration energy composed of two discrete frequencies. Electromechanical coupling models were established to analyze the magnetic forces, and to evaluate the power generation characteristics, which were verified by the experimental test. The optimal structure was selected through the comparison. With 2 m/s2 excitation acceleration, the optimal peak output power was 2.96 mW at 23.6 Hz and 4.76 mW at 32.8 Hz, respectively. The superiority of hybrid energy harvesting mechanism was demonstrated. The influences of initial center-to-center distances between two magnets and length of cantilever beam on output power were also studied. At last, the frequency sweep test was conducted. Both theoretical and experimental analyses indicated that the proposed MHEH produced more electric power over a larger operating bandwidth.

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