ANALYSIS OF THE RESPONSE OF A NONLINEAR DIFFERENTIAL EQUATION TO WHITE RANDOM EXCITATION

摘要

The response of the nonlinear equation to white noise excitation is determined experimentally for three values of € and three noise levels associated with each value of €. The response data is presented in terms of power spectral density, cumulative probability distribution, and phase plane trajectories. A high speed analog computer with a Gaussian white noise input was used to simulate the randomly forced equation. Ensembles of 7 ten second computer samples were recorded on magnetic tape;each sample contained the equivalent of 410 minutes of real-time data. Nine such ensembles were recorded (one ensemble for each € and noise setting). The power spectral density analysis of the data was made with a heterodyne wave analyzer and the results are presented in graphical and tabular form. The mean power spectral density is plotted and the standard deviation of the ensemble is calculated at each frequency of measurement as an indication of the statistical uncertainty.