Analysis of a Beam Made of Physical Nonlinear Material on Nonlinear Elastic Foundation under a Moving Concentrated Load

A prismatic beam made of a behaviorally nonlinear material was analyzed under a concentrated load moving with a known velocity on a nonlinear elastic foundation with a reaction [ q_e = -K₁W(1+ K₂W²)]. the vibration equation of motion was derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it was found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear and there are finite values for the deflection, stress and bending moment of the beam when