Response of beams resting on linear and nonlinear elastic foundations and subjected to harmonic high-speed moving loading

Abstract

Analytical solution technique that provides fast, efficient and accurate results is developed for the fourth-order nonlinear differential equations describing the transverse vibrations of a beam on an elastic foundation. The method of solution developed is based on a recent novel method of calculation, the Adomian Modified Decomposition Method (AMDM). AMDM has advantages of solving without discretization, linearization, perturbation, or a priori assumptions, all of which has the potential to change the physics of the problem. The accuracy and the convergence speed of the method are validated against exact solutions. The beam is analyzed using two existing beam theories, namely, Euler-Bernoulli and Timoshenko beam theories. For the foundation widely used one-parameter Winkler and two-parameter Pasternak foundations are used. Numerical calculations of vibration frequencies and mode shape functions are performed. Effect of a foundation parameters and loadings on beam vibrations are analyzed and discussed.