On dynamic response of semi-infinite rod inserted in a random medium

The dynamic response of a semi-infinite rod inserted in an elastic random medium is analysed using a functional expansion due to Adomian. The solution is represented as an infinite series of multiple integrals. The dimensionless approximate average solution for displacement field and dynamic-stiffness coefficient of the rod is obtained. This paper is an attempt to account for the stochastic changes in the elastic properties of the medium surrounded the rod. Closed form. analytical solution and numerical results are presented for the exponential correlation function. The parametric analysis, based on the second and fourth order approximation, indicates strong influence of the randomness of medium on the dynamic response especially in the vicinity of cutoff frequency.