Random Vibration Of A Simple Oscillator Under Different Excitations

Many real engineering systems can be modelled adequately as single degree of freedom (SDOF) linear systems. Recently, the behaviour of such systems under random excitation has become the focus of considerable attention in their own right. The usefulness and applicability of random vibration of linear SDOF systems is discussed. The basic model we have considered in this paper is a single degree of freedom linear mass-spring-damper system, or oscillator. It is shown that in the deterministic situation, the fixed point at the origin is asymptotically stable. Our main purpose is to study the behaviour of the system under random excitation. Different stochastic specifications of the excitation are considered. It is shown that the system undergoes large fluctuations if the damping factor is small. If the system is critically damped, then the fluctuations are relatively small. In case of overdamping, the fluctuations are very small and the system is effectively deterministic. A comparative study of the results is presented through computer simulation.