Lower Bounds for Eigenvalues via Rayleigh's Method
Publication: Journal of Engineering Mechanics
Volume 115, Issue 6
Abstract
This note summarizes several formulas for lower bounds to fundamental eigenvalues with suitable examples to illustrate their relative merits.
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References
1.
Bert, C. W. (1984a). “Use of symmetry in applying the Rayleigh‐Schmidt method to static and free‐vibration problems.” Indust. Math., 34, Part 1, 65–67.
2.
Bert, C. W. (1984b). “Improved technique for estimating buckling loads.” J. Engrg. Mech., ASCE, 110(12), 1655–1665.
3.
Collatz, L. (1948). Eigenwertprobleme. Chelsea Publishing Co., New York, N.Y.
4.
Langhaar, H. L. (1962). Energy methods in applied mechanics. John Wiley and Sons, New York, N.Y.
5.
Ly, B. (1987). “A lower bound for buckling loads.” Indust. Math., 37, Part 1, 1–9.
6.
Schmidt, R. (1974). “Several stability problems of plates and membranes subjected to liquid loads.” Indust. Math., 24, Part 1, 41–48.
7.
Schmidt, R. (1987). “Ly's lower bound to fundamental frequencies of free vibrations.” Indust. Math., 37, Part 2, 139–145.
8.
Schreyer, H. L., and Shih, P.‐Y. (1973). “Lower bounds to column buckling loads.” J. Engrg. Mech. Div., ASCE, 99(5), 1011–1022.
9.
Shih, P.‐Y., and Schreyer, H. L. (1978). “Lower bounds to fundamental frequencies and buckling loads of columns and plates.” Int. J. Solids and Struct., 14, 1013–1026.
10.
Temple, G., and Bickley, W. G. (1956). Rayleigh's principle. Dover Publications, New York, N.Y.
11.
Weinstein, A., and Stenger, W. (1972). Methods of intermediate problems for eigenvalues. Academic Press, New York, N.Y.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 115 • Issue 6 • June 1989
Pages: 1365 - 1370
Copyright
Copyright © 1989 ASCE.
History
Published online: Jun 1, 1989
Published in print: Jun 1989
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