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dc.contributor.authorOstoja-Starzewski, Martin.-
dc.description.abstractAbstract: We show that a Markov property of disturbance propagation forms the basis for a study of wavefronts in graph representable microstructures. Stochastic Huygens' minor principle is developed to analyze wavefront propagation in 1-D, 2-D, and 3-D models of material microstructures. A diffusion approximation is obtained for microstructures with grains described by piecewise linear constitutive laws. A new general method of solution to transient wave problems in such microstructures is developed: The method uses solutions from deterministic problems as a reference basis for an analysis of field fluctuations and scatter in stochastic media. The wavefront is modeled as a random field in space-time governed by a Markovian propagator. Explicit formulas for random arrivals in space-time and random modulation of pulses are obtained from this diffusion approximation. The key coefficients appearing in these formulas are calculated in the dimensionless setting of a 1-D linear elastic setting for a wide range of statistics of material properties. Finally, a local averaging process is proposed to obtain various smoothing approximations of this random field.en_US
dc.description.sponsorshipUnited States. Defense Nuclear Agency. Purdue University.en_US
dc.publisherStructures Laboratory (U.S.)en_US
dc.relation.ispartofseriesContract Report;SL-92-2-
dc.subjectGranular materialsen_US
dc.subjectMarkov processesen_US
dc.subjectRandom mediaen_US
dc.subjectStochastic analysisen_US
dc.subjectWave propagationen_US
dc.subjectDiffusion processesen_US
dc.subjectElastic solidsen_US
dc.titlePlane wave propagation in random granular mediaen_US
dc.typeTechnical Reporten_US
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