On the regularization of impact without collision: the Painlevé paradox and compliance
نویسندگان
چکیده
We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and the indeterminate Painlevé paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies.
منابع مشابه
Numerical Experiments with the Painlevé Paradox: Rigid Body vs. Compliant Contact
The existence and (non-)uniqueness of rigid multibody problems with impact, contact and friction is discussed by means of the renowned Painlevé paradox. Different approaches to solve such contact problems, their pros and cons and their connections are discussed.
متن کاملThe Painleve paradox in contact mechanics
The 120-year old so-called Painlevé paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal and rotational degrees-of-freedom such that the effective normal force becomes attractive rather than repulsive. Despite a rich literature, the forward evolu...
متن کاملA Parametric Study on the Progressive Collapse Potential of Steel Buildings under Truck Collision
In this paper, the initiation and propagation of structural damage in a building due to the truck collision to one of its corner columns were investigated. For this purpose, a three-dimensional 4-story moment resisting steel frame with intermediate ductility was considered. The structure was designed using ETABS software under standard dead, live, and earthquake loads, and then impact loading w...
متن کاملPeriodic motion and bifurcations induced by the Painlevé paradox ✩
In this paper we study the periodic motion and bifurcations of the Frictional Impact Oscillator, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Impact Oscillator contains the basic mechanism for a hopping phenomenon observed in many practical applications. We will show that the hopping or bouncing motion in th...
متن کاملExperimental Investigation of the Painlevé Paradox in a Robotic System
This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work [28] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results clearly show that a tangential impact does ex...
متن کامل