The Maximum Response of a Linear Mechanical Oscillator to Stationary and Nonstationary Random Excitation

This report considers the peak response behavior of a mass excited, linear mechanical oscillator when the applied random excitation is either stationary or nonstationary. The stationary random excitation is Gaussian bandwidth limited white noise and the nonstationary random excitation is Gaussian bandwidth limited white noise shaped in time by (1) a rectangular envelope function or (2) a half-sine envelope function. Thus, the nonstationary excitation appears as a pulse of white noise shaped as either a rectangle or a half-sine. Using data from an analog computer study, two topics are explored in detail. (1) the expected maximum peak response in a finite time interval for a specified probability of occurrence; and (2) a measure of the time duration for the oscillator to achieve stationarity in its response. The peak response is expressed as parametric, dimensionless plots of the peak rms response ratio and a dimensionless time parameter. In this form, the oscillator response to stationary white noise and to the pulsed random excitation can be conveniently compared and can be used to estimate directly the time duration for an oscillator to achieve stationarity in its response. It is found that for values of the dimensionless time parameter greater than about one, the stationary results can be applied to conservatively predict the oscillator peak response to the pulsed excitation. For both stationary and non stationary excitations, the peak behavior is noted to be dependent on the oscillator damping for a small number of response cycles. As the number of response cycles becomes large, the peak to rms response behavior tends to become independent of damping.