ELASTODYNAMIC MODELING AND SIMULATION OF AN AXIALLY ACCELERATING BEAM

This paper aims to develop an accurate nonlinear mathematical model which may describe the coupled in-plane motion of an axially accelerating beam. The Extended Hamilton's Principle was utilized to derive the partial differential equations governing the motion of the simply supported beam. The set of the ordinary differential equations were approximated by means of the Assumed Mode Method (AMM). The derived elastodynamic model took into account the geometric non-linearity and the coupling between the transverse and longitudinal vibrations. The developed equations were solved numerically using the Runge-Kutta method and the obtained results were presented in terms of the vibrational response graphs and the corresponding phase-plane portraits. The system dynamic characteristics were explored with a major focus on the influence of the velocity, acceleration and force magnitude on the natural frequency and vibrations amplitude at different modes of vibrations. The obtained results showed that the transverse natural frequency decreased significantly at the specified range of the imposed axial velocity. Also it was found that the axial velocity has a minimal influence on the longitudinal natural frequency.