Study on Parametric Resonance of Vertical Cantilevered Piezoelectric Energy Harvester with End Mass and Its Characteristics
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摘要: 为了改善参数共振压电俘能器的俘能特性，提出在竖直梁的自由端固结一个质量块。利用拉格朗日方程和高斯定律建立了系统的机电耦合方程，并进行了数值仿真。仿真结果表明，梁从竖直的单稳态系统转变为屈曲的双稳态系统的临界末端质量Mc为0.0509 kg。当梁的阻尼比为0.05，末端质量从0增加到Mc时，参数共振激励阈值从47.5 m/s2减小到趋向于0；当M大于Mc时，对于任何阻尼比的梁，激励阈值都为零，并且当外激励的幅值和频率使得梁处于两稳态势阱间的大幅周期运动时，俘能器才可以产生出较高的输出功率。Abstract: In order to improve the harvesting behaviors of parametric resonance piezoelectric energy harvester, it is proposed to install a mass block at the end of vertical cantilevered beam. Based on the Lagrange equation and Gauss law, the coupling equation between the mechanical system and electric system of energy harvester is derived and numerical simulations of its dynamic characteristics are carried out. The critical end mass Mc of the beam from monostable system into bistable system is 0.0509 kg. When the damping ratio of beam is 0.05 and the end mass increases from 0 to Mc, the excitation threshold of occurring parametric resonance will decrease from 47.5 m/s2 to 0. When the end mass M is larger than Mc, the excitation threshold is zero for any damping ratio of the beam, and the output of harvesting energy would be higher only when the cantilever beam oscillates periodically between the two stable positions under the excitation with proper amplitude and frequency.
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Key words:
- energy harvester /
- piezoelectric /
- parametric resonance /
- excitation threshold
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表 1 俘能器仿真参数
参数 梁 压电片 长度$(L,{L_{{p}}})/{\rm{mm}}$ 200 30 宽度$({w_{{b}}},{w_{{p}}})/{\rm{mm}}$ 16 16 厚度$({t_{{b}}},{t_{{p}}})/{\rm{mm}}$ 0.4 0.3 密度$\rho /{\rm{(kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}}{\rm{)}}$ 7165 － 杨氏模量$(E,{E_{{p}}})/{\rm{GPa}}$ 100 66 压电常数${d_{31}}/({\rm{pC}} \cdot {{\rm{N}}^{{\rm{ - 1}}}})$ － −190 介电常数${\varepsilon _{33}}/{\rm{(nF}} \cdot {{\rm{m}}^{{\rm{ - 1}}}}{\rm{)}}$ － 13.28 负载电阻$R/{\rm{M\Omega }}$ － 5 
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[1] 孙健, 李以贵, 刘景全, 等. 微压电式振动能量采集器的研究进展[J]. 微纳电子技术, 2009, 46(11): 673-677, 690SUN J, LI Y G, LIU J Q, et al. Trends of MEMS-based piezoelectric vibration energy harvesters[J]. Micronanoelectronic Technology, 2009, 46(11): 673-677, 690 (in Chinese) [2] KIM S G, PRIYA S, KANNO I. Piezoelectric MEMS for energy harvesting[J]. MRS Bulletin, 2012, 37(11): 1039-1050 doi: 10.1557/mrs.2012.275 [3] 蒋树农, 郭少华, 李显方. 单压电片悬臂梁式压电俘能器效能分析[J]. 振动与冲击, 2012, 31(19): 90-94JIANG S N, GUO S H, LI X F. Performance analysis for a unimorph cantilever piezoelectric harvester[J]. Journal of Vibration and Shock, 2012, 31(19): 90-94 (in Chinese) [4] 唐刚, 刘景全, 马华安, 等. 微型压电振动能量采集器的研究进展[J]. 机械设计与研究, 2010, 26(4): 61-64, 70TANG G, LIU J Q, MA H A, et al. A survey on research of micro piezoelectric vibration energy harvesters[J]. Machine Design and Research, 2010, 26(4): 61-64, 70 (in Chinese) [5] 李金田, 文玉梅. 压电式振动能量采集装置研究进展[J]. 现代电子技术, 2011, 34(18): 184-189 doi: 10.3969/j.issn.1004-373X.2011.18.056LI J T, WEN Y M. A survey on research of piezoelectric vibration energy acquisition device[J]. Modern Electronics Technique, 2011, 34(18): 184-189 (in Chinese) doi: 10.3969/j.issn.1004-373X.2011.18.056 [6] DAQAQ M F, STABLER C, QAROUSH Y, et al. Investigation of power harvesting via parametric excitations[J]. Journal of Intelligent Material Systems and Structures, 2009, 20(5): 545-557 doi: 10.1177/1045389X08100978 [7] ABDELKEF A, NAYFEH A H, HAJJ M R. Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters[J]. Nonlinear Dynamics, 2012, 67(2): 1147-1160 doi: 10.1007/s11071-011-0059-6 [8] MAM K, PEIGNEY M, SIEGERT D. Finite strain effects in piezoelectric energy harvesters under direct and parametric excitations[J]. Journal of Sound and Vibration, 2017, 389: 411-437 doi: 10.1016/j.jsv.2016.11.022 [9] JIA Y, YAN J Z, SOGA K, et al. A parametrically excited vibration energy harvester[J]. Journal of Intelligent Material Systems and Structures, 2014, 25(3): 278-289 doi: 10.1177/1045389X13491637 [10] JIA Y, YAN J Z, SOGA K. Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude[J]. Smart Materials and Structures, 2014, 23(6): 065011 doi: 10.1088/0964-1726/23/6/065011 [11] JIA Y, SESHIA A A. An auto-parametrically excited vibration energy harvester[J]. Sensors and Actuators A: Physical, 2014, 220: 69-75 doi: 10.1016/j.sna.2014.09.012 [12] LAN C B, QIN W Y, DENG W Z. Energy harvesting by dynamic unstability and internal resonance for piezoelectric beam[J]. Applied Physics Letters, 2015, 107(9): 093902 doi: 10.1063/1.4930073 [13] FIROOZY P, KHADEM S E, POURKIAEE S M. Power enhancement of broadband piezoelectric energy harvesting using a proof mass and nonlinearities in curvature and inertia[J]. International Journal of Mechanical Sciences, 2017, 133: 227-239 doi: 10.1016/j.ijmecsci.2017.08.048 [14] FRISWELL M I, ALI S F, BILGEN O, et al. Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass[J]. Journal of Intelligent Material Systems and Structures, 2012, 23(13): 1505-1521 doi: 10.1177/1045389X12455722 [15] LAN C B, QIN W Y. Enhancing ability of harvesting energy from random vibration by decreasing the potential barrier of bistable harvester[J]. Mechanical Systems and Signal Processing, 2017, 85: 71-81 doi: 10.1016/j.ymssp.2016.07.047 [16] ERTURK A, INMAN D J. A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters[J]. Journal of Vibration and Acoustics, 2008, 130(4): 041002 doi: 10.1115/1.2890402 [17] 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): 025009 doi: 10.1088/0964-1726/18/2/025009 -
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