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Structural Engineering and Mechanics Volume 14, Number 6, December 2002 , pages 679-698 DOI: https://doi.org/10.12989/sem.2002.14.6.679 |
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Comparative study on dynamic analyses of non-classically damped linear systems |
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Annalisa Greco and Adolfo Santini
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| Abstract | ||
| In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction oncept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces. | ||
| Key Words | ||
| dynamic response; non-classical damping; Ritz method; Lanczos vectors; complex modal analysis. | ||
| Address | ||
| Dipartimento di Ingegneria Civile ed Ambientale, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy Dipartimento di Meccanica e Materiali, University of Reggio Calabria, Feo di Vito, 89060 Reggio Calabria, Italy | ||