Propagation of mechanical waves through a stochastic medium with spherical symmetry

Carlos G. Avendaño and J. Adrián Reyes

Physica A: Statistical Mechanics and its Applications, 2018, vol. 490, issue C, 161-170

Abstract: We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Keywords: Random medium; Elastic waves; Spherical symmetry (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:490:y:2018:i:c:p:161-170

DOI: 10.1016/j.physa.2017.08.024

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