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Dynamic boundary stabilization of a Reissner–Mindlin plate with Timoshenko beam
Author(s) -
Dalsen Marié GrobbelaarVan
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.506
Subject(s) - mathematics , transversal (combinatorics) , beam (structure) , timoshenko beam theory , vibration , boundary value problem , semigroup , mathematical analysis , boundary (topology) , stability (learning theory) , structural engineering , physics , engineering , quantum mechanics , machine learning , computer science
This paper is concerned with well‐posedness results for a mathematical model for the transversal vibrations of a two‐dimensional hybrid elastic structure consisting of a rectangular Reissner–Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial‐boundary‐value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd.