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Lamb's problem on random mass density fields with fractal and Hurst effects.

V V Nishawala1, M Ostoja-Starzewski1, M J Leamy2

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Summary

This study simulates wave propagation in an elastic half-space with random mass density using cellular automata (CA). It investigates how random field characteristics, like fractal dimension and Hurst parameter, affect the solution to Lamb's problem.

Keywords:
Hurst parametercellular automatafractal dimensionrandom mediawave propagation

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Area of Science:

  • Solid Mechanics
  • Computational Physics
  • Geophysics

Background:

  • Lamb's problem is a classic benchmark in seismology and solid mechanics.
  • Understanding wave propagation in heterogeneous media is crucial for geophysical exploration and material science.
  • Previous models often simplified the complexity of natural material properties.

Purpose of the Study:

  • To generalize Lamb's problem to an infinite elastic half-space with random fields (RFs) of mass density.
  • To investigate the impact of uncorrelated and correlated RFs (with fractal and Hurst characteristics) on wave propagation.
  • To analyze stochastic imperfection sensitivity in the planar stochastic Lamb's problem.

Main Methods:

  • Generalization of Lamb's problem for random fields of mass density.
  • Simulation of wave propagation using Cellular Automata (CA).
  • Evaluation of CA response to uncorrelated (white-noise) and correlated (Cauchy, Dagum) mass density RFs.
  • Analysis of fractal dimension and Hurst parameter effects on wave propagation.

Main Results:

  • CA successfully simulates wave propagation in elastic half-spaces with random mass density fields.
  • The study quantifies the response to varying coarseness of uncorrelated RFs.
  • The impact of multiscale mass density RFs (Cauchy, Dagum) on wave propagation is evaluated.
  • Stochastic imperfection sensitivity is assessed by comparing response variations to RF variations.

Conclusions:

  • Cellular automata provide a viable method for simulating wave propagation in complex media.
  • Both fractal dimension and Hurst parameter significantly influence the solution to the planar stochastic Lamb's problem.
  • The study highlights the importance of characterizing RFs for accurate modeling in geophysics and material science.