Reduced-Order Modeling of Energy Harvesters

2009 ◽  
Author(s):  
Thiago Seuaciuc-Oso´rio ◽  
Mohammed F. Daqaq
Keyword(s):  
Output Power ◽  
Cantilever Beam ◽  
Electromechanical Coupling ◽  
Single Mode ◽  
Exact Expression ◽  
Reduced Order ◽  
Energy Harvesters ◽  
Piezoelectric Cantilever ◽  
Design Values ◽  
Ritz Procedure

This work addresses the accuracy and convergence of reduced-order models (ROMs) of energy harvesters. Two types of energy harvesters are considered, a magnetostrictive rod in axial vibrations and a piezoelectric cantilever beam in traverse oscillations. The partial differential equations (PDEs) and associated boundary conditions governing the motion of these harvesters are obtained. The eigenvalue problem is then solved for the exact eigenvalues and modeshapes. Furthermore, an exact expression for the steady-sate output power is attained by direct solution of the PDEs. Subsequently, the results are compared to a ROM attained following the Rayleigh-Ritz procedure. It is observed that the eigenvalues and output power near the first resonance frequency are more accurate and has a much faster convergence to the exact solution for the piezoelectric cantilever beam. In addition, it is shown that the convergence is governed by two dimensionless constants, one that is related to the electromechanical coupling and the other to the ratio between the time constant of the mechanical oscillator and the harvesting circuit. Using these results, conclusions are drawn with regards to the design values for which the common single-mode ROM is accurate.

A Smart Device for Harnessing Energy From Aerodynamic Flow Fields

2009 ◽  
Author(s):  
Daniel St. Clair ◽  
Christopher Stabler ◽  
Mohammed F. Daqaq ◽  
Jian Luo ◽  
Gang Li
Keyword(s):  
Wind Energy ◽  
Cantilever Beam ◽  
Flow Rate ◽  
Excitation Frequency ◽  
Volumetric Flow Rate ◽  
Smart Device ◽  
Electric Load ◽  
Energy Harvesters ◽  
Air Chamber ◽  
Piezoelectric Cantilever

In this work, inspired by music playing harmonicas, we conduct a conceptual investigation of a coupled aero-electromechanical system for wind energy harvesting. The system consists of a piezoelectric cantilever unimorph structure embedded within an air chamber to mimic the vibration of the reeds in a harmonica when subjected to air flow. In principle, when wind blows into the air chamber, the air pressure in the chamber increases and bends the cantilever beam opening an air path between the chamber and the environment. When the volumetric flow rate of air past the cantilever is large enough, the energy pumped into the structure via the nonlinear pressure forces offset the intrinsic damping in the system setting the beam into self-sustained limit-cycle oscillations. These oscillations induce a periodic strain in the piezoelectric layer which produces a voltage difference that can be channeled into an electric load. Unlike traditional vibratory energy harvesters where the excitation frequency needs to match the resonant frequency of the device for efficient energy extraction, the nonlinearly coupled aero-elasto dynamics of this device guarantees autonomous vibration of the cantilever beam near its natural frequency as long as the volumetric flow rate is larger than a certain threshold. Experimental results are presented to demonstrate the ability of this device to harvest wind energy under normal wind conditions.

Fabrication and analytical modeling of transverse mode piezoelectric energy harvesters

2012 ◽  
Vol 1397 ◽  
Author(s):  
Seon-Bae Kim ◽  
Jung-Hyun Park ◽  
Seung-Hyun Kim ◽  
Hosang Ahn ◽  
H. Clyde Wikle ◽  
...  
Keyword(s):  
Output Power ◽  
Analytical Modeling ◽  
Energy Harvester ◽  
Power Conversion ◽  
Transverse Mode ◽  
Modified Model ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Interdigital Electrodes ◽  
Piezoelectric Cantilever

