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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