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Solvability of a model for the vibration of a beam with a damping tip body. (English) Zbl 1437.74007

Summary: We consider a model for the vibration of a beam with a damping tip body that appeared in a previous article. In this paper we derive a variational form for the motion of the beam and use it to prove that the model problem has a unique solution. The proofs are based on existence results for a general linear vibration model problem, in variational form. Finite element approximation of the solution is discussed briefly.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
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References:

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