Asymptotic Behavior of Eigenvalues for Finite, Inhomogeneous Elastic Rods

[+] Author and Article Information
Adnan H. Nayfeh

University of California, San Diego, La Jolla, Calif.

J. Appl. Mech 39(2), 595-597 (Jun 01, 1972) (3 pages) doi:10.1115/1.3422724 History: Received August 12, 1971; Online July 12, 2010


Asymptotic expressions for the eigenvalues and the corresponding eigenfunctions for the free vibrations of an inhomogeneous elastic rod with a finite length are derived. The derivation is based on the assumption that the elastic parameters and their derivatives vary continuously along the rod. A method which consists of a perturbation about the solutions of the homogeneous cases is used.

Copyright © 1972 by ASME
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