Parametric random excitation. II: White-noise parameters

The results of a companion paper (1) are extended here for the case of white-noise parameters. The problem is that of a harmonic oscillator with random force. These random processes are assumed to be stationary and Gaussian. The cases considered are: (1) In the limit as the correlation functions approach a delta function and thus the processes have white spectra; (2) where an iterative method is applied to the white-noise case; and (3) where a noniterative, direct method is applied to the white-noise problem. It is shown that whitenoise results can be obtained directly from the previous analysis using a limiting procedure. In addition, an exact solution is obtained using iterative and noniterative methods. This permits a simple error analysis by comparing the results of a truncated series with those of the exact solution. Qualitatively, it is possible to say that the better the white-noise spectra approximates the physical processes, the more accurate will be the truncated solution of Ret. 1.