Vibration tailoring of inhomogeneous rod that possesses a trigonometric fundamental mode shape

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

Journal of Sound and Vibration

Publication Status

Version of Record

Abstract

In this study, a special class of closed-form solutions for inhomogeneous rod is investigated. Namely, the following problem is considered: determine the distribution axial rigidity when the material density is given of an inhomogeneous rod so that the postulated fundamental trigonometric mode shape serves as an exact vibration mode. In this study, the associated semi-inverse problem is solved that results in the distributions of axial rigidity that together with a specified law of material density satisfy the governing eigenvalue problem. For comparison, the obtained closed-form solutions are contrasted with approximate solutions based on an appropriate polynomial shapes, serving as trial functions in an energy method. The obtained results are utilized for vibration tailoring, i.e. construction of the rod with a given natural frequency. © 2007 Elsevier Ltd. All rights reserved.

First Page

838

Last Page

842

DOI

10.1016/j.jsv.2007.06.079

Publication Date

1-22-2008

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