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: nd the distribution of the material density and the exural 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. Specically, 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 exural rigidity that together with a specic 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 corre- sponding 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.
Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation
CALIO', Ivo Domenico;
2004-01-01
Abstract
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: nd the distribution of the material density and the exural 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. Specically, 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 exural rigidity that together with a specic 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 corre- sponding 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.File | Dimensione | Formato | |
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Calio I. Elishakoff I. (2004). Closed form trigonometric solutions for inhomogeneous beam columns on elastic foundation International Journal of Structural Stability and Dynamics. Vol 4, p 139-146 ISSN 02194554.pdf
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