ABSTRACTA transverse (d33) mode piezoelectric cantilever was fabricated for energy harvesting. Various dimensions of interdigital electrodes (IDE) were deposited on a piezoelectric layer to examine the effects of electrode design on the performance of energy harvesters. Modeling was performed to calculate the output power of the devices. The estimation was based on Roundy’s analytical modeling derived for a d31 mode piezoelectric energy harvester (PEH). In order to apply the Roundy’s model to d33 mode PEH, the IDE configuration was converted to the area of top and bottom electrodes (TBE). The power conversion in d33 mode PEH was commonly estimated by the product of piezoelectric layer’s thickness and finger electrode’s length. In addition, the spacing between fingers was regarded as gap between top and bottom electrodes. However, the output power in a transverse mode PEH increases continuously with the increase of finger spacing, which does not correspond to experimental results. In this research, the dimension of IDE was converted to that of TBE using conformal mapping, and variation of power of PEH was remodeled. The modified model suggests that the maximum power in a transverse mode PEH is obtained when the finger spacing is identical with effective finger spacing. The output power then decreases when finger spacing is larger than effective finger spacing. The decrease of efficiency may result from insufficient degree of poling and increased charged defect with increasing finger spacing.

Exploiting Bi-Stability to Enhance Energy Capture From Turbulent Flows

2015 ◽  
Author(s):  
Ali H. Alhadidi ◽  
Mohammed F. Daqaq
Keyword(s):  
Wind Tunnel ◽  
Turbulent Flows ◽  
Output Power ◽  
Turbulence Intensity ◽  
Bluff Body ◽  
Reynolds Numbers ◽  
Restoring Force ◽  
Energy Capture ◽  
Energy Harvesters ◽  
Piezoelectric Cantilever

This paper investigates utilizing a nonlinear (bi-stable) restoring force to enhance the transduction of galloping energy harvesters in turbulent flows. To that end, a harvester consisting of a piezoelectric cantilever beam augmented with a square-sectioned bluff body at the free end is considered. Two repulsive magnets located at the tip of the beam are used to introduce the bi-stable restoring force. Turbulence is generated in a wind tunnel using static-grid structures located in the upstream of the bluff body. Three different mesh screens with square bars are designed with different bar and mesh widths to control the Reynolds numbers and associated turbulence intensity. A series of wind tunnel tests are then used to experimentally investigate the response of the harvester with and without the tip magnets. Results demonstrate that the bi-stable restoring force can be used to improve the output power of the harvester for sufficiently large turbulence intensities.

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.

Utilizing Bi-Stability to Improve the Performance of Wake-Galloping Energy Harvesters in Unsteady Flow

2016 ◽  
Author(s):  
Ali H. Alhadidi ◽  
Mohammed F. Daqaq ◽  
Hamid Abderrahmane
Keyword(s):  
Wind Tunnel ◽  
Unsteady Flow ◽  
Output Power ◽  
Bluff Body ◽  
Unsteady Flows ◽  
Reynolds Numbers ◽  
Flow Conditions ◽  
Restoring Force ◽  
Energy Harvesters ◽  
Piezoelectric Cantilever

This paper investigates exploiting a bi-stable restoring force to enhance the transduction of wake-galloping energy harvesters in unsteady flows. To that end, a harvester consisting of a piezoelectric cantilever beam augmented with a square-sectioned bluff body at the free end is considered. Two repulsive magnets located at the tip of the beam are used to introduce the bi-stable restoring force. Unsteadiness is generated in a wind tunnel using static-grid structures located in the upstream of the bluff body. Three different mesh screens with square bars are designed with different bar and mesh widths to control the Reynolds numbers and associated unsteadiness. A series of wind tunnel tests are then used to experimentally investigate the response of the harvester with and without the tip magnets. Results demonstrate that the bi-stable restoring force can be used to improve the output power of the harvester under unsteady flow conditions.

