Inhomogeneous Timoshenko beam equations | Zendy

Arosio Alberto | Zendy; Panizzi Stefano | Zendy; Paoli Maria Gabriella | Zendy

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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.

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