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.
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A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and Shear
H. C. Lee
Rensselaer Polytechnic Institute, Troy, N. Y.
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Lee, H. C. (June 1, 1963). "A Generalized Minimum Principle and Its Application to the Vibration of a Wedge With Rotatory Inertia and Shear." ASME. J. Appl. Mech. June 1963; 30(2): 176–180. https://doi.org/10.1115/1.3636508
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