Analysis of Power Generating Performance for Unimorph Cantilever Piezoelectric Beams With Interdigitated Electrodes

2005 ◽  
Author(s):  
Changki Mo ◽  
Sunghwan Kim ◽  
William W. Clark
Keyword(s):  
Low Power ◽  
Cantilever Beam ◽  
Piezoelectric Materials ◽  
Design Parameters ◽  
Interdigitated Electrode ◽  
Power Generators ◽  
Energy Harvesters ◽  
Piezoelectric Cantilever ◽  
Power Harvester ◽  
Unimorph Cantilever

A great amount of research has been done to determine whether piezoelectric materials can be used as power generators for a variety of portable and low power consuming devices. Among the possibilities for energy harvesters, the 31-type cantilever piezoelectric benders have been generally used. In this work a unimorph piezoelectric cantilever beam with the interdigitated electrode pattern was examined. The focus of this paper was to develop a model and propose design parameters to improve the power generating performance of the interdigitated piezoelectric power harvester.

Modeling and Analysis of Piezoelectric Bimorph Cantilever for Vibration Energy Harvesting

2012 ◽  
Vol 610-613 ◽  
pp. 2583-2588
Author(s):  
Jun Jie Gong ◽  
Ying Ying Xu ◽  
Zhi Lin Ruan
Keyword(s):  
Energy Harvesting ◽  
Cantilever Beam ◽  
Electromechanical Coupling ◽  
Theory Of Elasticity ◽  
Vibration Energy ◽  
Piezoelectric Bimorph ◽  
Vibration Energy Harvesting ◽  
Output Displacement ◽  
Fea Model ◽  
Piezoelectric Cantilever

The vibration energy can be converted to electrical energy directly and efficiently using piezoelectric cantilever beam based on piezoelectric effect. Since its structure is simple and its working process is unpoisonous to the environment, the piezoelectric cantilever beam can be used in various fields comprehensively. The present paper perform an analysis on the vibration energy harvesting problem of piezoelectric bimorph cantilever beam. The piezoelectric cantilever model has been formulated using the theory of elasticity mechanics and piezoelectric theory. A prototype of piezoelectric power generator is set up to do vibration test, and the electromechanical coupling FEA model under vibration load is built to simulate its output displacement, stress and voltage. The present numerical results of piezoelectric bimorph cantilever coincide well with our related experimental results, which shows the validity of the present FEA model and the relate results.

Tunable Piezoelectric Cantilever Beams for Energy Harvesting

Aerospace ◽  
2006 ◽  
Author(s):  
David Charnegie ◽  
Changki Mo ◽  
Amanda A. Frederick ◽  
William W. Clark
Keyword(s):  
Cantilever Beam ◽  
Electromechanical Coupling ◽  
Mechanical Energy ◽  
Piezoelectric Element ◽  
Electrical Energy ◽  
Vibration Source ◽  
Frequency Range ◽  
Piezoelectric Cantilever ◽  
Tip Mass ◽  
Shunt Circuit

Over the past several years, there has been increasing interest in harvesting energy from ambient vibrations in the environment by converting mechanical energy into electrical energy. A popular method is to use a piezoelectric cantilever beam. In order to harvest the most energy with the device, the beam's fundamental mode must be excited. However, this is not always possible due to manufacturing of the device or fluctuations in the vibration source. By being able to change the frequencies of the beam, the device can be more effective in harvesting energy. In this paper, a model for a three layered piezoelectric cantilever beam utilizing a shunt tuning circuit will be presented. The fundamental frequency of a cantilever beam is dependent on the stiffness and mass of the beam. Either adding a tip mass to the end of the beam or increasing the dimensions of the beam can alter the mass. The stiffness of the beam is a function of the geometry, mechanical properties, and the electromechanical coupling of the piezoelectric element. In this paper we prepare the use of a piezoelectric layer with an attached shunt circuit for tuning its stiffness, and thus the beam frequency. The piezoelectric coefficients of this layer and its shunt circuit determine the amount of electromechanical coupling. By varying the shunt circuit, the beam can be tuned to a certain frequency. This paper presents a study of the effects additional harvesting and tuning layers have on the amount of tuning and generated power in the beam. These additional layers will add more piezoelectric material as well as mass to the beam and therefore there will be a balance between the amount of harvested energy and the tunable frequency range. By quantifying the effects of these parameters, it will be easier to design a harvester to be used in a particular frequency range as well as to produce a certain level of power.

