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Rayleigh quotient for non-conservative discrete systems

Rayleigh quotient for non-conservative discrete systems
Rayleigh quotient for non-conservative discrete systems
Rayleigh quotient is extended to non-conservative systems when the modes become complex due to the presence of damping. A critique of recently proposed quotients in this context is presented. Two new quotients are proposed here which provide approximation for the complex eigenvalues when the trial vectors approximate the actual latent vectors. The stationary values of the quotients proposed here coincide with the complex latent-roots of the system. In case of the first quotient, the complex trial vectors belong to the state-space. For the second, they belong to the configuration space. The expressions in the numerator and the denominator of these quotients involve bilinear forms as opposed to those in the original non-dissipative setting where they are quadratic forms. An example is given to illustrate the claimed stationarity of the proposed quotients.
Bhaskar, A.
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Bhaskar, A.
d4122e7c-5bf3-415f-9846-5b0fed645f3e

Bhaskar, A. (2010) Rayleigh quotient for non-conservative discrete systems. RASD 2010 - 10th International Conference on Recent Advances in Structural Dynamics, Southampton, United Kingdom. 12 - 14 Jul 2010. 11 pp .

Record type: Conference or Workshop Item (Paper)

Abstract

Rayleigh quotient is extended to non-conservative systems when the modes become complex due to the presence of damping. A critique of recently proposed quotients in this context is presented. Two new quotients are proposed here which provide approximation for the complex eigenvalues when the trial vectors approximate the actual latent vectors. The stationary values of the quotients proposed here coincide with the complex latent-roots of the system. In case of the first quotient, the complex trial vectors belong to the state-space. For the second, they belong to the configuration space. The expressions in the numerator and the denominator of these quotients involve bilinear forms as opposed to those in the original non-dissipative setting where they are quadratic forms. An example is given to illustrate the claimed stationarity of the proposed quotients.

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Published date: 2010
Venue - Dates: RASD 2010 - 10th International Conference on Recent Advances in Structural Dynamics, Southampton, United Kingdom, 2010-07-12 - 2010-07-14

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Local EPrints ID: 155963
URI: https://eprints.soton.ac.uk/id/eprint/155963
PURE UUID: 8182f6a7-79e8-4dac-a57a-9180c296c3a0

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Date deposited: 02 Jun 2010 08:59
Last modified: 22 Oct 2018 16:33

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