The non linear system under study consists on the bouncing ball problem. Focusing on the n-T periodic solutions and the permanent contact motion, simulations performed underline the effect of spring-damper contact model in comparison with the classical restitution coefficient. Both approaches are implemented in an adimensional way. For the restitution coefficient approach, iterating maps are easy to obtain after some assumptions. On the contrary, the spring-damper model leads to transcendental equations needing the use of numerical continuation methods. The damping ratio is defined as a function of the restitution coefficient. The effect of the contact stiffness is studied. For high values of the contact stiffness, the spring-damper model has the same behavior as the restitution coefficient model as the impact duration gets shorter. Predictions of the two models diverge when the contact stiffness decreases. Results are illustrated by time histories and Poincare´ Maps of dynamic responses. This paper aims to be guideline to quantify the error made by making the assumptions required for a restitution coefficient model.

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