ELASTODYNAMIC MODELING AND SIMULATION OF AN AXIALLY ACCELERATING BEAM

摘要

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 a simply supported beam. The set of the ordinary differential equations were obtained by means of the assumed mode method. The derived elastodynamic model took into account the geometric non-linearity, the time-dependent axial velocity 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 system natural frequencies. The system dynamic characteristics were explored with a major focus on the influence of the velocity, acceleration and the excitation force frequency. The obtained results showed that the natural frequency decreased significantly at high axial velocities. Also it was found that the system may exhibit unstable behavior at high accelerations.