The analysis of a Beam Made of Physical Nonlinear Material on Elastic Foundation Under a Harmonic Load

  ABSTRACT: A prismatic beam made of a behaviorally nonlinear material situated on nonlinear elastic foundation is analyzed under a moving harmonic load moving with a known velocity. The vibration equation of motion    is 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 is found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear, and in this case there are finite values for the deflection, stress and bending moment of the beam.