It is uniformly known that the buckling modes of uniform columns are given by trigonometric,namely,harmonic, functions. For inhomogeneous columns the buckling modes usually are derived via special functions including Bessel and Lommel functions. Recently it was demonstrated that the buckling modes of speciŽ c inhomogeneous columns assume a simple polynomial form. The question posed in the title of this study therefore naturally arises. It is shown that the reply to this query is afŽ rmative. Four cases of harmonically varying buckling modes are postulated and semi-inverse problems are solved that result in the distributions of the  flexural rigidity compatible to the preselected modes and to speciŽ ed axial load distributions. In all cases the closed-form solutions are obtained for the eigenvalue parameter.

Can harmonic functions constitute closed-form buckling modes of inhomogeneous columns?

CALIO', Ivo Domenico;
2002

Abstract

It is uniformly known that the buckling modes of uniform columns are given by trigonometric,namely,harmonic, functions. For inhomogeneous columns the buckling modes usually are derived via special functions including Bessel and Lommel functions. Recently it was demonstrated that the buckling modes of speciŽ c inhomogeneous columns assume a simple polynomial form. The question posed in the title of this study therefore naturally arises. It is shown that the reply to this query is afŽ rmative. Four cases of harmonically varying buckling modes are postulated and semi-inverse problems are solved that result in the distributions of the  flexural rigidity compatible to the preselected modes and to speciŽ ed axial load distributions. In all cases the closed-form solutions are obtained for the eigenvalue parameter.
closed form solution; inhomogeneous columns
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/23246
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