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Modal identification of self‐adjoint distributed‐parameter systems
Author(s) -
Norris Mark A.,
Silverberg Larry
Publication year - 1989
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290180504
Subject(s) - rayleigh quotient , orthogonality , distributed parameter system , modal , eigenvalues and eigenvectors , quotient , eigenfunction , mathematics , mathematical analysis , rayleigh–ritz method , boundary value problem , physics , geometry , differential equation , pure mathematics , chemistry , quantum mechanics , polymer chemistry
A new method is introduced for the identification of modal quantities of self‐adjoint distributed‐parameter systems. The method uses the temporal and spatial orthogonality properties of distributed‐parameter systems to form a pseudo‐Rayleigh quotient. The stationary values of the pseudo‐Rayleigh quotient can be determined by the solution of an eigenvalue problem, where the eigenvalues and eigenfunctions provide the frequencies and natural modes of the distributed‐parameter system. By way of formulation, the method is insensitive to zero mean measurement noise and is applicable to continuous as well as discrete systems. Numerical examples are presented in which the modal quantities of a simply‐supported beam and a discrete model of a membrane are identified. The results are compared with another modal identification technique, namely, the Ibrahim time domain method.