负刚度非线性系统的回复力曲面参数辨识方法

胡方圆; 刘清华; 曹军义; 张颖

doi:10.7652/xjtuxb202104011

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负刚度非线性系统的回复力曲面参数辨识方法

更新时间：2025-07-09

- 负刚度非线性系统的回复力曲面参数辨识方法
- Restoring Force Surface-Based Parameter Identification Method for Negative Stiffness Nonlinear System
- 西安交通大学学报 2021年55卷第4期页码：95-106
- 作者机构：
  
  西安交通大学现代设计及转子轴承系统教育部重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2020-08-22。作者简介: 胡方圆(1996—),女,硕士生;曹军义(通信作者),男,教授。基金项目: 国家自然科学基金资助项目(51975453)
- DOI：10.7652/xjtuxb202104011
  中图分类号： TH39
- 网络首发：2021-04-10，
  
  纸质出版：2021
- 稿件说明：
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胡方圆, 刘清华, 曹军义, 等. 负刚度非线性系统的回复力曲面参数辨识方法[J]. 西安交通大学学报, 2021,55(4):95-106.

Restoring Force Surface-Based Parameter Identification Method for Negative Stiffness Nonlinear System[J]. 2021, 55(4): 95-106.
胡方圆, 刘清华, 曹军义, 等. 负刚度非线性系统的回复力曲面参数辨识方法[J]. 西安交通大学学报, 2021,55(4):95-106. DOI： 10.7652/xjtuxb202104011.

Restoring Force Surface-Based Parameter Identification Method for Negative Stiffness Nonlinear System[J]. 2021, 55(4): 95-106. DOI： 10.7652/xjtuxb202104011.

摘要

针对负刚度非线性振子回复力的辨识困难问题

提出了一种基于回复力曲面的时域非参数辨识方法。对比分析了位移微分和加速度积分的数值处理方法

给出了利用实验数据绘制4种典型负刚度振子三维回复力曲面图及提取刚度力和阻尼力的方法。研究结果表明:对4种负刚度振子的数值模拟

多项式刚度力和阻尼力系数的辨识精度都可达95%以上。通过搭建实验平台对不同加速度水平下的多稳态振子进行了扫频实验

并基于设计方法建立了多稳态振子的回复力表面

表面识别结果与实测回复力面吻合较好

验证了回复力曲面法辨识负刚度非线性振子的有效性。该研究为能量俘获及振动控制领域的非线性研究提供了一种可行的方法。

Abstract

Aiming at the difficulty in identifying the restoring force of a nonlinear oscillator with negative stiffness

a time-domain nonparametric identification method based on restoring force surface is proposed. The numerical processing schemes of displacement differentiation and acceleration integration are compared and analyzed. A method for drawing three-dimensional restoring force surface diagrams of four typical negative stiffness oscillators and extracting stiffness and damping restoring forces by experimental data is given. This approach shows that the identification accuracy of the polynomial stiffness force and the damping force coefficient can reach more than 95% in the numerical simulation of the four negative stiffness vibrators. Frequency sweep experiment is carried out on the multi-stable oscillators at different acceleration levels by building an experimental platform. Following the designing idea

the restoring force surface of the multi-stable state vibrator is constructed. The surface recognition result coincides with the measured restoring force surface

which verifies the effectiveness of the complex force surface method in identifying the negative stiffness nonlinear oscillators

and this method is also applicable to the nonlinear analysis in the fields of energy harvesting and vibration control.

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references

HARNE R L, WANG K W. Harnessing bistable structural dynamics [M]. Chichester, UK: John Wiley & Sons Ltd., 2017: 181-290.

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.

ZHU Pei, REN Xingmin, QIN Weiyang, et al. Improving energy harvesting in a tri-stable piezomagnetoelastic beam with two attractive external magnets subjected to random excitation [J]. Archive of Applied Mechanics, 2017, 87(1): 45-57.

周生喜, 曹军义, ERTURK A, 等. 压电磁耦合振动能量俘获系统的非线性模型研究 [J]. 西安交通大学学报, 2014, 48(1): 106-111.

ZHOU Shengxi, CAO Junyi, ERTURK A, et al. Nonlinear model for piezoelectric energy harvester with magnetic coupling [J]. Journal of Xi'an Jiaotong University, 2014, 48(1): 106-111.

