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

Abstract

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

Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects

“…To what extent is the average solution for a heterogeneous random medium different from the classical solution for a homogeneous medium? While various stochastic models have been developed to incorporate the spatial random fluctuations in wave propagation studies, the present paper continues the recent research line [9] aimed at grasping the fractal and Hurst characteristics of typically observed natural patterns [7] in transient wave propagation. Such effects are represented in Cauchy and Dagum random fields (RFs) [3,13], which have been developed over the past two decades.…”

“…Such effects are represented in Cauchy and Dagum random fields (RFs) [3,13], which have been developed over the past two decades. In particular, whereas [9] was focused on the in-plane Lamb's problem, this paper studies its anti-plane version, which deals with a transient out-of-plane load applied at the free surface of half-space. The resulting wave motion is pure shear, horizontally polarized, also called SH wave.…”

“…However, since the Cauchy and Dagum RFs have no explicit spectral densities (i.e., Fourier transforms of covariances), passing to the frequency domain is not pursued. Effectively, the study of wave motion has to be carried out directly in the time domain, just as recently employed in the in-plane stochastic Lamb's problem [9]. Therefore, our strategy involves running numerical solutions of the transient wave problem on realizations of the RF, and repeating them in the Monte Carlo sense in order to assess the statistics of responses.…”

“…The classical in-plane Lamb's problem was studied both theoretically and experimentally [1,2]. The in-plane Lamb's problem on random mass density fields with fractal and Hurst effects was studied numerically in [9,10,11], where both pressure (P) and Rayleigh (R) waves were considered. The present study concentrates on the shear wave analysis.…”

“…The present study concentrates on the shear wave analysis. We use the same material properties as in Dally's experimental study [2] and Nishawala's numerical simulation [9]. The material is CR-39 with Young's modulus 3.85 GP a (559ksi), Poisson's ratio 1/3, and mass density 1, 300 kg/m 3 .…”