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The main aim of this paper is to demonstrate the application of the generalized stochastic perturbation techniąue to model the lognormal random variables in structural mechanics. This is done to study probabilistic characteristics of the eigenvibrations for the high telecommunication towers with random stiffness, which are modeled as the linear elastic 3D trusses. The generalized perturbation technique based on the Taylor expansion is implemented using the Stochastic Finite Element Method in its Response Function version. The main difficulty here, in a comparison to this techniąue previous applications, is a necessity of both odd and even order terms inclusion in all the Taylor expansions. The hybrid numerical approach combines the traditional FEM advantages with the symbolic computing and its visualization power and it enables for a verification of probabilistic convergence of the entire computational procedure.
Rocznik
Tom
Strony
279--290
Opis fizyczny
Bibliogr. 10 poz., wykr.
Twórcy
autor
autor
- Department of Steel Structures, Faculty of Cyvil Engineering, Architecture and Environmental Engineering Technical University of Łódź, AL Politechniki 6, 90-924 Łódź, Marcin.Kaminski@p.lodz.pl
Bibliografia
- [1] H. Benaroya. Random eigenvalues, algebraic methods and structural dynamie models. Appl. Math. Comput., 52(1): 37-66, 1992.
- [2] T.J.R. Hughes. The Finite Element Method - Linear Static and Dynamie Finite Element Analysis. Dover Publications, Inc., New York, 2000.
- [3] M. Kamiński. Generalized perturbation-based stochastic finite element method in elastostatics. Comput. & Struci., 85(10): 586-594, 2007.
- [4] M. Kamiński, J. Szafran. Random eigenvibrations of elastic structures by the response function method and the generalized stochastic perturbation technique. Arch. Civil & Mech. Engrg., 10(1), 33-48, 2010.
- [5] M. Kleiber. Introduction to the Finite Element Method (in Polish). PSB, Warsaw, 1986.
- [6] M. Kleiber, T.D. Hien. The Stochastic Finite Element Method. Wiley, Chichester, 1992.
- [7] S. Mehlhose, J. vom Scheidt, R. Wunderlich. Random eigenvalue problems for bending vibrations of beams. Z. Angew. Math. Mech, 79(10): 693-702, 1999.
- [8] P.B. Nair, A.J. Keane. Ań approximate solution scheme for the algebraic random eigenvalue problem. J. Sound & Vibr., 260(1): 45-65, 2003..
- [9] H.J. Pradlwater, G.I. Schueller, G.S. Szekely. Random eigenvalue problems for large systems. Comput. & Struct, 80(27): 2415-2424, 2002.
- [10] C. Soize. Random matrix theory and non-parametric; model of random uncertainties in yibration analysis. J. Sound & Vibr., 263(4): 893-916, 2003.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPB8-0009-0024