A Wavelet Approach for the Analysis of Bending Waves in a Beam on Viscoelastic Random Foundation
This paper deals with the mathematical model of dynamic behaviour of a beam resting on viscoelastic random foundation for which the modulus of subgrade reaction is assumed to be a homogeneous random function of the space variable. An approximate analytical solution for the fourth-order differential equation with random parameters is obtained in the case of a ∞ C -class correlation function. This higher order regularity of correlation function implies the regularity of associated stochastic function  in the sense of the mean-square analysis . The numerical results for the average displacement have been obtained by using Bourret’s approximation method. A special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in the numerical examples.
Patrick Sean Keogh
P. Koziol et al., "A Wavelet Approach for the Analysis of Bending Waves in a Beam on Viscoelastic Random Foundation", Applied Mechanics and Materials, Vols. 5-6, pp. 239-246, 2006