TY - JOUR

T1 - Simulation of a random differential equation

AU - Rehak, M.

AU - Benaroya, H.

N1 - Funding Information:
This document was prepared under the sponsorship of the Air Force Office of Scientific Research (AFOSC) under Contract F49620-84-C-0009. Dr. A. Amos of the Air Force Office of Scientific Research is sincerely thanked for financial support, as well as for his enthusiastic encouragement of this continuing effort. Neither the U.S. Government nor any person acting on behalf of the U.S. Government assumes any liability from the use of the information contained in this document.

PY - 1988/3

Y1 - 1988/3

N2 - The problem considered is that of a second-order differential equation with stochastic parameters. Time-dependent random coefficients may assume both positive and negative values when modeling parametric excitations. As there is no exact solution in the case of colored noise random coefficients, one must use approximate techniques. We presently investigate an iterative procedure. The quality of this approximation to the exact solution is verified with a Monte Carlo simulation. The particular example considered is that of a harmonic oscillator with a time-dependent random stiffness and excited by an external random forcing function. After a brief review of the iterative method, and an outline of the design of the Monte Carlo simulation, an extensive parametric study is presented to establish ranges of parameter values for which the approximation is valid. This comparison study leads to a design criterion for the mathematical modeling of structures with parametric uncertainties. We are interested in using information from studies such as this to understand the behavior of large-scale structures.

AB - The problem considered is that of a second-order differential equation with stochastic parameters. Time-dependent random coefficients may assume both positive and negative values when modeling parametric excitations. As there is no exact solution in the case of colored noise random coefficients, one must use approximate techniques. We presently investigate an iterative procedure. The quality of this approximation to the exact solution is verified with a Monte Carlo simulation. The particular example considered is that of a harmonic oscillator with a time-dependent random stiffness and excited by an external random forcing function. After a brief review of the iterative method, and an outline of the design of the Monte Carlo simulation, an extensive parametric study is presented to establish ranges of parameter values for which the approximation is valid. This comparison study leads to a design criterion for the mathematical modeling of structures with parametric uncertainties. We are interested in using information from studies such as this to understand the behavior of large-scale structures.

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U2 - 10.2514/3.20288

DO - 10.2514/3.20288

M3 - Article

AN - SCOPUS:0023966997

SN - 0731-5090

VL - 11

SP - 173

EP - 178

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

IS - 2

ER -