Dynamic behaviour of a beam subjected to a force of time-dependent frequency

Abstract

It is a well-known fact that, for an ideal system in which damping is ignored, the deflection of a beam becomes infinite for the case where the constant frequency of a steady-state external force is equal to the critical frequency of the beam. In this paper, the external force is assumed to be proportional to sin( at 2 2 + bt 3 3 ) with respect to time, where a and b are constants, and the effect of time-dependent frequency on the dynamic behaviour of the beam is investigated. Integrations involved in the theoretical results are carried out by Simpson's rule. From the results of the theoretical analysis, it is evident that the maximum values of the dynamic deflection are much affected by the time-dependence of the frequency of the external force when it passes through the critical frequency, increasing or decreasing.