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A nonlinear elastic beam system with inelastic contact constraints. (English) Zbl 1076.74029
Summary: We study freely propagating inertial, i.e., unforced, waves, in an elastic beam constrained so that all motion takes place above and on a flat, rigid support surface, subject to a gravitational force and a compressive longitudinal load. Contact between the beam and the support surface is assumed to be completely inelastic. A nonlinear beam model is used, incorporating a quartic extension of the familiar quadratic potential energy functional for the standard Euler-Bernoulli model. After briefly reviewing the rationale for the model and some of its properties, as developed in earlier articles, we present existence and uniqueness results for the constrained system obtained with the use of a “penalty function” approach involving the addition of a “uni-directional friction” dissipative term, active only when the constraint is violated, to the unconstrained system.

MSC:
74J30 Nonlinear waves in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74M15 Contact in solid mechanics
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