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On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle. (English) Zbl 0860.73028
Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. One end of the beam is clamped, while the other end is free. The horizontal motion of the free end is restricted by the presence of a stationary obstacle, and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by the friction. The contact and friction at this end are modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and the Coulomb’s law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of the Coulomb’s law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74Hxx Dynamical problems in solid mechanics
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