Formulation of a Stochastic Semi Analytical Finite Element Method for Uncertain Media

Abstract eng:
In the present work, the stochastic semi analytical finite element (S.S.A.F.E) method for uncertain media is formulated. This method leads to the characterisation of the guided wave propagation through the classical linearization of the governing equation of motion. In probabilistic methods, uncertainty in the parameters is considered and is represented by a random variable. The statistics of the propagation constants and the wave modes are offered. The current study extends the S.A.F.E. techniques to stochastic media through the second order perturbation. A parametric approach for uncertainties treatments is considered and combined to the S.A.F.E. technique. The originality of this paper is the study of the second order perturbation. The sensitivity and the precision of the S.S.A.F.E. approach is treated through the second order perturbation introduced in the structural parameters. The question of the statistics of wave characteristics is considered. The second order perturbation of the propagation constants is investigated. The numerical accuracy and the computational efficiency of the method are demonstrated by comparison with analytical results. Comparisons between numerical results and Monte Carlo simulations of the second order stochastic formulation are among the offered originalities of this work.

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