This article is cited in 4 papers

A contact problem for a viscoelastic plate and an elastic beam

T. S. Popova

North-Eastern Federal University, 48 Kulakovsky str., 677000 Yakutsk

Abstract: We consider the problem of contact of a viscoelastic plate with an elastic beam. For characterizing the viscoelastic deformation of the plate, we use hereditary integrals. We present a differential statement of the problem with conditions having the form of a system of equalities and inequalities in the domain of possible contact and prove its equivalence to a variational inequality. We establish the unique solvability and the existence of the derivative of a solution with respect to time. The limit problem is considered with the parameter of bending rigidity of the plate tending to infinity.

Keywords: viscoelasticity, beam, plate, hereditary integral, variational inequality, nonpenetration condition.

UDC: 517.95

Received: 18.11.2015

DOI: 10.17377/sibjim.2016.19.304

 English version: Journal of Applied and Industrial Mathematics, 2016, 10:3, 404–416

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