Existence of Stick-Slip Periodic Solutions in a Dry Friction Oscillator
LI Qun-Hong1**, CHEN Yu-Ming1, QIN Zhi-Ying2
1College of Mathematics and Information Science, Guangxi University, Nanning 530004 2School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050054
Existence of Stick-Slip Periodic Solutions in a Dry Friction Oscillator
LI Qun-Hong1**, CHEN Yu-Ming1, QIN Zhi-Ying2
1College of Mathematics and Information Science, Guangxi University, Nanning 530004 2School of Mechanical and Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang 050054
摘要The stick-slip behavior in friction oscillators is very complicated due to the non-smoothness of the dry friction, which is the basic form of motion of dynamical systems with friction. In this paper, the stick-slip periodic solution in a single-degree-of-freedom oscillator with dry friction is investigated in detail. Under the assumption of kinetic friction being the Coulomb friction, the existence of the stick-slip periodic solution is considered to give out an analytic criterion in a class of friction systems. A two-parameter unfolding diagram is also described. Moreover, the time and states of motion on the boundary of the stick and slip motions are semi-analytically obtained in a single stick-slip period.
Abstract：The stick-slip behavior in friction oscillators is very complicated due to the non-smoothness of the dry friction, which is the basic form of motion of dynamical systems with friction. In this paper, the stick-slip periodic solution in a single-degree-of-freedom oscillator with dry friction is investigated in detail. Under the assumption of kinetic friction being the Coulomb friction, the existence of the stick-slip periodic solution is considered to give out an analytic criterion in a class of friction systems. A two-parameter unfolding diagram is also described. Moreover, the time and states of motion on the boundary of the stick and slip motions are semi-analytically obtained in a single stick-slip period.
LI Qun-Hong**;CHEN Yu-Ming;QIN Zhi-Ying
. Existence of Stick-Slip Periodic Solutions in a Dry Friction Oscillator[J]. 中国物理快报, 2011, 28(3): 30502-030502.
LI Qun-Hong**, CHEN Yu-Ming, QIN Zhi-Ying
. Existence of Stick-Slip Periodic Solutions in a Dry Friction Oscillator. Chin. Phys. Lett., 2011, 28(3): 30502-030502.
[1] Qin Z Y and Lu Q S 2007 Chin. Phys. Lett. 24 886
[2] Ji Y and Bi Q S 2010 Chin. Phys. Lett. 27 060503
[3] Den Hartog J P 1931 Trans. Am. Soc. Mech. Eng. 53 107
[4] Hong H K and Liu C S 2000 J. Sound Vib. 229 1171
[5] Hong H K and Liu C S 2001 J. Sound Vib. 244 883
[6] Feeny B, Guran A, Hinrichs N and Popp K 1998 Amer. Soc. Mech. Eng. 51 321
[7] Galvanetto U 2001 J. Sound Vib. 248 653
[8] di Bernardo M, Kowalczyk P and Nordmark A 2002 Physica D 170 175
[9] Kowalczyk P and di Bernardo M 2005 Physica D 204 204
[10] Yang S P and Guo S Q 2009 J. Vib. Shock 28 43 (in Chinese)
2011, Vol. 28 
