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.