Effect of Winkler Foundation on the Dynamic Analysis of Euler- Bernoulli Beam Resting on Elastic Foundation Using Integral Numerical Method

This study examined how a Winkler foundation influences the dynamic analysis of an Euler-Bernoulli beam placed on an elastic foundation by employing an Integral-Numerical method, which simplifies to an ordinary differential equation using a series representation of the Heaviside function. The dynamic responses of the beam, including normalized deflection and bending moment, were analyzed for various velocity ratios under conditions of moving loads and moving masses. In general, a closed-form solution for the generalized mathematical model of a prismatic beam was derived using a symbolic programming technique with MAPLE 18. The findings indicated that the inclusion of an elastic foundation along with adequate reinforcement in beams and beam-like structures decreases vibration intensity, ensures safe load passage, and extends the lifespan of the beam.