A Distributed Parameters Model for Broadband Energy Harvesting From Nonlinear Vibration of the Piezoelectric System

محورهای موضوعی : Mechanical Engineering

M.M Zamani ¹ (Department of Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)
Mohammad Abbasi ² (Department of Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)
Fariborz Forouhandeh ³ (Department of Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)

تاریخ دریافت : 1401/08/10 تاریخ پذیرش : 1401/10/14 تاریخ انتشار : 1401/12/10

کلید واژه: Time and frequency responses, Nonlinear vibration, 2D-BPEH, Harvesting voltage, Distributed parameter model,

چکیده مقاله :

To the extent of the usable bandwidth of the piezoelectric energy harvesters (PEH) and progress the harvesting proficiency, a 2-DOF bistable PEH (2D-BPEH) with an elastic substructure is developed to show the strengthened nonlinear large-amplitude periodic vibration performances. Introducing the substructure, which is demonstrated by the mass-spring sub-system added between the distributed bimorph beam and exciting base, dynamic motions of the beam is expected to reproduce high energy trajectories and large deflections. Due to raising the accuracy of the model and results, the key novelty of the present study is to consider the mathematical model of composite smart bimorph beam with the aid of distributed parameters model and Von Karman strain relations. With the help of Hamilton’s principle, Electro mechanic modeling of the 2-DOF system has been derived and three coupled equations are consequent utilizing the Galerkin method. Primarily deflection and voltage frequency response curves are calculated analytically; then, the model has been compared and validated by the results of the 2-DOF PEH model with lumped parameter beam in the literature. Numerical results indicate that accurate designing of 2-DOF piezoelectric energy harvester parameters could intensely enhance the generating voltage and at a broader exciting frequency band. The results have shown that the 2-DOF bistable PEH coupled with elastic substructure as a magnifier harvests extra electrical power at specific input frequencies and operates at larger bandwidth than routine PEHs.

چکیده انگلیسی:

To the extent of the usable bandwidth of the piezoelectric energy harvesters (PEH) and progress the harvesting proficiency, a 2-DOF bistable PEH (2D-BPEH) with an elastic substructure is developed to show the strengthened nonlinear large-amplitude periodic vibration performances. Introducing the substructure, which is demonstrated by the mass-spring sub-system added between the distributed bimorph beam and exciting base, dynamic motions of the beam is expected to reproduce high energy trajectories and large deflections. Due to raising the accuracy of the model and results, the key novelty of the present study is to consider the mathematical model of composite smart bimorph beam with the aid of distributed parameters model and Von Karman strain relations. With the help of Hamilton’s principle, Electro mechanic modeling of the 2-DOF system has been derived and three coupled equations are consequent utilizing the Galerkin method. Primarily deflection and voltage frequency response curves are calculated analytically; then, the model has been compared and validated by the results of the 2-DOF PEH model with lumped parameter beam in the literature. Numerical results indicate that accurate designing of 2-DOF piezoelectric energy harvester parameters could intensely enhance the generating voltage and at a broader exciting frequency band. The results have shown that the 2-DOF bistable PEH coupled with elastic substructure as a magnifier harvests extra electrical power at specific input frequencies and operates at larger bandwidth than routine PEHs.

منابع و مأخذ:

1. Talebitooti R., Darvish Gohari H., Zarastvand M., Loghmani A., 2019, A robust optimum controller for suppressing radiated sound from an intelligent cylinder based on sliding mode method considering piezoelectric uncertainties, Journal of Intelligent Materials Systems and Structures 30(20): 3066-3079.


2.  Darvish Gohari H., Zarastvand M., Talebitooti R., Loghmani A., Omidpanah M., 2020, Radiated sound control from a smart cylinder subjected to piezoelectric uncertainties based on sliding mode technique using self-adjusting boundary layer, Aerospace Scienceand Technology 106: 106141.


3. Darvish Gohari H., Zarastvand M., Talebitooti R., Shahbazi R., 2021, Hybrid control technique for vibroacoustic performance analysis of a smart doubly curved sandwich structure considering sensor and actuator layers, Journal of Sandwich Structures and Materials 23(5): 1453-1480.


4. Asadijafari M.H., Zarastvand M.R., Talebitooti R., 2021, The effect of considering Pasternak elastic foundation on acoustic insulation of the finite doubly curved composite structures, Composite Structures 256: 113064.


5. Hou Y., 2017, Flexible ionic diodes for low-frequency mechanical energy harvesting, Advanced Energy Materials 7(5): 1601983.


6. Beeby S.P., 2007, A micro electromagnetic generator for vibration energy harvesting, Journal of Micromechanics and Microengineering 17(7): 1257.


7. Harne R.L., Wang K. W., 2013, A review of the recent research on vibration energy harvesting via bistable systems, Smart Materials and Structures 22(2): 23001.


8. Aboulfotoh N.A., Arafa M.H., Megahed S.M., 2013, A self-tuning resonator for vibration energy harvesting, Sensors and Actuators A: Physical 201: 328-334.


9. Bai X., Wen Y., Li P., Yang J., Peng X., Yue X., 2014, Multi-modal vibration energy harvesting utilizing spiral cantilever with magnetic coupling, Sensors and Actuators A: Physical 209: 78-86.


10. Wu X., Lee D.-W., 2015, Magnetic coupling between folded cantilevers for high-efficiency broadband energy harvesting, Sensors and Actuators A: Physical 234: 17-22.


