Extremum properties of the generalized Rayleigh quotient associated with flutter instability
Authors:
K. Huseyin and R. H. Plaut
Journal:
Quart. Appl. Math. 32 (1974), 189-201
MSC:
Primary 34C99; Secondary 49G99
DOI:
https://doi.org/10.1090/qam/430427
MathSciNet review:
430427
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Abstract: The extremum properties of the generalized Rayleigh quotient related to flutter instability are investigated. It is shown that, in addition to the well-known stationary property, under certain circumstances the quotient exhibits maximum-minimum properties which are in contrast to those of the classical Rayleigh quotient. One consequence is that an approximate method of stability analysis using these results leads to a lower bound as opposed to an upper bound in the classical case. The results are applied to multiple-parameter systems and a physical interpretation is given for the generalized Rayleigh quotient, leading to the proof of a convexity theorem.
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Lord Rayleigh, Theory of sound, vol. 1, Macmillan, New York, 1929; Dover, New York, 1945, sec. 88
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K. Huseyin and R. H. Plaut, The elastic stability of two-parameter nonconservative systems, J. Appl. Mech. 40, 175–180 (1973)
R. H. Plaut, Determining the nature of instability in nonconservative problems, AIAA J. 10, 967–968 (1972)
P. Lancaster, On eigenvalues of matrices dependent on a parameter, Num. Math. 6, 377–387 (1964)
R. H. Plaut and K. Huseyin, Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems, AIAA J. 11, 250–251 (1973)
P. F. Papkovich, Works on the structural mechanics of ships, vol. 4, Moscow, 1963 (in Russian)
J. D. Renton, Buckling of frames composed of thin-wall members, in A. H. Chilver, editor, Thin-walled structures, Wiley, New York, 1967, pp. 1–59
K. Huseyin and J. Roorda, The loading-frequency relationship in multiple eigenvalue problems, J. Appl. Mech. 38, 1007–1011 (1971)
K. Huseyin and H. Leipholz, Divergence instability of multiple-parameter circulatory systems, Quart. Appl. Math. 31, 185–197 (1973)
F. Buckens, Über Eigenwertscharen, Öst. Ing. Arch. 12, 82–93 (1958)
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Article copyright:
© Copyright 1974
American Mathematical Society