Design of a polynomially inhomogeneous bar with a tip mass for specified mode shape and natural frequency

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

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

In this study the closed form solution is obtained, apparently for the first time, for the free vibration inhomogeneous bar with a tip mass. It is remarkable that while a vibrations study the homogeneous bar with free tip leads to transcendental equation, here, in the case of the inhomogeneous bar, a closed form polynomial solution is obtained. If the mass ratio between the bar's mass and the concentrated mass is specified, numerical evaluation is needed for the axial rigidity coefficients' ratio; on the other hand, for specified mass ratios closed form solution is reported. © 2005 Elsevier Ltd. All rights reserved.

First Page

1004

Last Page

1012

DOI

10.1016/j.jsv.2005.02.043

Publication Date

11-4-2005

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