新型欧拉屈曲梁非线性动力吸振器的实现及抑振特性研究
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摘要
将欧拉屈曲梁和线性弹簧并联使用,构建非线性动力吸振器。建立了安装欧拉屈曲梁非线性动力吸振器的系统动力学模型。利用谐波平衡法推导了主从振系的频响方程组。利用四阶龙格-库塔法对比计算了在瞬态激励和多频稳态激励条件下,未安装吸振器、安装线性和非线性吸振器时主振系在时间域和频率域的响应特性。在此基础上,开展欧拉屈曲梁的初始挠度、初始倾角和阻尼系数对其振动抑制性能的影响分析。结果表明:所提欧拉屈曲梁设计参数成功构建了非线性动力吸振器;与安装线性吸振器前后的主振系响应相比,对主振系的抑振效果明显;欧拉屈曲梁初始挠度和阻尼系数存在最优值;初始倾角增大可增强非线性动力吸振器的振动抑制能力。
Combining an Euler buckled beam and a linear positive stiffness spring in parallel,a new novel improved nonlinear vibration absorber was designed and built.According to its structure,a systematic dynamic model with strong nonlinear characteristics of a structure system with the new novel absorber installed was established.Based on the nonlinear dynamic equations,the system's frequency response equations were derived using the harmonic balance method.Meanwhile,under conditions of transient input and multi-frequency steady input,the system's dynamic equations without any absorber,with a linear absorber and a nonlinear absorber,respectively were solved using the four-order Runge-Kutta method in time-domain and frequency-domain.In addition,the influences of initial deflection,oblique angle and damping coefficient of Euler buckled beam on the system's vibration suppression performance were studied.The calculating results showed that a typical nonlinear dynamic absorber was constructed successfully based on the provided design parameters of Euler buckled beam;comparing the vibration responses of the main mass without any absorber and those with the nonlinear absorber,the nonlinear absorber has a better vibration-attenuation performance;the initial deflection and damping coefficient of Euler buckled beam have the optimal values;with increase in the initial oblique angle,the vibration supperession ability of the nonlinear vibration absorber is improved.
Combining an Euler buckled beam and a linear positive stiffness spring in parallel,a new novel improved nonlinear vibration absorber was designed and built.According to its structure,a systematic dynamic model with strong nonlinear characteristics of a structure system with the new novel absorber installed was established.Based on the nonlinear dynamic equations,the system's frequency response equations were derived using the harmonic balance method.Meanwhile,under conditions of transient input and multi-frequency steady input,the system's dynamic equations without any absorber,with a linear absorber and a nonlinear absorber,respectively were solved using the four-order Runge-Kutta method in time-domain and frequency-domain.In addition,the influences of initial deflection,oblique angle and damping coefficient of Euler buckled beam on the system's vibration suppression performance were studied.The calculating results showed that a typical nonlinear dynamic absorber was constructed successfully based on the provided design parameters of Euler buckled beam;comparing the vibration responses of the main mass without any absorber and those with the nonlinear absorber,the nonlinear absorber has a better vibration-attenuation performance;the initial deflection and damping coefficient of Euler buckled beam have the optimal values;with increase in the initial oblique angle,the vibration supperession ability of the nonlinear vibration absorber is improved.
引文
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[12]张建卓,李旦,董申,等.欧拉压杆在超低频垂向隔振系统中的应用研究[J].机械强度,2004,26(3):237-241.ZHANG Jian-zhuo,LI Dan,DONG Shen,et al.Study on Euler column spring used in ultra-low frequency vertical vibration isolation system[J].Journal of Mechanical Strength,2004,26(3):237-241.
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[15]McFarland D M,Bergman L A,Vakakis A F.Experimental study of non-linear energy pumping occurring at a single fast frequency[J].International Journal of Non-linear Mechanics,2005,40:891-899.
[2]Roberson R E.Synthesis of a nonlinear dynamic vibration absorber[J].Journal of the Franklin Institute,1952,254(3):205-220.
[3]Oueini S S,Chin C M,Nayfeh A H.Dynamics of a cubic nonlinear vibration absorber[J].Nonlinear Dynamics,1999,20(3):283-295.
[4]Pun D,Liu Y B.On the design of the piecewise linear vibration absorber[J].Nonlinear Dynamics,2000,22(4):393-413.
[5]Walsh P L,Lamancusa J S.A variable stiffness vibration absorber for minimization of transient vibrations[J].Journal of Sound and Vibration,1992,158(2):195
[6]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.
[7]Zhu S J,Zheng Y F,Fu Y M.Analysis of nonlinear dynamics of a two-degree-of-freedom vibration system with nonlinear damping and nonlinear spring[J].Journal of Sound and Vibration,2004,271(1/2):1-11.
[8]楼京俊,唐斯密,朱石坚,等.改进的本质非线性吸振器宽频吸振参数域研究[J].振动与冲击,2011,30(6):218-222.LOU Jing-jun,TANG Si-mi,ZHU Shi-jian,et al.Parametric range of improved essentially nonlinear absorber on broad frequency band[J].Journal of Vibration and Shock,2011,30(6):218-222.
[9]赵艳影,徐鉴.时滞非线性动力吸振器的减振机理[J].力学学报,2008,40(1):98-105.ZHAO Yan-ying,XU Jian.Mechanical analysis of delayed nonlinear vibration absorber[J].Chinese Journal of Theoretical and Applied Mechanics,2008,40(1):98-105.
[10]唐斯密,朱石坚,楼京俊.非线性吸振器刚度调整策略研究[J].武汉理工大学学报,2011,35(1):163-171.TANG Si-mi,ZHU Shi-jian,LOU Jing-jun.Study on the tactic of adjusting stiffness of the nonlinear dynamic vibration absorber[J].Journal of Wuhan University of Technology,2011,35(1):163-171.
[11]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研究[J].机械工程学报,2013,49(6):89-94.LIU Xing-tian,HUANG Xiu-chang,ZHANG Zhi-yi,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.
[12]张建卓,李旦,董申,等.欧拉压杆在超低频垂向隔振系统中的应用研究[J].机械强度,2004,26(3):237-241.ZHANG Jian-zhuo,LI Dan,DONG Shen,et al.Study on Euler column spring used in ultra-low frequency vertical vibration isolation system[J].Journal of Mechanical Strength,2004,26(3):237-241.
[13]Winterflood J,Blair D G,Slagmolen B.High performance vibration isolation using springs in Euler column buckling mode[J]Physics Letters A,2002,300:122-130.
[14]殷小涛,孟再强,刘兴星,等.非规则弹性片高静低动的隔振特性[J].噪声与振动控制,2013,33(6):45-48.YIN Xiao-tao,MENG Zai-qiang,LIU Xing-xing,et al.High static stiffness and low dynamic stiffness isolation characteristics of irregular elastic sheets[J].Sound and Vibration Control,2013,33(6):45-48.
[15]McFarland D M,Bergman L A,Vakakis A F.Experimental study of non-linear energy pumping occurring at a single fast frequency[J].International Journal of Non-linear Mechanics,2005,40:891-899.