# Response of a Stochastic Linear System

*by*Janusz Szopa, Inst. of Theoretical Mechanics, Dept. of Mathematics and Physics, Silesian Technical Univ., Gliwice, Poland,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1981, Vol. 107, Issue 1, Pg. 1-11

**Document Type:**Journal Paper

**Abstract:**

A method is presented for determining the covariance function of response of a stochastic linear system in which coefficients and excitation are stochastic processes. Such a system is described by differential equations whose solution was searched for by means of perturbation method confined to the first approximation. These equations were converted into stochastic, integral Volterra equations of the second kind. Both the formula for covariance function of solution of the considered equation and the formula for the function of central moments of rth order of solution were calculated. The suggested method was verified numerically by computing the variance of response of a dynamical system with random variable mass for two types of stochastic excitations.

**Subject Headings:**Stochastic processes | Linear functions | Approximation methods | Excitation (physics) | Verification | Differential equations | Integral equations | Integrals

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