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Alternative Analytical Mean-Square Calculations for Dynamic Systems Subject to Random Inputs


 Output variables of linear dynamic systems subject to random inputs are often quantified by mean square calculations. Computationally, these involve integration of the frequency response magnitude squared over all frequency. Numerically, this is an easy task and analytically, methods exist to find mean square values as functions of transfer function (frequency response) coefficients. This paper develops further analytical techniques to calculate mean-square values as functions of system pole-zero locations and as functions of eigenproperties and system matrices. These other analytical representations may provide paths to further insight into dynamic system response and optimal design/tuning of dynamic systems.