Rayleigh’s quotients and eigenvalue bounds for linear dynamical systems

Autor:	Rubens G. Salsa, Daniel T. Kawano, Fai Ma
Rok vydání:	2022
Předmět:	Rayleigh's principle Linear dynamical systems Applied Mathematics Mechanical Engineering Rayleigh's quotient Mechanical Engineering & Transports Interdisciplinary Engineering Damping Eigenvalue bounds
Zdroj:	Archive of Applied Mechanics, vol 92, iss 3
ISSN:	1432-0681 0939-1533
DOI:	10.1007/s00419-022-02105-5
Popis:	The primary objective of this article is to demonstrate that Rayleigh’s quotient and its variants retain the usual properties of boundedness and stationarity even when the linear vibratory system is non-classically damped, extending previously accepted results that these quotients could attain stationarity when damping was proportional or the modal damping matrix was diagonally dominant. This conclusion is reached by allowing the quotients to be defined in complex space and using complex differentiation. A secondary objective is to show how these quotients and their associated eigenvalue problems can be combined to generate bounds on the system’s eigenvalues, an immediate consequence that follows from establishing boundedness and stationarity in complex space. The reported bounds are simple to compute and appear to be tighter than previous bounds reported in the literature.
Databáze:	OpenAIRE
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