Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method
| Autor: | Abdollah Borhanifar, Ali Zamiri, Amin Ghannadiasl |
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| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Differential equation Mechanical Engineering Applied Mathematics Mathematical analysis General Engineering Aerospace Engineering 02 engineering and technology Type (model theory) Industrial and Manufacturing Engineering Vibration Cross section (physics) Algebraic equation 020901 industrial engineering & automation Collocation method Automotive Engineering Laguerre polynomials Beam (structure) Mathematics |
| Zdroj: | Journal of the Brazilian Society of Mechanical Sciences and Engineering. 42 |
| ISSN: | 1806-3691 1678-5878 |
| DOI: | 10.1007/s40430-020-02332-3 |
| Popis: | Natural frequencies and free vibration are important characteristics of beams with non-uniform cross section. Hence, the solution for free vibrations of non-uniform beams is presented using a Laguerre collocation method. The elastically restrained beam model is based on the Euler–Bernoulli theory. Also, the non-uniform beam is rested on a non-uniform foundation (Winkler type). The Laguerre collocation method is introduced for solving the differential equation. This approach reduces the governing differential equation to a system of algebraic equations, and finally, the problem is greatly simplified. Properties of Laguerre polynomials and the operational matrix of derivation are first presented. Eventually, the proposed method is applied for solving the governing differential equation subject to initial conditions, and the results are compared with other results from the literature. |
| Databáze: | OpenAIRE |
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