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.
|Titolo:||Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation|
|Data di pubblicazione:||2004|
|Appare nelle tipologie:||1.1 Articolo in rivista|