On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle |
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Authors: | Kevin T Andrews M Shillor S Wright |
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Institution: | (1) Department of Mathematical Sciences, Oakland University, 48309-4401 Rochester, MI, USA |
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Abstract: | 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. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, 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 friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized.The work of the last two authors was supported in part by Oakland University Research Fellowships. |
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Keywords: | frictional contact Euler-Bernoulli beam Signorini unilateral condition dynamic vibrations Coulomb's law of dry friction normal compliance Kelvin-Voigt viscoelastic law |
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