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Well‐posedness of the equations governing the motions of a one‐dimensional hybrid thermo‐elastic structure
Author(s) -
Dalsen Marié GrobbelaarVan
Publication year - 2005
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.576
Subject(s) - mathematics , eigenvalues and eigenvectors , inertia , mathematical analysis , bending , galerkin method , vibration , boundary value problem , boundary (topology) , classical mechanics , physics , finite element method , quantum mechanics , thermodynamics
In this paper a model for the vibrations of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end, with a rigid body attached to its free end, is studied with a view to establishing the existence of a unique solution in a weak sense. The model takes account of the effect of stretching on bending and rotational inertia. By treating eigenvalue problems with the spectral parameter also in the boundary conditions, we are able to employ the method of Faedo–Galerkin approximations. Copyright © 2004 John Wiley & Sons, Ltd.