Invariant Imbedding Applied to Eigenvalue Problems in Mechanics

[+] Author and Article Information
E. M. Shoemaker

Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, Ill.

J. Appl. Mech 32(1), 47-50 (Mar 01, 1965) (4 pages) doi:10.1115/1.3625782 History: Received February 27, 1964; Online September 15, 2011


A formal method is presented for obtaining eigenvalues of ordinary differential equations associated with problems of buckling and vibration. The method utilizes the idea of invariant imbedding which has previously been applied to two point boundary value problems in transport theory and wave propagation. The present method reduces the eigenvalue problem to an initial value problem for a matrix of Riccati equations. The numerical solution of such formulations has proved to be generally more efficient than known methods.

Copyright © 1965 by ASME
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