基于多尺度法双稳态压电俘能器动力特性分析
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摘要
基于欧拉-伯努利梁假设,推导了双稳态悬臂式压电俘能系统的分布参数模型,建立了分析该模型的多尺度法并获得了系统的动力响应解析表达式,论证了多尺度法分析双稳态压电俘能器性能的可行性;研究了磁铁间距、外部激励的幅值、阻尼比、力电耦合系数、负载阻抗等参数对俘能系统性能的影响。结果表明:产生阱间运动的激励幅值阈值与激励频率、两磁铁间距有关,低于激励阈值仅有阱内运动产生;输出功率并不是随着力电耦合系数增大而增加,而是存在最优力电耦合系数产生最大的输出功率,力电耦合系数大于最优值后,阱间运动输出功率减小;随着两磁铁间距的增大,阱间运动的频带宽度减小;减小系统的阻尼比可以有效地拓宽系统的阱间运动频带并获得较高的输出功率。通过优化设计、合理地调节各参数,可以提高压电俘能系统的输出功率和拓宽系统的工作频带宽度。
Based on the Euler-Bernoulli beam assumption, the distributed parameter model of bistable piezoelectric cantilever energy harvesting system is deduced. The multiple scale method is exploited for analyzing this model. The analytical expressions of the system dynamic response are obtained. Feasibility of the multiple scale method is demonstrated for analyzing the performance of bistable piezoelectric energy harvester. This investigation is focused on the effects of gap distance between magnets, external excited amplitude, mechanical damping ratio, piezoelectric layer thickness and external resistance load on the performance of the energy harvesting system. The results show that the excitation threshold that produces the inter-well motion is related to the excitation frequency and the distance between two magnets. Below the excitation threshold, only the intra-well motion produces. The output power does not increase with the increase of the electromechanical coupling coefficient, but there is an optimal electromechanical coupling coefficient to produce the maximum output power. When the electromechanical coupling coefficient is greater than the optimal value, the inter-well motion output power decreases. As the distance between the two magnets increases, the bandwidth of inter-well motion decreases. Reducing the system damping ratio may effectively broaden the bandwidth of inter-well motion and leads to higher output power. Reasonable adjustment of various parameters may improve the output power of piezoelectric energy harvesting system and broaden the system operating frequency by optimizing design.
Based on the Euler-Bernoulli beam assumption, the distributed parameter model of bistable piezoelectric cantilever energy harvesting system is deduced. The multiple scale method is exploited for analyzing this model. The analytical expressions of the system dynamic response are obtained. Feasibility of the multiple scale method is demonstrated for analyzing the performance of bistable piezoelectric energy harvester. This investigation is focused on the effects of gap distance between magnets, external excited amplitude, mechanical damping ratio, piezoelectric layer thickness and external resistance load on the performance of the energy harvesting system. The results show that the excitation threshold that produces the inter-well motion is related to the excitation frequency and the distance between two magnets. Below the excitation threshold, only the intra-well motion produces. The output power does not increase with the increase of the electromechanical coupling coefficient, but there is an optimal electromechanical coupling coefficient to produce the maximum output power. When the electromechanical coupling coefficient is greater than the optimal value, the inter-well motion output power decreases. As the distance between the two magnets increases, the bandwidth of inter-well motion decreases. Reducing the system damping ratio may effectively broaden the bandwidth of inter-well motion and leads to higher output power. Reasonable adjustment of various parameters may improve the output power of piezoelectric energy harvesting system and broaden the system operating frequency by optimizing design.
引文
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[11]唐炜,王小璞,曹景军.非线性磁式压电振动能量采集系统建模与分析[J].物理学报,2014,63(24):72-85.(TANG Wei,WANGXiaopu,CAO Jingjun.Modeling and analysis of piezoelectric vibration energy harvesting system using permanent magnetics[J].Acta physica sinica,2014,63(24):72-85(in Chinese)).
[12]KIM P,YOON Y J,SEOK J.Nonlinear dynamic analyses on a magnetopiezoelastic energy harvester with reversible hysteresis[J].Nonlinear dynamics,2016,83(4):1823-1854.
