We study the dynamics of a mass, sliding on a dry surface and impacting against a rigid wall through a viscoelastic body, that we model as a straight rod of negligible mass. The problem comprises a constitutive model of the viscoelastic body with fractional derivatives of stress and strain, restrictions on the coefficients that follow from Clausius–Duhem inequality, and discontinuous inequality constraint conditions imposed by the Coulomb friction model. We show that the dynamics of the problem is governed by a single integro-differential inclusion. By use of the slack variable algorithm the problem was solved numerically. 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. Depending on the dry friction coefficient three different impact scripts are identified: rebound after the impact, capture in the approaching phase, and capture in the rebound phase.

We study the seismic response of two adjacent structures connected with a dry friction damper. Each of them consists of a viscoelastic rod and a rigid block, which can slide without friction along the moving base. A simplified earthquake model is used for modeling the horizontal ground motion. Energy dissipation is taken by the presence of the friction damper, which is modeled by the set-valued Coulomb friction law. Deformation of viscoelastic rods during the relative motion of the blocks represents another way of energy dissipation. The constitutive equation of a viscoelastic body is described by the fractional Zener model, which includes fractional derivatives of stress and strain. The problem merges fractional derivatives as non-local operators and theory of set-valued functions as the non-smooth ones. Dynamical behaviour of the problem is governed by a pair of coupled multi-valued differential equations. The posed Cauchy problem is solved by use of the Gr?nwald-Letnikov numerical scheme. The behaviour of the system is analyzed for different values of system parameters.

Konstrukcija u obliku stuba koja se sastoji od donjeg bloka (osnova) i gornjeg bloka, b) Uvećan detalj B 1 , c) Dekomponovani sistem.. .. .. .. .. . 2.2 Dinamiµ cki modeli neglatkog sistema u zavisnosti od relativne brzine bloka. 2.3 Faze kretanja neglatkog sistema tokom vremena.

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