Determination of natural responses of mechanical systems using correlation techniques

The natural responses of linear systems may be found by observation of the system's response to a known stimulus. In such tests, the observations required ore the response as a function of time when the stimulus is deterministic in form. In practical situations, the application of this method is often hampered by the presence in the response of extraneous noise and the necessity of using large-amplitude excitations. The difficulties of the method outlined may be avoided by using random stimuli and cross correlations to obtain a statistical estimate of the natural modes. This paper describes one application in which the critical speeds and relative deflection amplitudes of a machine shaft-rotor system were found with the system either stationary or running at some arbitrary speed.