11. Daqaq M.F., Bode D., 2011, Exploring the parametric amplification phenomenon for energy harvesting, Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering 225(4): 456-466.


12. Abdelkefi A., Nayfeh A.H., Hajj M.R., 2012, Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters, Nonlinear Dynamics 67(2): 1147-1160.


13. Daqaq M.F., Masana R., Erturk A., Quinn D.D., 2014, On the role of nonlinearities in vibratory energy harvesting : a critical review and discussion, Applied Mechanics Reviews 66(4): 040801.


14. Yang Z., Zhu Y., Zu J., 2015, Theoretical and experimental investigation of a nonlinear compressive-mode energy harvester with high power output under weak excitations, Smart Materials and Structures 24(2): 25028.


15. Jahani K., Aghazadeh P., 2016, Investigating the performance of piezoelectric energy harvester including geometrical, damping and material nonlinearities with the method of multiple scales, Modares Mechanical Engineering 16(4): 354-360.


16. Lin J.-T., Alphenaar B., 2010, Enhancement of energy harvested from a random vibration source by magnetic coupling of a piezoelectric cantilever, Journal of Intelligent Materials Systems and Structures 21(13): 1337-1341.


17. Zhao D., 2018, Analysis of single-degree-of-freedom piezoelectric energy harvester with stopper by incremental harmonic balance method, Materials Research Express 5(5): 55502.


18. Tang L., Yang Y., Soh C.K., 2010, Toward broadband vibration-based energy harvesting, Journal of Intelligent Materials Systems and Structures 21(18): 1867-1897.


19. Tang L., Yang Y., Soh C.-K., 2012, Improving functionality of vibration energy harvesters using magnets, Journal of Intelligent Materials Systems and Structures 23(13): 1433-1449.


20. Gammaitoni L., Hänggi P., Jung P., Marchesoni F., 2009, Stochastic resonance: a remarkable idea that changed our perception of noise, European Physical Journal B 69(1): 1-3.


21. Erturk A., Hoffmann J., Inman D.J., 2009, A piezomagnetoelastic structure for broadband vibration energy harvesting, Applied Physics Letters 94(25): 254102.


22. Ferrari M., Ferrari V., Guizzetti M., Andò B., Baglio S., Trigona C., 2010, Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters, Sensors and Actuators A: Physical 162(2): 425-431.


23. Stanton S.C., McGehee C.C., Mann B.P., 2010, Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator, Physica D: Nonlinear Phenomena 239(10): 640-653.


24. Stanton S.C., Owens B.A.M., Mann B.P., 2012, Harmonic balance analysis of the bistable piezoelectric inertial generator, Journal of Sound and Vibration 331(5): 3617-3627.


25. Karami M.A., Inman D.J., 2011, Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems, Journal of Sound and Vibration 330(23): 5583-5597.


26. Erturk A., Inman D.J., 2011, Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling, Journal of Sound and Vibration 330(10): 2339-2353.


27. Sebald G., Kuwano H., Guyomar D., Ducharne B., 2011, Simulation of a duffing oscillator for broadband piezoelectric energy harvesting, Smart Materials and Structures 20(7): 75022.


28. Sebald G., Kuwano H., Guyomar D., Ducharne B., 2011, Experimental duffing oscillator for broadband piezoelectric energy harvesting, Smart Materials and Structures 20(10): 102001.


29. Kim P., Seok J., 2014, A multi-stable energy harvester: Dynamic modeling and bifurcation analysis, Journal of Sound and Vibration 333(21): 5525-5547.


30. Zhao D., Gan M., Zhang C., Wei J., Liu S., 2018, Analysis of broadband characteristics of two degree of freedom bistable piezoelectric energy harvester, Materials Research Express 5(8):


31. Vasic D., Costa F., 2013, Modeling of piezoelectric energy harvester with multi-mode dynamic magnifier with matrix representation, International Journal of Applied Electromagnetics and Mechanics 43(3): 237-255.


32. Wang H., Shan X., Xie T., 2012, An energy harvester combining a piezoelectric cantilever and a single degree of freedom elastic system, Journal of Zhejiang University Science A 13(7): 526-537.


33. Zhou W., Penamalli G.R., Zuo L., 2011, An efficient vibration energy harvester with a multi-mode dynamic magnifier, Smart Materials and Structures 21(1): 15014.


34.  Aldraihem O., Baz A., 2011, Energy harvester with a dynamic magnifier, Journal of Intelligent Materials Systems and         Structures 22(6): 521-530.


35. Aladwani A., Arafa M., Aldraihem O., Baz A., 2012, Cantilevered piezoelectric energy harvester with a dynamic magnifier, Journal of Vibration and Acoustics 134(3): 31004.


36. Tang L., Wang J., 2017, Size effect of tip mass on performance of cantilevered piezoelectric energy harvester with a dynamic magnifier, Acta Mechanica 228(11): 3997-4015.


37. Tang L., Yang Y., 2012, A multiple-degree-of-freedom piezoelectric energy harvesting model, Journal of Intelligent Materials Systems and Structures 23(14): 1631-1647.


38. Wang G.-Q., Liao W.-H., 2016, A bistable piezoelectric oscillator with an elastic magnifier for energy harvesting enhancement, Journal of Intelligent Materials Systems and Structures 28(3): 392-407.


39. Erturk A., Inman D.J., 2009, An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations, Smart Materials and Structures 18(2): 25009.