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Inhomogeneous Timoshenko beam equations

✍ Scribed by Alberto Arosio; Stefano Panizzi; Maria Gabriella Paoli

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
452 KB
Volume
15
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The so‐called Timoshenko beam equation is a good linear model for the transverse vibrations of a homogeneous beam. Following the variational approach of Washizu, the governing equation is deduced in the case when the physical/geometrical parameters of the beam vary along its axis. The equation may not be studied by means of the iterated use of Fourier series. However, a convenient change of variables permits us to prove the well‐posedness of the associated Cauchy problem for a beam with sliding ends (the solution is intended in a mild sense). The proof is given in an abstract framework.

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