Hamilton, Ritz, and Elastodynamics

[+] Author and Article Information
C. D. Bailey

Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus, Ohio

J. Appl. Mech 43(4), 684-688 (Dec 01, 1976) (5 pages) doi:10.1115/1.3423956 History: Received July 01, 1975; Revised October 01, 1975; Online July 12, 2010


The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings.

Copyright © 1976 by ASME
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