一类摩擦碰撞振动系统的周期振动特性研究
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摘要
建立了一类两自由度摩擦碰撞振动系统的力学模型,确定Poincaré截面,通过数值仿真,分析了系统在简谐激振力作用下的周期碰撞振动特性,并讨论了传动带运动速度、传动带与质量块间的摩擦系数对系统周期碰撞振动特性的影响.研究结果表明系统的周期碰撞运动的形式呈现多样化,且在一定的系统参数下,传动带运行速度和摩擦系数的变化对系统的冲击速度影响不大,但对系统的动力学特性有较大的影响.
A two-degree of freedom vibro-impact system with dry friction is established.The periodic impact vibration characteristics of the system under the harmonic excitation force are analyzed by numerical simulation,then the influence of the velocity of the driving belt and the friction coefficient between the mass and driving belt on the periodic impact vibration characteristics of the system are discussed on the basis of determined Poincarésection.The studies show that the forms of periodic impact motion are diversified,and under certain parameters of the system,the changes of the velocity of the driving belt and the friction coefficient have a little influence on impact velocity of the system,but have a great influence on the dynamic characteristics of the system.
A two-degree of freedom vibro-impact system with dry friction is established.The periodic impact vibration characteristics of the system under the harmonic excitation force are analyzed by numerical simulation,then the influence of the velocity of the driving belt and the friction coefficient between the mass and driving belt on the periodic impact vibration characteristics of the system are discussed on the basis of determined Poincarésection.The studies show that the forms of periodic impact motion are diversified,and under certain parameters of the system,the changes of the velocity of the driving belt and the friction coefficient have a little influence on impact velocity of the system,but have a great influence on the dynamic characteristics of the system.
引文
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[2]De Souza,Silvio L T,Caldas,et al.Calculation of Lyapunov exponents in systems with impacts[J].Chaos,Solitons and Fractals,2004,19(3):569-579.
[3]Peterka F.Bifurcation and transition phenomena in an impact oscillator[J].Chaos,Solitons&Fractals,1996,7(10):1635-1647.
[4]Whiston G S.Singularities in vibro-impact dynamics[J].Journal of Sound and Vibration,1992,152(3):427-460.
[5]Humphries N,Piiroinen P T.A discontinuity-geometry view of the relationship between saddle-node and grazing bifurcations[J].Physica D,2012,241(22):1911-1918.
[6]Nordmark A B,Piiroinen P T.Simulation and stability analysis of impacting systems with complete chattering[J].Nonlinear Dynamics,2009,58(1/2):85-106.
[7]Hu H Y.Controlling chaos of a dynamical system with discontinuous vector field[J].Physica D,1997,106:1-8.
[8]Luo G W,Ma L,Lv X H.Dynamic analysis and suppressing chaotic impacts of a two-degree-of-freedom oscillator with a clearance[J].Nonlinear Analysis:Real World Applications,2009,10(2):756-778.