Geodesic
Earthquake response of adjacent structures with viscoelastic and friction dampers
Theoretical and applied mechanics, Tome 42 (2015) no. 4, p. 277 .

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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 a 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 Grünwald--Letnikov numerical scheme. The behaviour of the system is analyzed for different values of system parameters.
DOI : 10.2298/TAM1504277Z
Classification : 74D05 34C15
Keywords: earthquake, fractional derivative, viscoelasticity, set-valued Coulomb friction law 
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     title = {Earthquake response of adjacent structures with viscoelastic and friction dampers},
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Miodrag Žigić; Nenad Grahovac. Earthquake response of adjacent structures with viscoelastic and friction dampers. Theoretical and applied mechanics, Tome 42 (2015) no. 4, p. 277 . doi : 10.2298/TAM1504277Z. http://geodesic.mathdoc.fr/articles/10.2298/TAM1504277Z/

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