Exponential solutions for a longitudinally vibrating inhomogeneous rod

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 Mechanics of Materials and Structures

Publication Status

Version of Record

Abstract

A special class of closed form solutions for inhomogeneous rods is investigated, arising from the following problem: for a given distribution of the material density, find the axial rigidity of an inhomogeneous rod so that the exponential mode shape serves as the vibration mode. Specifically, for a rod clamped at one end and free at the other, the exponentially varying vibration mode is postulated and the associated semi-inverse problem is solved. This yields distributions of axial rigidity which, together with a specific law of material density, satisfy the governing eigenvalue problem. The results obtained can be used in the context of functionally graded materials for vibration tailoring, that is, for the design of a rod with a given natural frequency according to a postulated vibration mode.

First Page

1251

Last Page

1256

DOI

10.2140/jomms.2009.4.1251

Publication Date

1-1-2009

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