MOMENTS OF AN UNCERTAIN LINEAR-OSCILLATOR - ERRORS DUE TO TIME-DISCRETIZED APPROXIMATIONS TO WHITE-NOISE EXCITATION

Several first- and second-order moments are studied for an underdamped single-degree-of-freedom linear oscillator with arbitrarily large stiffness uncertainty. General analytical relations for the moments are found and numerically integrated in a time-discretized framework when the excitation is either mean-zero Gaussian white noise, or one of two discretized approximations to white noise: a stepwise constant load or a discrete impulse load (band-limited white noise). Several aspects of moment computation are addressed. The include: the effect of oscillator uncertainty on the range of step sizes over which either discretized load model approximates white noise; the relative convergence rates of the moments computed using the discretized load models to the true moments; and the behaviour of the approximate moments within each step. This latter topic is enlightening since the manner in which step-to-step error accumulation occurs becomes clear.