Fluctuations of a beam with clamped ends
| Autor: | Kamil B Sabitov |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, Vol 19, Iss 2, Pp 311-324 (2015) |
| Druh dokumentu: | article |
| ISSN: | 1991-8615 2310-7081 |
| DOI: | 10.14498/vsgtu1406 |
| Popis: | In this paper we study the initial problem for the equation of a beam with clamped ends. Uniqueness, existence and stability theorems are proved for the problem in the classes of regular and generalized solutions. Solution of the initial-boundary value problem is constructed in the form of a series in the system of eigenfunctions of one-dimensional spectral problem. We found the spectral problem eigenvalues as roots of the transcendental equation and the corresponding system of eigenfunctions. It is shown that the system of eigenfunctions is orthogonal and complete in L 2. On the basis of the completeness of the eigenfunctions the uniqueness theorem for the initial-boundary value problem for the equation of the beam is obtained. The generalized solution is defined as the limit of a sequence of regular solutions of the mean-square norm on the space variable. |
| Databáze: | Directory of Open Access Journals |
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