This paper deals with a continuous beam resting on elastic support with elastic modulus derived from a random process. Governing equations of the stochastic higher-order finite element method of the free vibration of the continuous beam were derived from Hamilton's principle. The random process of elastic modulus was discretized by averaging random variables in each element. A solution for the stochastic eigenvalue problem for the free vibration of the continuous beam was obtained by using the perturbation technique, in conjunction with the finite element method. Spectral representation was used to generate a random process and employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

This paper has developed a Finite Element Method (FEM) to calculate the dynamic response of a continuous sandwich beam resting on elastic support subjected to moving vehicles. The equation of motion is derived using the classical beam theory and FEM. The vehicle model is a two Degree of Freedom (2DOF) system that moves with a constant velocity. The governing equation of motion is integrated by applying the Wilson-θ time integration method to obtain the dynamic response in each time step. Numerical examples investigate the displacement of the sandwich beam with various values of the structure and vehicle velocity. The effects of the stiffness of elastic support and the vehicle velocity on displacement are studied.