Abstract

We study dynamics of a mass, moving on a straight line, and impacting against the rigid wall through a deformable body, that we model as a straight rod of negligible mass. The chosen constitutive model of the viscoelastic body comprises fractional derivatives of stress and strain and the restrictions on the coefficients that follow from Clausius Duhem inequality. We show that the dynamics of the problem is governed by a single differential equation of real order. The obtained equation was solved numerically. The comparison is made to the solution obtained by the Laplace transform and Post’s inversion formula. The predictions of the model concerning the duration of the impact, maximal values of the impacting force and deformation as well as the restitution coefficient are determined for several values of system parameters.

Issue Section:
Brief Notes
Keywords:
viscoelasticity, modelling, impact (mechanical), elastomers, elastic hysteresis
Topics:
Deformation, Laplace transforms, Dynamics (Mechanics), Differential equations, Constitutive equations, Elastomers, Stress, Modeling, Viscoelasticity
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