Closed-form Trigonometric Solutions for Inhomogeneous Beam-columns on Elastic Foundation
Autor(en): |
Ivo Caliò
Isaac Elishakoff |
---|---|
Medium: | Fachartikel |
Sprache(n): | Englisch |
Veröffentlicht in: | International Journal of Structural Stability and Dynamics, März 2004, n. 1, v. 4 |
Seite(n): | 139-146 |
DOI: | 10.1142/s0219455404001112 |
Abstrakt: |
In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method. |
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14.08.2019