title: Lamb's problem on random mass density fields with fractal and Hurst effects.
abstract: This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity. We first evaluate the response of CA to an uncorrelated mass density field, more commonly known as white-noise, of varying coarseness as compared to CA's node density. We then evaluate the response of CA to multiscale mass density RFs of Cauchy and Dagum type; these fields are unique in that they are able to model and decouple the field's fractal dimension and Hurst parameter. We focus on stochastic imperfection sensitivity; we determine to what extent the fractal or the Hurst parameter is a significant factor in altering the solution to the planar stochastic Lamb's problem by evaluating the coefficient of variation of the response when compared with the coefficient of variation of the RF.
authors.affiliation: Department of Mechanical Science and Engineering , Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, IL 61820, USA.
authors.forename: V V
authors.identifier: 0000-0002-8234-8080
authors.initials: VV
authors.lastname: Nishawala
authors.affiliation: Department of Mechanical Science and Engineering , Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, IL 61820, USA.
authors.forename: M
authors.identifier: 0000-0002-3493-363X
authors.initials: M
authors.lastname: Ostoja-Starzewski
authors.affiliation: George W. Woodruff School of Mechanical Engineering , Georgia Institute of Technology , 771 Ferst Drive, North West, Atlanta, GA 30332-0405, USA.
authors.forename: M J
authors.initials: MJ
authors.lastname: Leamy
authors.affiliation: Department of Mathematics , Technical University Federico Santa Maria , Valparaiso, Chile.
authors.forename: E
authors.initials: E
authors.lastname: Porcu
keywords: Hurst parameter; cellular automata; fractal dimension; random media; wave propagation