CAO Junyi, ZHOU Shengxi, INMAN D J, et al. Nonlinear dynamic characteristics of variable inclination magnetically coupled piezoelectric energy harvesters [J]. Journal of Vibration and Acoustics, 2015, 137(2): 021015.

ZHOU Zhiyong, QIN Weiyang, ZHU Pei. Improve efficiency of harvesting random energy by snap-through in a quad-stable harvester [J]. Sensors and Actuators: A Physical, 2016, 243: 151-158.

NAMMARI A, CASKEY L, NEGRETE J, et al. Fabrication and characterization of non-resonant magneto-mechanical low-frequency vibration energy harvester [J]. Mechanical Systems and Signal Processing, 2018, 102: 298-311.

MALATKAR P, NAYFEH A H. A plethora of nonlinear dynamics phenomena observed in a simple cantilever plate [C]∥Proceedings of ASME 2003 International Design Engineering Technical Conferences and Computer and Information in Engineering Conference. New York, USA: ASME, 2008: 2603-2610.

VAKAKIS A F, EWINS D J. Effects of weak non-linearities on modal analysis [J]. Mechanical Systems and Signal Processing, 1994, 8(2): 175-198.

CHATTERJEE A, VYAS N S. Stiffness non-linearity classification through structured response component analysis using Volterra series [J]. Mechanical Systems and Signal Processing, 2001, 15(2): 323-336.

BENDAT J S, PALO P A, COPPOLINO R N. A general identification technique for nonlinear differential equations of motion [J]. Probabilistic Engineering Mechanics, 1992, 7(1): 43-61.

GONDHALEKAR A C, PETROV E P, IMREGUN M. Parameters identification for nonlinear dynamic systems via genetic algorithm optimization [J]. Journal of Computational and Nonlinear Dynamics, 2009, 4(4): 041002.

MARCHESIELLO S, GARIBALDI L. A time domain approach for identifying nonlinear vibrating structures by subspace methods [J]. Mechanical Systems and Signal Processing, 2008, 22(1): 81-101.

ANASTASIO D, FASANA A, GARIBALDI L, et al. Nonlinear dynamics of a Duffing-like negative stiffness oscillator: modeling and experimental characterization [J]. Shock and Vibration, 2020, 2020: 1-13.

FELDMAN M. Nonparametric identification of asymmetric nonlinear vibration systems with the Hilbert transform [J]. Journal of Sound and Vibration, 2012, 331(14): 3386-3396.

COHEN N, BUCHER I, FELDMAN M. Slow-fast response decomposition of a bi-stable energy harvester [J]. Mechanical Systems and Signal Processing, 2012, 31: 29-39.

MASRI S F, CAUGHEY T K. A nonparametric identification technique for nonlinear dynamic problems [J]. Journal of Applied Mechanics, 1979, 46(2): 433-447.

MASRI S F, SASSI H, CAUGHEY T K. Nonparametric identification of nearly arbitrary nonlinear systems [J]. Journal of Applied Mechanics, 1982, 49(3): 619-628.

CRAWLEY E F, O'DONNELL K J. Force-state mapping identification of nonlinear joints [J]. AIAA Journal, 1987, 25(7): 1003-1010.

KERSCHEN G, LENAERTS V, GOLINVAL J C. VTT benchmark: application of the restoring force surface method [J]. Mechanical Systems and Signal Processing, 2003, 17(1): 189-193.

SUN W, LI X. Nonlinear joint parameter identification for bolted beam structure [J]. Journal of Vibration Engineering, 2013, 26(2): 26-28.

ANASTASIO D, MARCHESIELLO S. Experimental characterization of friction in a negative stiffness nonlinear oscillator [J]. Vibration, 2020, 3(2): 132-148.

KERSCHEN G, GOLINVAL J C, WORDEN K. Theoretical and experimental identification of a non-linear beam [J]. Journal of Sound and Vibration, 2001, 244(4): 597-613.

WORDEN K. Data processing and experiment design for the restoring force surface method: part I Integration and differentiation of measured time data [J]. Mechanical Systems and Signal Processing, 1990, 4(4): 295-319.

JIANG H, CHEN Q. Application of restoring force surface method in particle damper research [J]. Journal of Vibration, Measurement and Diagnosis, 2007, 27(3): 228-231.

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