Guided wave propagation in uncertain elastic media Faker Bouchoucha a,⇑ , Mohamed Najib Ichchou b , Mohamed Haddar a a Unit of Dynamics of the Mechanical Systems (UDSM), National School of Engineers of Sfax, BP, W3038 Sfax, Tunisia b Laboratory of Tribology and Dynamics of Systems (LTDS), Ecole Centrale de Lyon – 36 Avenue Guy de Collongues, 69130 Ecully, France article info Article history: Received 25 October 2011 Received in revised form 1 July 2012 Accepted 2 July 2012 Available online 11 July 2012 Keywords: Stochastic wave finite element Uncertain media Forced response abstract In this paper, the authors present a numerical approach to study the guided elastic wave propagation in uncertain elastic media. Stochastic wave finite element method (S.W.F.E.M) formulation with consider- ation of spatial variability of material and geometrical properties is developed for probabilistic analysis of structures. The uncertain material properties are modelled as a set of random fields. The idea is to con- sider the random fields as a supplementary dimension of the problem through the spatial discretisation using the finite elements process. The stochastic forced response is formulated to study the stochastic dynamical behavior of the structure using the appropriate boundary conditions. In this work, a SWFE approach is employed in order to analyse the stochastic wave propagation and the numerical accuracy. The computational efficiency of the method is demonstrated by comparison with Monte Carlo simulations. Ó 2012 Elsevier B.V. All rights reserved. Contents 1. Introduction ......................................................................................................... 303 2. Stochastic wave finite element method (SWFEM) formulation................................................................. 304 3. Wave propagation in uncertain periodic waveguide ......................................................................... 305 4. Numerical results and discussion ........................................................................................ 306 5. Conclusion .......................................................................................................... 311 References .......................................................................................................... 312 1. Introduction Guided waves are still a subject of intensive research such as structural forms occur in several engineering areas. This research focuses on the study of guided wave properties and applications. Among the primary properties of guided waves to be given, we can mention the dispersion curve and the mode shapes. Dispersion curves give the velocity-frequency relationship for all the modes which may propagate in the studied structure. The guided wave mode shape gives the distribution of displacements in the normal section to the propagation axis. A wave finite element method (W.F.E.M) formulation provides an effective way to calculate the dispersion curves of complex guided structures and investigates there properties [1–4]. In the literature, however, most of founded numerical issues of wave propagation simulations are mainly limited to deterministic media. Numerical guided wave techniques characterisation in spa- tially homogeneous random media is investigated in this paper. The finite element method has been weakening in dealing with variation of structural uncertain parameters. In this context, the concept of a random field [5] should be studied. Due to the com- plexity of the structure, the perturbation of its parameters that arises from material and geometrical variability is often much higher than conventional standard structures. An accurate predic- tion of the uncertainty in performance of cylindrical pipes by intro- ducing random variables or fields is thus desired. The uncertainties are often present in geometric properties, material characteristics and boundary conditions of the model. These variables are taken into account in models according to the both parametric [6,7] and non-parametric [8] approaches. Ichchou et al [6] considered the wave propagation features in random guided elastic media through the Stochastic Wave Finite Element Method (S.W.F.E.M) using a parametric probabilistic technique. In this paper, a parametric approach for uncertainties treat- ments is considered and combined to the WFE technique. The 0041-624X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2012.07.001 ⇑ Corresponding author. E-mail address: fakersbouchoucha@yahoo.fr (F. Bouchoucha). Ultrasonics 53 (2013) 303–312 Contents lists available at SciVerse ScienceDirect Ultrasonics journal homepage: www.elsevier.com/locate/ultras