Abstract
An application of soft and hard impact models to represent vibro-impact systems is reconsidered. The conditions that the two collision models have to satisfy to be equivalent in terms of energy dissipation are discussed and key features of the resulting soft impact models are demonstrated. Then, it is examined what effect will be exerted on the behavior of a vibro-impact system when an additional elastic-damping element and external forcing are used. Both methods are shown to yield the same results for a stiff base with a low rate of energy dissipation; however, when the soft impact model is applied to either the base with low stiffness or even the stiff base with a high rate of energy dissipation, different results are obtained than in the case of the hard impact model.
Highlights
In recent years, many researchers have focused their attention on the vibration analysis of mechanical systems with impacts
The conditions that the two collision models have to satisfy to be equivalent in terms of energy dissipation are discussed and key features of the resulting soft impact models are demonstrated
It is examined what effect will be exerted on the behavior of a vibro-impact system when an additional elastic-damping element and external forcing are used. Both methods are shown to yield the same results for a stiff base with a low rate of energy dissipation; when the soft impact model is applied to either the base with low stiffness or even the stiff base with a high rate of energy dissipation, different results are obtained than in the case of the hard impact model
Summary
Many researchers have focused their attention on the vibration analysis of mechanical systems with impacts. When the duration of collision and a dependence of the coefficient of restitution on velocity are taken into account, models referred to as soft collisions, enabling a more accurate description of the collision process, are obtained. In these models, impacts are simulated by means of linear or nonlinear elastic-damping structures It should be made clear that regardless of the approach used to model the collision, the resulting system is always strongly nonlinear Due to their highly nonlinear nature, vibro-impact systems can exhibit a variety of dynamic behaviors like chaotic motion, intermittency, Devil’s attractors, a Feigenbaum scenario, mirror hysteresis, and different types of grazing bifurcations
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