DYNAMIC FINITE-ELEMENT ANALYSIS OF A BEAM ON RANDOM FOUNDATION

The interaction between the structure and foundation of a beam on a random foundation is studied using the stochastic finite element method. The modulus foundation reaction is treated as random in position due to the natural variability of most natural soils and too much simplification of the foundation reaction. The perturbation method is adopted to obtain the stochastic dynamic response of a beam resting on a random foundation loaded with a deterministic transverse dynamic load. Once the global finite element equation of motion is established. the perturbation technique can be applied to the equation to produce a series of system differential equations which are readily solved one by one by modal expansion, then the stochastic response can be evaluated from these solutions. Finally, some of the statistical results computed from the perturbation method are checked by the Monte Carlo simulation method.