Anti-plane shear lamb’s problem on random mass density fields with fractal and hurst effects

This paper reports a study of transient dynamic responses of the anti-plane shear Lamb’s problem on random mass density field with fractal and Hurst effects. Cellular automata (CA) is used to simulate the shear wave propagation. Both Cauchy and Dagum random field models are used to capture fractal dimension and Hurst effects in the mass density field. First, the dynamic responses of random mass density are evaluated through a comparison with the homogenerous computational results and the classical theoretical solution. Then, a comprehensive study is carried out for different combinations of fractal and Hurst coefficients. Overall, this investigation determines to what extent fractal and Hurst effects are significant enough to change the dynamic responses by comparing the signal-to-noise ratio of the response versus the signal-to-noise ratio of the random field.