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Propagation of mechanical waves through a stochastic medium with spherical symmetry

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  • Avendaño, Carlos G.
  • Reyes, J. Adrián

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.

Suggested Citation

  • Avendaño, Carlos G. & Reyes, J. Adrián, 2018. "Propagation of mechanical waves through a stochastic medium with spherical symmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 161-170.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:161-170
    DOI: 10.1016/j.physa.2017.08.024
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    Cited by:

    1. Liu, Hu & Lv, Zheng, 2018. "Vibration and instability analysis of flow-conveying carbon nanotubes in the presence of material uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 85-103.

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