Vol.5 No.4 (July 2015)
The Analysis of Grazing Periodic Motions in a Single Degree of Freedom Vibro-Impact System with Double Constrains
徐洁琼 ：广西大学数学与信息科学学院，广西 南宁
The stability of grazing periodic motion in a single degree of freedom vibro-impact system with double constrains is analyzed. The Poincaré mapping near the grazing trajectory is established by using the discontinuity mapping method. And the stability criterion of double grazing periodic motion is obtained. According to the criterion, it is demonstrated that local attractors do not exist near the double grazing trajectory, i.e., the grazing bifurcation is discontinuous. Finally, validity of the theoretical analysis is verified by the numerical results.
徐洁琼 (2015) 一类双约束单自由度碰振系统的擦边运动分析。 理论数学， 5， 121-128. doi: 10.12677/PM.2015.54019
Shaw, S.W. (1985) The dynamics of a harmonically excited system having rigid amplitude constraints: part II-Chaotic motions and global biburcations. Journal of Applied Mechanics, 52, 459-464.
Whiston, G.S. (1992) Singularities in vibro-impact dynamics. Journal of Sound and Vibration, 152, 427-460.
Nordmark, A.B. (1991) Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound and Vibration, 145, 279-297.
Fredriksson, M.H. and Norddmark, A.B. (2000) On normal form calculations in impact oscillators. Proceedings of the Royal Society London A, 456, 315-329.
di Bernardo, M., Budd, C.J. and Champneys, A.R. (2001) Normal form maps for grazing bifurcation in n-dimensional piecewise-smooth dynamical systems. Physic D, 160, 222-254.
Foale, S. and Bishop, S.R. (1992) Dynamical complexities of forced impacting. Philosophical Transactions of the Royal Society London A, 338, 547-556.
Luo, A.C.J. (2004) On the symmetry of solution in non-smooth dynamical systems with two constraints. Journal of Sound and Vibration, 273, 1118-1126.
Luo, G.W., Zhang, Y.L., Chu, Y.D. and Zhang, J.G. (2007) Co-dimension two bifurcations fixed points in a class of vibratory systems with symmetrical rigid stops. Nonlinear Analysis: Real World Applications, 9, 1272-1292.