Analysis of a Beam under Moving Loads

Abstract: It is assumed that a beam made of material has a physical nonlinear behavior. This beam is analyzed under the moving concentrated and distributed continuous loads. The vibration equations of motion are derived from the Hamilton's Principle and Euler–Lagrange Equation. In this study, the amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam has been calculated. At the state of concentrated moving load,  the obtained analytic solution has been exemplified. The results of this study indicate that when the material of the beam is considered physically nonlinear, there is no critical velocity and the resonance phenomenon doesn’t happen.

Keywords:

Keywords Moving load , Hamilton Principle , Euler , Lagrange Equation , Duffing Equation , Resonance