Dynamic Analysis of a Free-Free Beam

Abstract

The dynamic problem of a free-free beam with lumped masses distributed along the beam is researched. Effects of magnitude and position of lumped masses on bending mode and natural frequency of a free-free beam is studied. Method of lumped masses proposed in this paper is used to determine dynamic bending curves and natural frequencies. Least square method is used to give function fitting of the bending curves. The dynamic equations of a free-free beam are established by Lagrange method. Numerical simulation for dynamic response of the beam is carried out by MATLAB. The simulation results show that an impulsive load applied on the center of mass of the beam will result in small bending stress. However, a given larger impulsive load acting on one end or two ends of the beam will cause larger bending stress and plastic deformation at a cross-section and result in final failure.