Analysis Of Discrete Vibratory Systems With Parameter Uncertainties, Part II: Impulse Response

Abstract

This paper is a continuation of its companion (Part I) in which a new analytical method was proposed to estimate the first and second moments of eigenvalues for a linear time-invariant, proportionally damped, discrete vibratory system with uncertain parameters. In this part, the force amplitude is also considered as a random variable, but its time history is assumed to be deterministic. Based on certain simplifying assumptions and given probabilistic eigenvalue solutions, the first two moments of response in both modal and physical domains are estimated. First, an impulse excitation is considered and single- and two-degree-of-freedom system examples are used to illustrate the proposed method. Unlike the commonly used first order perturbation technique, our method does not include any secular terms. It is verified by comparing predictions with the benchmark Monte Carlo simulation. Second, a convolution integral formulation is developed for harmonic and other excitations. One example case is considered to illustrate and validate the proposed approach. Overall, our method overcomes the deficiencies of first order perturbation technique and is reasonably accurate and computationally inexpensive.