Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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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DOI: https://doi.org/10.1090/qam/430427
Article copyright: © Copyright 1974 American Mathematical Society


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