Dynamic analysis of large structures with uncertain parameters based on coupling component mode synthesis and perturbation method

Abstract This paper presents a methodological approach to compute the stochastic eigenmodes of large FE models with parameter uncertainties based on coupling of second order perturbation method and component mode synthesis methods. Various component mode synthesis methods are used to optimally reduce the size of the model. The statistical first two moments of dynamic response of the reduced system are obtained by the second order perturbation method. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures for large FE models with uncertain parameters are presented.

[1]  Masanobu Shinozuka,et al.  Monte Carlo solution of structural dynamics , 1972 .

[2]  F. Bourquin,et al.  Component mode synthesis and eigenvalues of second order operators : discretization and algorithm , 1992 .

[3]  Hongping Zhu,et al.  Substructure based approach to finite element model updating , 2011 .

[4]  C. S. Manohar,et al.  DYNAMIC ANALYSIS OF FRAMED STRUCTURES WITH STATISTICAL UNCERTAINTIES , 1999 .

[5]  G. Schuëller,et al.  Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches , 2009 .

[6]  N. Impollonia,et al.  Improved dynamic analysis of structures with mechanical uncertainties under deterministic input , 2000 .

[7]  R. Macneal A hybrid method of component mode synthesis , 1971 .

[8]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[9]  Roger Ghanem,et al.  Numerical solution of spectral stochastic finite element systems , 1996 .

[10]  S. Rubin Improved Component-Mode Representation for Structural Dynamic Analysis , 1975 .

[11]  R. Guyan Reduction of stiffness and mass matrices , 1965 .

[12]  D. Sarsri,et al.  Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models , 2011 .

[13]  Humberto Contreras,et al.  The stochastic finite-element method , 1980 .

[14]  D. Tran,et al.  Component mode synthesis methods using interface modes. Application to structures with cyclic symmetry , 2001 .

[15]  N. Bouhaddi,et al.  Improved free-interface substructures representation method , 2000 .

[16]  G. Stefanou The stochastic finite element method: Past, present and future , 2009 .

[17]  Timothy P. Waters,et al.  Component mode synthesis as a framework for uncertainty analysis , 2009 .