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Inhomogeneous Timoshenko beam equations
Author(s) -
Arosio Alberto,
Panizzi Stefano,
Paoli Maria Gabriella
Publication year - 1992
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.1670150903
Subject(s) - mathematics , timoshenko beam theory , beam (structure) , mathematical analysis , iterated function , fourier series , vibration , homogeneous , fourier transform , cauchy distribution , physics , quantum mechanics , combinatorics , optics
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.