An Approach to Calculating Random Vibration Integrals

Abstract

Integrals required for the determination of the response statistics of an arbitrary order linear and time-invariant dynamic system under stationary excitation are examined. These integrals are found as the solution of a set of linear algebraic equations. The application of the derived general formula is exemplified by considering as excitation models white noise, band-limited white noise, and other important stationary random processes. Besides random vibration applications, the derived formula has purely mathematical merit and can be used for the calculation of complicated integrals encountered in a variety of other technical fields.