Dynamic response of a bar embedded in semi-infinite medium: stochastic approach

Abstract

The idealized problem of the dynamic response of a bar with random modulus of elasticity, embedded in a randomly inhomogeneous semi-infinite medium, is analysed. The analytical approximate average solution is obtained on the basis of two different methods. Adomian's decomposition method leads to the solution for the average displacement, dynamic-stiffness coefficient and variance function which are represented by the series of multiple integrals. On the other hand closed form analytical solution is obtained on the basis of Bourret's approximation using Laplace transform and residue theorem. The numerical example is presented. The wider parametric study can be easily carried out employing Maple V and Mathematica system.