A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and Shear

[+] Author and Article Information
H. C. Lee

Rensselaer Polytechnic Institute, Troy, N. Y.

J. Appl. Mech 30(2), 176-180 (Jun 01, 1963) (5 pages) doi:10.1115/1.3636508 History: Received June 20, 1962; Online September 16, 2011


The minimum principle and step-by-step iteration method are generalized for coupled simultaneous differential equations in order to obtain an approximate solution for the flexural vibration frequencies of a wedge with rotatory inertia and shear effects. This procedure avoids the difficulty of solving the nonself-adjoint equation which results when the simultaneous equations for bending slope and displacement are combined into a single differential equation. The upper and lower bounds of the first two eigenvalues are established and a comparison is made with the classical Kirchhoff solution where the rotatory inertia and shear are neglected.

Copyright © 1963 by ASME
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