Coupling Neumann development and component mode synthesis methods for stochastic analysis of random structures

Driss Sarsri


In this paper, we propose a method to calculate the first two moments (mean and variance) of the structural dynamics response of a structure with uncertain variables and subjected to random excitation. For this, Newmark method is used to transform the equation of motion of the structure into a quasistatic equilibrium equation in the time domain. The Neumann development method was coupled with Monte Carlo simulations to calculate the statistical values of the random response. The use of modal synthesis methods can reduce the dimensions of the model before integration of the equation of motion. Numerical applications have been developed to highlight effectiveness of the method developed to analyze the stochastic response of large structures.



- R.R. Craig, M.C.C. Bampton, Coupling of substructures for dynamics analysis. AIAA J. 6(7) (1968) 1313-1319.

- R.H. MacNeal, A hybrid method of component mode synthesis, Comput. Struct. 1(1971) 581-601.

- D.M. Tran, Component mode synthesis methods using interface modes. Application to structures with cyclic symmetry, Comput. Struct. 79(1) (2001) 209-222.

- M. Shinozuka, Monte Carlo solution of structural dynamics, Comput. Struct. 2(1972) 855- 874.

- M. Kleiber, T.D. Hien, The stochastic finite element method: Basic Perturbation Technique and Computer Implementation, Ed. Jhon Wiley, 1992.

- G. Muscolino, G. Ricciardi, N. Impollonia, Improved dynamic analysis of structures with mechanical uncertainties under deterministic input, Prob. Eng. Mech. 15(2) (2000) 199-212.

- R. Li, R. Ghanem, Adaptative polynomial chaos expansions applied to statistics of extremes in non-linear random vibration. Prob. Eng. Mech. 13(1998) 125-136.

- M.D. Shields, G. Deodatis, Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes. Comput. struct. 126(2013) 149-163.

- L. Zhao, Q. Chen, Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation, Comput. Struct. 77(6) (2000) 651-657.

- G. Stefanou, The stochastic finite element method: Past, present and future. Comput. Meth. App. Mech. Eng. 198(2009) 1031-1051.

- G.I. Schuëller, H.J. Pradlwarter, Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches. Eng. Struct. 31(11) (2009) 2507-2517.

- D. Sarsri, L. Azrar, A. Jebbouri, A. El Hami, Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models. Comput. Struct. 89(2011) 346-356.

- L. Hinke, F. Dohnal, B.R. Mace, T.P. Waters, N.S. Ferguson, Component mode synthesis as a framework for uncertainty analysis. J. Sound Vib. 324(2009) 161–178.


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