Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force

This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time Scales. Under three to-one-internal resonance condition applying nonlinear normal modes the steady state stability analysis of the beam’s vibrations is performed. Then the effect of changing the value of different parameters on the beam’s dynamic response and the steady state stability analysis is investigated.