Vibrations of a beam between two stops. (English) Zbl 1013.74033

Kuttler, Kenneth L.; Shillor, Meir

Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 8, No. 1, 93-110 (2001).

Summary: We establish the existence of weak solutions for a model that describes the vibrations of a beam which has one of its ends constrained between two stops. The contact at the free end is modeled either by the classical Signorini unilateral condition, for rigid stops, or by the normal compliance condition, for flexible stops. The beam is considered either elastic or viscoelastic. We prove the uniqueness of weak solution for the problem with viscoelastic beam with normal compliance.

MSC:

74H45	Vibrations in dynamical problems 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

Keywords:

dynamic contact; impact; viscoelastic beam; constrained vibrations; elastic beam; existence; weak solutions; Signorini unilateral condition; rigid stops; normal compliance condition; uniqueness