Can a trigonometric function serve both as the vibration and the buckling mode of an axially graded structure?

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

Mechanics Based Design of Structures and Machines

Publication Status

Version of Record

Abstract

It is well known that for homogeneous beams that have simply supported or guided ends a trigonometric function serves both as a vibration and a buckling mode. The research in this paper shows that, remarkably, the same result is valid for some axially graded beams. Specifically, three cases of harmonically varying vibration modes are postulated and the associated semi-inverse problems that result in the distributions of elastic modulus that together with a specific variation of material density and axial load distribution satisfy the governing eigenvalue problem for the inhomogeneous Bemoulli-Euler beam are solved. In all cases the closed-form solutions are obtained for the natural frequency. Those closed-form solutions are contrasted with approximate solutions based on appropriate polynomial functions, serving as trial functions in an energy method.

First Page

401

Last Page

421

DOI

10.1081/SME-200028002

Publication Date

1-1-2004

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