Nonparametric stochastic modeling satisfying the causality principle for viscoelastic structures in computational structural dynamics

Rémi Capillon (1) , Christophe Desceliers (1) , Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

In this paper, we are interested in the specificities of uncertainty modeling for linearly viscoelastic 3D dynamical structures described in the frequency domain using the nonparametric probabilistic approach of uncertainties, consisting in replacing the matrices of the mean reduced-order model by random matrices. In the context of linear viscoelasticity, the causality of the system implies a relationship induced by the Hilbert transform between its frequency-dependent stiffness and damping matrices (also known as the Kramers-Kronig, or K-K, relations). The frequency-dependent random stiffness and damping matrices cannot be modeled as independent random matrices without violating the causality. Consequently, the stochastic model of these frequency-dependent random matrices must verify the K-K relations, yielding a statistical dependence between the stiffness and damping matrices [1]. The influence of this statistical dependence will be shown in the numerical studies presented. After summarizing the theoretical construction of the stochastic model and a presentation of computational issues, in particular concerning the computation of the Hilbert transform, we will show results obtained from Monte Carlo simulations for a simple composite structures in the frequency domain. This structure, designed as a study case, is composed of a three-layers plate with two viscoelastic layers and a central purely elastic layer. We will also give insight on the behavior of the constructed stochastic model subjected to several levels of uncertainty. References [1] C. Soize, I.E. Poloskov, Time-domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation, Computers and Mathematics with Applications, 64 (11), 3594-3612, 2012

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]

Rémi Capillon, Christophe Desceliers, Christian Soize. Nonparametric stochastic modeling satisfying the causality principle for viscoelastic structures in computational structural dynamics. UNCECOMP 2015, 1st ECCOMAS Thematic International Conference on Uncertainty Quantification in Computational Sciences and Engineering, May 2015, The Island of Crete, Greece. ⟨hal-01158286⟩