刚度递增式非光滑纯非线性吸振器的幅频响应特性研究

摘要
图/表
参考文献(27)
相关文章 (15)

全文: PDF (1467 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要简谐激励幅值增大到一定程度时，光滑纯非线性吸振器会使主振子产生高分支响应，从而发生突发性失效，为避免失效发生，提出非光滑吸振器的方案。该吸振器在振幅较小时，具有较低的刚度系数，当振幅大于临界值后，刚度系数能够显著增加。利用复变量-平均法推导出系统的慢变方程，并运用最小二乘法分别获得连接光滑和非光滑吸振器的主振子的幅频响应。研究表明，通过合理控制弹簧间隙，非光滑吸振器可以有效抑制高分支响应的发生，激励幅值较小时，两种吸振器的性能非常接近，当系统承受中等激励时，光滑吸振器具有较好的吸振性能，当激励幅值进一步增加，非光滑吸振器则具有显著优势。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	陈建恩1
	2
	张维兴1
	2
	胡文华1
	2
	孙敏3

关键词 ：非光滑, 吸振器, 纯非线性, 高分支

Abstract：When the amplitude of simple harmonic excitation increases to a certain extent, smooth pure nonlinear vibration absorber can make its main oscillator produce higher branch response, and cause sudden failure.Here, in order to avoid failure, a scheme of non-smooth vibration absorber was proposed.It was shown that it has lower stiffness coefficient during its amplitude being smaller; when its amplitude is larger than the critical value, its stiffness coefficient can increase significantly.The complex variable average method was used to derive the slowly-varying dynamic equation of the system, and amplitude-frequency responses of the main oscillator connected with smooth and non-smooth absorbers were obtained, respectively using the least square method.The study showed that the non-smooth absorber can effectively suppress the occurrence of higher branch response through reasonably controlling spring gap; when the excitation amplitude is smaller, performances of the two kinds of absorbers are very close to each other; when the system is under medium excitation, the smooth absorber has better vibration absorption performance; when the excitation amplitude further increases, the non- smooth absorber has a significant superiority.

Key words： non-smooth vibration absorber pure nonlinearity higher branch

收稿日期: 2020-01-02 出版日期: 2021-06-15

引用本文:

陈建恩1,2，张维兴1,2，胡文华1,2，孙敏3 . 刚度递增式非光滑纯非线性吸振器的幅频响应特性研究[J]. 振动与冲击, 2021, 40(11): 170-175.
CHEN Jianen1,2, ZHANG Weixing1,2, HU Wenhua1,2, SUN Min3. Amplitude-frequency response characteristics of non-smooth pure nonlinear vibration absorber with increasing stiffness. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(11): 170-175.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I11/170

