Analysis of bending waves in beam on viscoelastic random foundation using wavelet technique

This paper deals with the mathematical model of dynamic behaviour of the beam resting on viscoelastic random foundation. It is considered by assuming the modulus of subgrade reaction to be a homogeneous random function of space variable. The problem is governed by the fourth-order differential equation with random parameters. The main results of this article are the approximate analytical solutions for the displacement field, variance and dynamic-stiffness coefficient. It has been made a comparison of numerical results obtained by using two different methods: Adomian’s decomposition and Bourret’s approximation. The special method of finding inverse Laplace transform based on the wavelet theory is adopted and used in numerical examples. For making numerical calculations and plots the programs in MATHEMATICA have been prepared.