Constructing the axial stiffness of longitudinally vibrating rod from fundamental mode shape

Author Type

Faculty

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

International Journal of Solids and Structures

Publication Status

Version of Record

Abstract

It is shown that inhomogeneous rods of uniform cross-section with the same material density variation and the same length, but with different boundary conditions and different elastic modulus variations along the axes of the rods have coincident fundamental natural frequency. The rods have different mode shapes that stem from the static displacements of the associated uniform rods, under uniformly distributed loads. These interesting properties appear in combination with other unanticipated results; namely, the natural frequency expression for any polynomial variation of the material density can be expressed in a unified manner, and depends solely on two coefficients: one coefficient describing material density and the other associated with elastic modulus variation. © 2001 Elsevier Science Ltd. All rights reserved.

First Page

3443

Last Page

3452

DOI

10.1016/S0020-7683(00)00267-5

Publication Date

3-30-2001

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