基于欧拉梁的准零刚度隔振系统动力特性分析

摘要/Abstract

摘要： 将两端受轴向压力的欧拉梁和线性弹簧并联，组成一个具备高静刚度和低动刚度的准零刚度隔振器。通过对隔振系统进行静力分析，给出系统具备准零刚度特性所需的条件。利用谐波平衡法求解系统的振动微分方程，分析系统的幅频特性，给出了系统的力传递率，讨论了阻尼、激励力等参数对系统传递率的影响。最后分析了该隔振系统的跳跃频率。研究结果表明：激励力以及初始偏移量的增大会使系统的隔振效果变差，因此要控制激励力的大小并尽量避免超载；阻尼比的选取需要综合考虑高频的隔振效果和有效隔振频率范围。

关键词: 欧拉梁, 准零刚度系统, 谐波平衡法, 力传递率, 跳跃频率

Abstract: Combining the Euler beam under axial pressures with a positive stiffness spring, a quasi-zero-stiffness vibration isolation system was obtained, which had high static stiffness and low dynamic stiffness characteristics. The requirements of the quasi-zero-stiffness system were achieved through the static characteristic analyses. The harmonic balance method was used to solve the dynamic differential equations. The steady state and amplitude frequency response of the system were also analysed. The influences of parameters such as damping and exciting forces on the force transmissibility of the system were discussed. At last, the jumping frequencies of the system were analysed. The results show that the increase of the exciting force and the initial offset make the effects of vibration isolation of system worse, therefore the amplitude of the exciting force should be controlled, and the overload should be avoided. To choose the proper damping ratio, the vibration isolation effect at high frequencies and the effective isolation frequency range should be considered comprehensively.

Key words: Euler beam, quasi-zero-stiffness system, harmonic balance method, force transmissibility, jumping frequency

中图分类号:

O328

高双, 朱翔, 谌宗琦, 李天匀. 基于欧拉梁的准零刚度隔振系统动力特性分析[J]. 中国机械工程.

Gao Shuang, Zhu Xiang, Shen Zongqi, Li Tianyun. Analyses on Dynamics Characteristics of a Quasi-zero-stiffness Vibration Isolation System Based on Euler Beam[J]. China Mechanical Engineering.

参考文献

[1]Carrella A, Brennan M J, Waters T P, et al. Force and Displacement Transmissibility of a Nonlinear Isolator with High Static Low Dynamic Stiffness[J]. International Journal of Mechanical Sciences, 2012, 55(1): 22-29.

[2]Zhou J, Wang X, Xu D, et al. Nonlinear Dynamic Characteristics of a Quasi-zero Stiffness Vibration Isolator with Cam-roller-spring Mechanisms[J]. Journal of Sound and Vibration, 2015, 346(1):53-69.

[3]Xu D, Yu Q, Zhou J, et al. Theoretical and Experimental Analyses of a Nonlinear Magnetic Vibration Isolator with Quasi Zero Stiffness Characteristic[J]. Journal of Sound and Vibration, 2013, 332(14):3377-3389.

[4]Le T D, Ahn K K. A Vibration Isolation System in Low Frequency Excitation Region Using Negative Stiffness Structure for Vehicle Seat[J]. Journal of Sound and Vibration, 2011, 330(26):6311-6335.

[5]白晓辉, 白鸿柏, 郝慧荣, 等. 正负刚度并联机构动力学分析及隔振仿真[J]. 机械工程师, 2009(11):87-89.

Bai Xiaohui，Bai Honkbai, Hao Huirong, et al. The Dynamic Analysis and Simulation of Positive and Negative Stiffness in Parallel[J]. Mechanical Engineer, 2009(11):87-89.

[6]彭献, 张施详. 一种准零刚度被动隔振系统的非线性共振响应分析[J]. 湖南大学学报(自然科学版), 2011, 38(8):34-39.

Peng Xian, Zhang Shixiang. Nonlinear Resonance Response Analysis of a Kind of Passive Isolation System with Quasi-zero Stiffness[J]. Journal of Hunan University(Natural Sciences), 2011, 38(8):34-39.

[7]徐道临, 余奇平, 周加喜, 等. 准零刚度隔振系统跳跃频率区间隔振研究[J]. 中国机械工程, 2014, 25(2): 230-235.

Xu Daolin, Yu Qiping, Zhou Jiaxi, et al. Study on Vibration Attenuation in Jumping Frequency Interval of Quasi-zero Stiffness Vibration Isolator[J]. China Mechanical Engineering,2014, 25(2):230-235.

[8]Lan C, Yang S, Wu Y. Design and Experiment of a Compact Quasi-zero-stiffness Isolator Capable of a Wide Range of Loads[J]. Journal of Sound and Vibration, 2014, 333(20):4843-4858.

[9]Liu X, Huang X, Hua H. On the Characteristics of a Quasi-zero Stiffness Isolator Using Euler Buckled Beam as Negative Stiffness Corrector[J]. Journal of Sound and Vibration, 2013, 332(14):3359-3376.

[10]刘兴天, 黄修长, 张志谊, 等. 激励幅值及载荷对准零刚度隔振器特性的影响[J]. 机械工程学报, 2013, 49(6):89-94.

Liu Xingtian, Huang Xiuhang, Zhang Zhiyi, et al. Influence of Excitation Amplitude and Load on the Characteristics of Quasi-zero Stiffness Isolator[J]. Journal of Mechanical Engineering, 2013,49(6):89-94.

[11]刘兴天, 孙靖雅, 肖锋, 等. 准零刚度微振动隔振器的原理和性能研究[J]. 振动与冲击, 2013, 32(21):69-73.

Liu Xingtian，Sun Jingya, Xiao Feng, et al. Principle and Performance of a Quasi-zero Stiffness Isolator for Micro-vibration Isolation[J]. Journal of Vibration and Shock, 2013, 32(21):69-73.

[12]Huang X, Liu X, Sun J, et al. Vibration Isolation Characteristics of a Nonlinear Isolator Using Euler Buckled Beam as Negative Stiffness Corrector: A Theoretical and Experimental Study[J]. Journal of Sound and Vibration, 2014, 333(4):1132-1148.

[13]徐博侯, 曲绍兴. 非线性力学导论[M].杭州: 浙江大学出版社, 2012.

[14]高雪，陈前，滕汉东.液固混合介质隔振系统的主共振分析[J]. 机械工程学报, 2012, 48(15):90-95.

Gao Xue, Chen Qian, Teng Handong. Primary Resonance Analysis of Solid and Liquid Mixture Vibration Isolation System [J]. Journal of Mechanical Engineering, 2012,48(15):90-95.