Impulsive control of sticking motion in van der Pol one-sided constraint system

Effect of Method Type on the Response of Continuum Vibro‐Impact

“…Nordmark and Piiroinen studied the chattering of the vibro-impact system, and the local discontinuous mapping is proposed [18]. Additionally, Luo et al studied the relationship between dynamic response and system parameters for 2 DOF systems, focusing on the effect of excitation frequency and gap size on the response and discussed the "chattering-sticking" motion of the system [24]; he also studied the "chattering-sticking" motion of the traditional gear system and discussed the occurrence and disappearance of sticking motion, as well as the maintenance condition of the sticking motion [25]; meanwhile, Li et al evaluated the control of sticking motion by means of the impulse control method, which shows that this method can effectively suppress sticking motion but also introduces sticking motion for systems with specific parameters [26]; Luo et al studied the "chattering-sticking" motion of a vibro-impact system with large dissipation and discussed the relationship between the coefficient of restitution and the sticking motion characteristics [27].…”

Stochastic Responses of Lightly Nonlinear Vibroimpact System with Inelastic Impact Subjected to External Poisson White Noise Excitation

“…In the Hertz contact model, the contact force between two elastic bodies is assumed to be proportional to the 3/2 (sometimes with different values) power of the relative displacement between them. By means of the two models, many interesting dynamical behaviors were observed such as chaos motion and bifurcations [10,11], Hopf bifurcation [12], grazing bifurcation [13,14], torus bifurcation [15], chattering bifurcation [16,17], sticking motion [18,19], and border collision bifurcation [20].…”