Forced Lateral Vibration of Beam Carrying a Concentrated Mass

Abstract

Abstract In this paper a study is made of the problem of the lateral vibration of a simply supported beam with a concentrated mass attached at its mid-point. A force assumed to act at the mass in a direction normal to the length of the beam is represented by a sinusoidally time-varying function. The homogeneous form of the Bernoulli-Euler beam equation is solved considering the problem as one with time-dependent boundary conditions. To represent an important case of forced vibrations the solution is transformed to give the deflection and bending strain caused by a pulse type of load. Curves are plotted whereby the contributions to deflection and strain from the higher modes of vibration may be examined as functions of the ratio of attached mass to mass of beam. Results of computations for a specific beam and set of masses are presented, as well as experimental results for the same beam with similar pulse-type loads applied. Oscillograms show rather trenchantly the slow transition of the mass-beam system toward a one-degree-of-freedom system as the concentrated mass is increased.