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Vibrations of a beam between obstacles. Convergence of a fully discretized approximation. (English) Zbl 1106.74057
Summary: We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini complementary conditions between the displacement and the shear stress. For this infinite-dimensional contact problem, we propose a family of fully discretized approximations, and their convergence is proved. Moreover, some examples of implementation are presented. The results obtained here are also valid in the case of a beam oscillating between two longitudinal rigid obstacles.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M15 Contact in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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