［1］GENDELMAN V.Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators［J］.Nonlinear Dynamics, 2001, 25(1/2/3): 237-253.
［2］KERSCHEN G, LEE Y S, VAKAKIS A F, et al.Irreversible passive energy transfer in coupled oscillators with essential nonlinearity［J］.Society for Industrial and Applied Mathematics, 2006, 66(2): 648-679.
［3］LU Z, WANG Z X, ZHOU Y, et al.Nonlinear dissipative devices in structural vibration control: a review［J］.Journal of Sound and Vibration, 2018, 423: 18-49.
［4］CHEN H Y, MAO X Y, DING H, et al.Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks［J］.Mechanical Systems and Signal Processing, 2020, 135: 106383.
［5］ZHANG Y W, ZHANG Z, CHEN L Q, et al.Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks［J］.Nonlinear Dynamics, 2015, 82(1/2): 61-71.
［6］孙敏, 陈建恩, 陈焕林.并联和串联非线性能量阱的吸振效能对比研究［J］.哈尔滨工程大学学报, 2018, 39(10): 1727-1732.
SUN Min, CHEN Jianen, CHEN Huanlin.Comparison on vibration absorption efficiency of parallel and series nonlinear energy sinks［J］.Journal of Harbin Engineering University, 2018, 39(10): 1727-1732.
［7］GRINBERG I, LANTON V, GENDELMAN O V.Response regimes in linear oscillator with 2DOF nonlinear energy sink under periodic forcing［J］.Nonlinear Dynamics, 2012, 69(4): 1889-1902.
［8］MANEVITCH L I, SIGALOV G, ROMEO F, et al.Dynamics of a linear oscillator coupled to a bistable light attachment: analytical study［J］.Journal of Applied Mechanics, 2013, 81(4): 041011.
［9］GOURC E, MICHON G, SEGUY S, et al.Targeted energy transfer under harmonic forcing with a vibro-impact nonlinear energy sink: analytical and experimental developments［J］.Journal of Vibration and Acoustics, 2015, 137(3): 031008.
［10］WEI Y M, WEI S, ZHANG Q L, et al.Targeted energy transfer of a parallel nonlinear energy sink［J］.Applied Mathematics and Mechanics, 2019, 40(5): 621-630.
［11］GENDELMAN O V, SIGALOV G, MANEVITCH L I, et al.Dynamics of an eccentric rotational nonlinear energy sink［J］.Journal of Applied Mechanics, 2012, 79(1): 011012.
［12］BENAROUS N, GENDELMAN O V.Nonlinear energy sink with combined nonlinearities: enhanced mitigation of vibrations and amplitude locking phenomenon［J］.Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 230(1): 21-33.
［13］AL-SHUDEIFAT M A.Asymmetric magnet-based nonlinear energy sink［J］.Journal of Computational and Nonlinear Dynamics, 2015, 10: 014502.
［14］BENACCHIO S, MALHER A, BOISSON J, et al.Design of a magnetic vibration absorber with tunable stiffnesses［J］.Nonlinear Dynamics, 2016, 85(2): 893-911.
［15］FEUDO S L, TOUZE C, BOISSON J, et al.Nonlinear magnetic vibration absorber for passive control of a multi-storey structure［J］.Journal of Sound and Vibration, 2019, 438: 33-53.
［16］GEORGIADES F, VAKAKIS A F, MCFARLAND D M, et al.Shock isolation through passive energy pumping caused by nonsmooth nonlinearities［J］.International Journal of Bifurcation and Chaos, 2005, 15(6): 1989-2001.
［17］GENDELMAN O V.Targeted energy transfer in systems with non-polynomial nonlinearity［J］.Journal of Sound and Vibration, 2008, 315: 732-745.
［18］LAMARQUE C H, GENDELMAN O V, SAVADKOOHI A T, et al.Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink［J］.Acta Mechanica, 2011, 221(1/2): 175-200.
［19］SHUI X, WANG S M.Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness［J］.Mechanical System and Signal Processing, 2018, 100: 330-343.
［20］ZANG J, YUAN T C, LU Z Q, et al.A lever-type nonlinear energy sink［J］.Journal of Sound and Vibration, 2018, 437: 119-134.
［21］LIU Y, MOJAHE A, BERGMAN L A, et al.A new way to introduce geometrically nonlinear stiffness and damping with an application to vibration suppression［J］.Nonlinear Dynamics, 2019, 96(3): 1819-1845.
［22］ZANG J, CHEN L Q.Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink［J］.Acta Mechanica Sinica, 2017 33(4): 801-822.
［23］CHEN J E, HE W, ZHANG W, et al.Vibration suppression and higher branch responses of beam with parallel nonlinear energy sinks［J］.Nonlinear Dynamics, 2018, 91(2): 885-904.
［24］STAROSVETSKY Y, GENDELMAN O V.Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system［J］.Journal of Sound and Vibration, 2008, 312: 234-256.
［25］STAROSVETSKY Y, GENDELMAN O V.Vibration absorption in systems with a nonlinear energy sink: nonlinear damping［J］.Journal of Sound and Vibration, 2009, 324(3/4/5): 916-939.
［26］VAKAKIS A F, GENDELMAN O V, KERSCHEN G, et al.Nonlinear targeted energy transfer in mechanical and structural systems［M］.Berlin: Springer, 2008.
［27］张伟，胡文华，曹东兴，等.一种刻画振动系统周期振幅与系统参数的关系的方法:201410144087.X［P］.2017-04-05.