[13]DAQAQ M F,MASANA R,ERTURK A,et al.On the role of nonlinearities in vibratory energy harvesting:a critical review and discussion[J].Applied mechanics reviews,2014,66(4):040801-1-040801-23.
[14]SZEMPLILISKA-STUPNICKA W,RUDOWSKI J.Steady states in the twin-well potential oscillator:computer simulations and approximate analytical studies[J].Chaos,1993,3(3):375-385.
[15]胡海岩.应用非线性动力学[M].北京:航空工业出版社,2000.(HUHaiyan.Applied nonlinear dynamics[M].Beijing:Chinese Aviation Industrial Publishing House,2000(in Chinese)).
[2]ERTURK A,INMAN D J.An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations[J].Smart materials and structures,2009,18(2):25009-25018.
[3]唐礼平,王建国.一种具有新型动力放大器压电悬臂梁俘能器计算模型和解析解[J].计算力学学报,2017,34(5):650-656.(TANGLiping,WANG Jianguo.Modeling and analytical solution of piezoelectric cantilevered energy harvester with a new dynamic magnifier[J].Chinese journal of computational mechanics,2017,34(5):650-656(in Chinese)).
[4]STANTON S C,MCGEHEE C C,MANN B P.Nonlinear dynamics for broadband energy harvesting:investigation of a bistable piezoelectric inertial generator[J].Physica D nonlinear phenomena,2010,239(10):640-653.
[5]STANTON S C,OWENS B A M,MANN B P.Harmonic balance analysis of the bistable piezoelectric inertial generator[J].Journal of sound and vibration,2012,331(15):3617-3627.
[6]LIU W Q,BADEL A,FORMOSA F,et al.Novel piezoelectric bistable oscillator architecture for wideband vibration energy harvesting[J].Smart materials and structures,2013,22(3):035013.
[7]LIU W,FORMOSA F,BADEL A.Optimization study of a piezoelectric bistable generator with doubled voltage frequency using harmonic balance method[J].Journal of intelligent material systems and structures,2017,28(5):671-686.
[8]ERTURK A,INMAN D J.Broadband piezoelectric power generation on high-energy orbits of the bistable duffing oscillator with electromechanical coupling[J].Journal of sound and vibration,2011,330(10):2339-2353.
[9]孙舒,曹树谦.双稳态压电悬臂梁发电系统的动力学建模及分析[J].物理学报,2012,61(21):210505.(SUN Shu,CAO Shuqian.Dynamic modeling and analysis of a bistable piezoelectric cantilever power generation system[J].Acta physica sinica,2012,61(21):210505(in Chinese)).
[10]TANG L,YANG Y,SOH C K.Improving functionality of vibration energy harvesters using magnets[J].Journal of intelligent material systems and structures,2012,23(23):1433-1449.
[11]唐炜,王小璞,曹景军.非线性磁式压电振动能量采集系统建模与分析[J].物理学报,2014,63(24):72-85.(TANG Wei,WANGXiaopu,CAO Jingjun.Modeling and analysis of piezoelectric vibration energy harvesting system using permanent magnetics[J].Acta physica sinica,2014,63(24):72-85(in Chinese)).
[12]KIM P,YOON Y J,SEOK J.Nonlinear dynamic analyses on a magnetopiezoelastic energy harvester with reversible hysteresis[J].Nonlinear dynamics,2016,83(4):1823-1854.
[13]DAQAQ M F,MASANA R,ERTURK A,et al.On the role of nonlinearities in vibratory energy harvesting:a critical review and discussion[J].Applied mechanics reviews,2014,66(4):040801-1-040801-23.
[14]SZEMPLILISKA-STUPNICKA W,RUDOWSKI J.Steady states in the twin-well potential oscillator:computer simulations and approximate analytical studies[J].Chaos,1993,3(3):375-385.
[15]胡海岩.应用非线性动力学[M].北京:航空工业出版社,2000.(HUHaiyan.Applied nonlinear dynamics[M].Beijing:Chinese Aviation Industrial Publishing House,2000(in Chinese)).