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

Author Type

Outside Researcher

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

AIAA Journal

Publication Status

Version of Record

Abstract

It is uniformly known that the buckling modes of uniform 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 specific 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 affirmative. 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 specified axial load distributions. In all cases the closed-form solutions are obtained for the eigenvalue parameter.

First Page

2532

Last Page

2537

DOI

10.2514/2.1598

Publication Date

1-1-2002

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