Design parameter variation and structural response

Romstad, Karl M.; Hutchinson, J. R.; Runge, K. H.

doi:10.1002/nme.1620050305

Cited by 18 publications

(5 citation statements)

References 4 publications

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“…The impact of this truncation error, however, can be indirectly accessed: a converged solution should indicate that the truncation error is negligible. The validity of this truncated version of modal expansion was previously demonstrated for dynamic analyses [22,23] and model updating as well [10].…”

Section: A New Formulation For Identification Of Joint Stiffnessesmentioning

confidence: 90%

A New Method for Structural Model Updating and Joint Stiffness Identification

Li¹

2002

Mechanical Systems and Signal Processing

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Section: A New Formulation For Identification Of Joint Stiffnessesmentioning

confidence: 90%

A New Method for Structural Model Updating and Joint Stiffness Identification

Li¹

2002

Mechanical Systems and Signal Processing

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“…We rewrite equations (1) and (2) in the following forms: Equations (6) and (7) imply that the differential coefficients of the eigenvalues and eigenvectors with regard to s at s = O are expressed by using the eigenvalues and eigenvectors at s = O themselves. Then the differential equations for those values may be derived by applying the expressions (6) and (7) to the intermediate state at s = s during the modification.…”

Section: Dijferential Equations For Eigenvalues and Eigenvectorsmentioning

confidence: 99%

Eigenvalue reanalysis by improved perturbation

Inamura

1988

Numerical Meth Engineering

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SUMMARYA new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations. The special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification, and that the computer run time spent by this method is far shorter than that of revised analysis by FEM when only a few selected modes are used in the form ofan approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. The efficiency of the proposed method has been verified by applying it to a simple spring-mass model as well as a 600 degrees-offreedom model which receive structural modification.

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“…e expressions were applicable only to self-adjoint systems, and the numerical examples used only contained real eigenvalues and were restricted to small perturbations in the system. Romstad et al [2] formulated a power-series perturbation approach and applied the method to structural systems in order to find perturbed distinct or repeated eigenvalues and eigenvalue sensitivities. However, the systems they analyzed were symmetric and undamped.…”

Section: Introductionmentioning

confidence: 99%

Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems

Philip

Shin

2018

Shock and Vibration

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Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. ey will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation method, the eigenvalue perturbation theory is used to formulate a first-order and a second-order approximation of the eigensolutions of symmetric and asymmetric systems. In the incremental perturbation method, the straightforward approach is extended to analyze systems with large perturbations using an iterative scheme. Finally, in the triple product method, the accuracy of the approximate eigenvalues is significantly improved by exploiting the orthogonality conditions of the perturbed eigenvectors. All three methods require only the eigensolutions of the nominal or unperturbed system, and in application, they involve simple matrix multiplications. Numerical experiments show that the proposed methods achieve accurate results for systems with and without damping and for systems with symmetric and asymmetric system matrices.

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Design parameter variation and structural response

Cited by 18 publications

References 4 publications

A New Method for Structural Model Updating and Joint Stiffness Identification

A New Method for Structural Model Updating and Joint Stiffness Identification

Eigenvalue reanalysis by improved perturbation

Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems

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