动摩擦作用下含间隙碰撞振动系统的动力学分析
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摘要
研究在非光滑因素间隙及摩擦作用下的强非线性系统动力学行为。将Dankowicz动摩擦模型引进力学系统中,给出振子受力判断条件,结合数值仿真分析,探讨摩擦诱导振动及其它关键参数对系统动力学特性的影响。结果表明,系统在不同参数下存在复杂多样的摩擦诱导振动形式:稳定周期摩擦振动、概周期摩擦黏滞振动、概周期瞬时摩擦诱导振动、颤振碰撞、摩擦诱导黏滞擦边碰撞振动及摩擦诱导黏滞混沌振动等。
The dynamical behavior of a strong non-linear system with clearance containing non-smooth factors and friction was investigated. Dankowicz kinetic friction model was introduced into the system,the judgment condition for the oscillator force-bearing was deduced. Combined with the numerical simulation,the friction induced vibration and the effects of other key parameters on the dynamic characteristics of the system were explored. The results showed that under different parameters,there are complex and various forms of friction-induced vibration in the system,such as,stable periodic friction vibration,quasi-periodic friction sticky vibration,quasi-periodic instantaneous friction induced vibration,flutter impact,friction induced sticky impact vibration,friction induced sticky chaotic vibration,etc.
The dynamical behavior of a strong non-linear system with clearance containing non-smooth factors and friction was investigated. Dankowicz kinetic friction model was introduced into the system,the judgment condition for the oscillator force-bearing was deduced. Combined with the numerical simulation,the friction induced vibration and the effects of other key parameters on the dynamic characteristics of the system were explored. The results showed that under different parameters,there are complex and various forms of friction-induced vibration in the system,such as,stable periodic friction vibration,quasi-periodic friction sticky vibration,quasi-periodic instantaneous friction induced vibration,flutter impact,friction induced sticky impact vibration,friction induced sticky chaotic vibration,etc.
引文
[1]LUO A C J,THAPA S.Periodic motions in a simplified brake system with a periodic excitation[J].Communications in Nonlinear Science and Numerical Simulation,2009,14(5):2389-2414.
[2]CONE K M,ZADOKS.A numerical study of an impact oscillator with the addition of dry friction[J].Journal of Sound and Vibration,1995,188(5):659-683.
[3]LUO G W,LX H,MA L.Periodic-impact motions and bifurcations in dynamics of a plastic impact oscillator with a frictional slider[J].European Journal of Mechanics-A/Solids,2008,27(6):1088-1107.
[4]SOOBBARAYEN K,BESSET S,SINOU J J.Noise and vibration for a self-excited mechanical system with friction[J].Applied Acoustics,2013,74(10):1191-1204.
[5]LICSKG,CSERNK G.On the chaotic behaviour of a simple dry-friction oscillator[J].Mathematics and Computers in Simulation,2014,95(1):55-62.
[6]丁旺才,张有强.干摩擦对碰撞振动系统周期运动的影响分析[J].振动与冲击,2009,28(6):110-112.DING Wangcai,ZHANG Youqiang.Analysis of dry friction on vibro-impact system period motion effect[J].Journal of Vibration and Shock,2009,28(6):110-112.
[7]钱大帅,刘占生,刘镇星,等.干摩擦振子双黏着运动响应的级数形式解及黏滑边界分析[J].振动与冲击,2013,32(9):73-78.QIAN Dashuai,LIU Zhansheng,LIU Zhenxing,et al.Series solution of double-stick motion response of dry friction oscillator and stick-slip boundary analysis[J].Journal of Vibration and Shock,2013,32(9):73-78.
[8]LIU Y,EKATERINA P,MARIAN W,et al.Forward and backward motion control of a vibro-impact capsule system[J].International Journal of Non-Linear Mechanics,2015,70(4):30-46.
[9]HOFFMANN N P.Linear stability of steady sliding in point contacts with velocity dependent and Lu Gre type friction[J].Journal of Sound and Vibration,2007,301(3/4/5):1023-1034.
[10]DANKOWICZ H.On the modeling of dynamic friction phenomena[J].Applied Mathematics and Mechanics,1999,79(6):399-409.
[11]DANKOWICZ H,NORDMARK A B.On the origin and bifurcations of stick-slip oscillations[J].Physica D Nonlinear Phenomena,2000,136(3):280-302.
[12]ARGATOV I,BUTCHER E A.On the iwan models for laptype bolted joints[J].International Journal of Non-Linear Mechanics,2011,46(2):347-356.
[13]SAHA A,WIERCIGROCH M,JANKOWSKI K,et al.Investigation of two different friction models from the perspective of friction-induced vibrations[J].Tribology International,2015,90(10):185-197.
[2]CONE K M,ZADOKS.A numerical study of an impact oscillator with the addition of dry friction[J].Journal of Sound and Vibration,1995,188(5):659-683.
[3]LUO G W,LX H,MA L.Periodic-impact motions and bifurcations in dynamics of a plastic impact oscillator with a frictional slider[J].European Journal of Mechanics-A/Solids,2008,27(6):1088-1107.
[4]SOOBBARAYEN K,BESSET S,SINOU J J.Noise and vibration for a self-excited mechanical system with friction[J].Applied Acoustics,2013,74(10):1191-1204.
[5]LICSKG,CSERNK G.On the chaotic behaviour of a simple dry-friction oscillator[J].Mathematics and Computers in Simulation,2014,95(1):55-62.
[6]丁旺才,张有强.干摩擦对碰撞振动系统周期运动的影响分析[J].振动与冲击,2009,28(6):110-112.DING Wangcai,ZHANG Youqiang.Analysis of dry friction on vibro-impact system period motion effect[J].Journal of Vibration and Shock,2009,28(6):110-112.
[7]钱大帅,刘占生,刘镇星,等.干摩擦振子双黏着运动响应的级数形式解及黏滑边界分析[J].振动与冲击,2013,32(9):73-78.QIAN Dashuai,LIU Zhansheng,LIU Zhenxing,et al.Series solution of double-stick motion response of dry friction oscillator and stick-slip boundary analysis[J].Journal of Vibration and Shock,2013,32(9):73-78.
[8]LIU Y,EKATERINA P,MARIAN W,et al.Forward and backward motion control of a vibro-impact capsule system[J].International Journal of Non-Linear Mechanics,2015,70(4):30-46.
[9]HOFFMANN N P.Linear stability of steady sliding in point contacts with velocity dependent and Lu Gre type friction[J].Journal of Sound and Vibration,2007,301(3/4/5):1023-1034.
[10]DANKOWICZ H.On the modeling of dynamic friction phenomena[J].Applied Mathematics and Mechanics,1999,79(6):399-409.
[11]DANKOWICZ H,NORDMARK A B.On the origin and bifurcations of stick-slip oscillations[J].Physica D Nonlinear Phenomena,2000,136(3):280-302.
[12]ARGATOV I,BUTCHER E A.On the iwan models for laptype bolted joints[J].International Journal of Non-Linear Mechanics,2011,46(2):347-356.
[13]SAHA A,WIERCIGROCH M,JANKOWSKI K,et al.Investigation of two different friction models from the perspective of friction-induced vibrations[J].Tribology International,2015,90(10):185-197.