TY - JOUR ID - 72120 TI - The analysis of a Beam Made of Physical Nonlinear Material on Elastic Foundation Under a Harmonic Load JO - International Journal of Engineering JA - IJE LA - en SN - 1025-2495 AU - Mardani, Esfandiar AD - Civil Eng., Urmia University Y1 - 2013 PY - 2013 VL - 26 IS - 5 SP - 509 EP - 514 KW - KEY WORDS Physical nonlinear KW - Harmonic moving load KW - Hamilton Principle KW - Euler KW - Lagrange Equation Dufing Equation KW - Critical velocity KW - Resonance DO - N2 -   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. UR - https://www.ije.ir/article_72120.html L1 - https://www.ije.ir/article_72120_d27c2b4a9cad79dab7b52f82f3587ac4.pdf ER -