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Exact deflation in the complex modal analysis of low-rank non-classically damped structures
- Source :
-
Engineering Structures . Dec2012, Vol. 45, p496-508. 13p. - Publication Year :
- 2012
-
Abstract
- Abstract: This paper presents the complex modal analysis for a proportionally damped structure equipped with linear non-proportionally damped viscous elements (substructures or discrete real devices) giving a low-rank contribution (r) to the non-proportional part of the damping matrix. Using the classical undamped modes and a special low-rank matrix update formulation of the problem, the original Quadratic Eigenproblem (QEP) is hugely deflated, without approximations, to an equivalent Rational Eigenproblem (REP) of dimension r ≪ n (), as an alternative to the linearized Standard Eigenproblem of order 2n over the complex field. The existence of classical modes in non-classically damped structures is also discussed. The REP is solved by the homotopy method: a robust predictor–corrector continuation algorithm is designed in order to determine the required eigenpairs. Some applications to simple models of both traditional and base-isolated structures, together with an outline of future work, end the paper. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 01410296
- Volume :
- 45
- Database :
- Academic Search Index
- Journal :
- Engineering Structures
- Publication Type :
- Academic Journal
- Accession number :
- 79873189
- Full Text :
- https://doi.org/10.1016/j.engstruct.2012.06.023