scholarly journals Theoretical analysis of dynamic property for piezoelectric cantilever triple-layer benders with large piezoelectric and electromechanical coupling coefficients

2016 ◽  
Vol 06 (03) ◽  
pp. 1650017 ◽  
Author(s):  
Li Jiao Gong ◽  
Cheng Liang Pan ◽  
Qiao Sheng Pan ◽  
Zhi Hua Feng
Keyword(s):  
Electromechanical Coupling ◽  
Coupling Coefficients ◽  
Bending Rigidity ◽  
Dynamic Features ◽  
Energy Harvesters ◽  
Response Characteristics ◽  
Triple Layer ◽  
Piezoelectric Cantilever ◽  
Circular Frequency ◽  
Conventional Models

Ferroelectric single crystals, such as PZN-PT, provide novel prospects in piezoelectric bending devices such as actuators, sensors or energy harvesters because of their extraordinarily large piezoelectric coefficients. However, large errors may occur in some analyses on electromechanical behaviors using the conventional models. We find the bending rigidity of piezoelectric composited bender is affected not only by thickness, width and the modulus of elasticity of the different layers but also electromechanical coupling coefficients (EMCCs) of the piezoelectric material and the larger EMCCs mean more marked effect. This paper focuses on the derivation of the applied input excitation and output response characteristics in the circular frequency domain for piezoelectric cantilever triple-layer benders (PCTBs), taking into account the secondary piezoelectric effect. Analytic dynamic descriptions of such actuators and transducers are obtained. Based on the presented models dynamic features of PCTB composed of PZN-8%PT are calculated, and numerical results coincide with simulations using the finite element method (FEM).

scholarly journals Experimental Research on Wind-Induced Flag-Swing Piezoelectric Energy Harvesters

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jianjun Liu ◽  
Xianghua Chen ◽  
Yujie Chen ◽  
Hong Zuo ◽  
Qun Li
Keyword(s):  
Energy Harvesting ◽  
Cantilever Beam ◽  
Wind Field ◽  
Electromechanical Coupling ◽  
Energy Harvester ◽  
Coupling Effect ◽  
Green Energy ◽  
External Resistance ◽  
Piezoelectric Energy ◽  
Piezoelectric Cantilever

Piezoelectric cantilever beams, which have simple structures and excellent mechanical/electrical coupling characteristics, are widely applied in energy harvesting. When the piezoelectric cantilever beam is in a wind field, we should consider not only the influence of the wind field on piezoelectric beam but also the electromechanical coupling effect on it. In this paper, we design and test a wind-induced flag-swing piezoelectric energy harvester (PEH). The piezoelectric cantilever beam may vibrate in the wind field by affixing a flexible ribbon to the free end as the windward structure. To fulfill the goal of producing electricity, the flexible ribbon can swing the piezoelectric cantilever in a wind-induced unstable condition. The experimental findings demonstrate that the flag-swing PEH performs well in energy harvesting when the wind field is excited. When the wind speed is 15 m/s, the peak-to-peak output AC voltage may reach 13.88 V. In addition, the voltage at both ends of the closed-loop circuit’s external resistance is examined. The maximum electric power of the PEH may reach 43.4 μW with an external resistance of 650 kΩ. After passing through the AC-DC conversion circuit, the flag-swing PEH has a steady DC voltage output of 1.67 V. The proposed energy harvester transforms wind energy from a wind farm into electrical energy for supply to low-power electronic devices, allowing for the creation and use of green energy to efficiently address the issue of inadequate energy.

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