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.
2004
Closed-form solutions; inhomogeneous beam-columns; elastic foundation
File in questo prodotto:
File Dimensione Formato  
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

solo gestori archivio

Tipologia: Documento in Post-print
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 169.81 kB
Formato Adobe PDF
169.81 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/36647
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 32
  • ???jsp.display-item.citation.isi??? ND
social impact