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Second‐order sensitivity analysis in vibration and buckling problems
Author(s) -
Godoy Luis A.,
Taroco Edgardo O.,
Feuoo Raul A.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620372305
Subject(s) - eigenvalues and eigenvectors , buckling , sensitivity (control systems) , vibration , mathematics , perturbation (astronomy) , path (computing) , mathematical analysis , structural engineering , computer science , engineering , physics , acoustics , quantum mechanics , electronic engineering , programming language
A perturbation approach for the first‐ and second‐order sensitivity analysis of eigenvalue problems, as they arise in buckling and vibration of structural systems, is presented. A particular feature introduced in the formulation is the dependence of all matrices that model the problem not only on the design parameter, but also on a pre‐critical state. Thus, the sensitivity of the response of the fundamental path in buckling problems, or a pre‐stressed state, in vibration problems, are introduced in the analysis. Two techniques are considered in this work: the direct and the adjoint methods. First‐ and second‐order sensitivity equations for eigenvalues and eigenvectors are obtained, and it is shown that second‐order sensitivity of an eigenvalue can be accomplished by using only one adjoint problem.