Journal ArticleDOI
Multiple Impacts of a Ball Between Two Plates—Part 2: Mathematical Modelling
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In this article, a mathematical model is developed to portray the vibroimpacts of a steel sphere which is trapped between two flat steel plates with clearance, while the plates are oscillated by an electromagnetic shaker.Abstract:
A mathematical model is developed to portray the vibroimpacts of a steel sphere which is trapped between two flat steel plates with clearance, while the plates are oscillated by an electromagnetic shaker. Data from a long series of experimental observations are reported in Part 1 of this paper [53]. The aim is to determine a law of motion by which a computer simulation can satisfactorily reproduce the major characteristics of the observed movement. During each impact the motion of the ball is taken to be a brief half wave, due to the highly nonlinear forces of surface compliance and surface damping. Modelling is by analog simulation. It was found first that linearization of the surface stiffness does not reproduce the observed phenomena. The mathematical model formulated is that the motion of the ball during contact is governed by the equation mx + cx1.5 x + kx1.5 = 0, where x is the penetration, c is a damping constant, and kx1.5 is the Hertzian force of compliance. The results of experiments can be corroborated only on the basis of a variable damping coefficient cxn with n = 3/2.read more
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Proceedings ArticleDOI
On the dynamics and stability of an inclined impact pair
P.J. Sherman,Anil K. Bajaj +1 more
Survey of impact damper performance
TL;DR: In this article, an overall picture of the impact damper is obtained by using time-history solutions of the system motion for the oscillator in free decay. But the overall picture cannot be obtained by analysis of steady-state forced response.
Journal ArticleDOI
Effect of nonlinear impact damping with non-integer compliance exponent on gear dynamic characteristics
Abstract: A nonlinear impact damping model of single-degree-of-freedom spur cylindrical gear with backlash and time-varying stiffness was established. Systematic analyses of the dynamic responses were performed. First, the nonlinear damping coefficient was considered as a constant parameter with two types of compliance exponent, meanwhile, dynamic factors were adopted to depict the dynamic characteristics. Second, the bifurcation graphs were plotted, where the damping coefficient was obtained along with the impact velocity and coefficient of restitution. The results show that light and heavy load conditions have an effect on the responses when the compliance exponent is integer. On the contrary, when the compliance exponent is non-integer, the dynamic responses are slightly affected, namely the system is more stable than the former situation.
Journal ArticleDOI
A numerical method for the forced nonlinear vibration
Ock Hyun Kim,Byung-Ho Lee +1 more
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