|
|
论文:2017,Vol:35,Issue(4):669-675 |
|
|
引用本文： |
|
|
朱培, 任兴民, 秦卫阳, 杨永锋, 王元生, 周志勇. 非线性双稳态压电俘能系统在有界噪声与谐和激励下的Melnikov混沌运动阈值分析[J]. 西北工业大学学报 |
|
|
Zhu Pei, Ren Xingmin, Qin Weiyang, Yang Yongfeng, Wang Yuansheng, Zhou Zhiyong. The Analysis of Melnikov Chaotic Motion Threshold of Nonlinear Bistable Piezoelectric Energy Harvester System Subjected Bounded Noise and Harmonic Excitation[J]. Northwestern polytechnical university |
|
|
|
|
|
|
|
| 非线性双稳态压电俘能系统在有界噪声与谐和激励下的Melnikov混沌运动阈值分析 |
|
| 朱培, 任兴民, 秦卫阳, 杨永锋, 王元生, 周志勇 |
|
| 西北工业大学 力学与土木建筑学院, 陕西 西安 710072 |
| 摘要: |
| 研究了在有界噪声与谐和激励作用下非线性双稳态压电俘能系统的动力学响应特性。基于随机Melnikov理论推导出了系统发生阱间混沌运动的条件。通过数值模拟发现系统在临界阈值处由单阱运动演变为双阱混沌运动并验证了理论分析的有效性。研究结果表明有界噪声幅值和阻抗对系统发生同宿分岔有较大影响，随着非线性阻尼系数增加，系统由混沌运动变为周期运动，Wiener过程强度参数越大，系统混沌吸引子的面积就越大。 |
| 关键词:
双稳态
随机Melnikov
混沌
有界噪声
谐和激励
|
|
| The Analysis of Melnikov Chaotic Motion Threshold of Nonlinear Bistable Piezoelectric Energy Harvester System Subjected Bounded Noise and Harmonic Excitation |
|
| Zhu Pei, Ren Xingmin, Qin Weiyang, Yang Yongfeng, Wang Yuansheng, Zhou Zhiyong |
|
| School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| In this paper the dynamic response of nonlinear bi-stable piezoelectric nonlinear energy harvester system subjected bounded noise and harmonic excitations is investigated. The condition of starting chaotic motion is obtained based on Melnikov method. The results of numerical simulation show that the system could transform intra-well motion to inter-well motion near to a certain threshold, which verified the availability of theoretical analysis. The numerical results show that the amplitude of bounded noise and impedance have a significantly influence on homoclinic bifurcation. The state of system will change from chaotic motion into periodic motion. Chaotic attractor area will increase by increasing the intensity of Wiener process parameter. |
| Key words:
bi-stability
random Melnikov
chaos
bounded noise
harmonic excitation
|
|
| 收稿日期: 2017-02-06
修回日期:
|
| DOI: |
| 基金项目: 国家自然科学基金（11672237、11272257）、航空科学基金（2013ZB08001）、航天科技创新基金（2016kc060013）与中央高校基本科研业务费（3102016ZY016）资助 |
| 通讯作者:
Email： |
| 作者简介: 朱培(1984—),西北工业大学博士研究生,主要从事非线性动力及压电俘能等研究。
|
|
|
|
|
|
|
|
参考文献: |
|
|
[1] Robert B. Energy Harvesting and Wireless Sensors: A Review of Recent Developments[J]. Sensor Review, 2009, 29(3): 194-199
[2] Wang H J, Meng Q F. Analytical Modeling and Experimental Verification of Vibration-Based Piezoelectric Bimorph Beam with a Tip-Mass for Power Harvesting[J]. Mechanical Systems and Signal Processing, 2013, 36(1): 193-209
[3] Anton S R, Sodano H A. A Review of Power Harvesting Using Piezoelectric Materials[J]. Smart Materials and Structures, 2007, 16(3): R1-R21
[4] Erturk A, Inman D J. Broadband Piezoelectric Power Generation on High-Energy Orbits of the Bistable Duffing Oscillator with Electro-Mechanical Coupling[J]. Journal of Sound and Vibration, 2011, 10(330): 2339-2353
[5] Moon F C, Holmes P J. A Magnetoelastic Strange Attractor[J]. Journal of Sound and Vibration, 1979, 65(2): 275-296
[6] 高毓璣, 冷永刚, 范胜波, 赖志慧. 弹性支撑双稳压电悬臂梁振动响应及俘能研究[J]. 物理学报, 2014, 63(9): 090501 Gao Y J, Leng Y G, Fan S B, Lai Z H. Studies on Vibration Response and Energy Harvesting of Elastic-Supported Bistable Piezoelectric Cantilever Beams[J]. Acta Physica Sinica, 2014, 63(9): 090501 (in Chinese)
[7] Bulsara A R, Schieve W C, Jacobs E W. Homoclinic Chaos in Systems Perturbed by Weak Langevin Noise[J]. Physical Review A, 1990, 41(2): 668-681
[8] 徐伟, 孙中奎, 杨晓丽. 谐和激励与有界噪声作用下具有同宿和异宿轨道的Duffing振子的混沌运动[J]. 物理学报, 2006, 55(4): 1678-1686 Xu W, Sun Z K, Yang X L. Influence of Harmonic and Bounded Noise Excitations on Chaotic Motion of Duffing Oscillator with Homoclinic and Heteroclinic Orbits[J]. Acta Physica Sinica, 2006, 55(4): 1678-1686 (in Chinese)
[9] Siewe M S, Tchawoua C, Woafo P. Melnikov Chaos in a Periodically Driven Rayleigh-Duffing Oscillator[J]. Mechanics Research Communications, 2010, 37(4): 363-368
[10] 韩强, 张善元, 杨桂通. 一类非线性动力系统混沌运动的研究[J]. 应用数学和力学, 1999, 20(8): 776-782 Han Q, Zhang S Y, Yang G T. The Study on the Chaotic Motion of a Nonlinear Dynamical System[J]. Applied Mathematics and Mechanics, 1999, 20(8): 776-782 (in Chinese)
[11] Stanton S C, Erturk A, Mann B P, Inman D J. Nonlinear Piezoelectricity in Electroelastic Energy Harvesters: Modeling and Experimental Identification[J]. Journal of Applied Physics, 2010, 108(1): 074903 |
|
|
|
|
|
|
|
