Random vibration frequency response analysis of nonlinear systems based on volterra series

Volterra series is a powerful mathematical tool fornonlinear system analysis, which is essentially an extension of theconvolution operation from linear systems to nonlinear systems. In thisstudy, based on the Volterra series, an analytical expression is derived tocalculate the power spectrum density (PSD) for the output of nonlinearsystems subjected to Gaussian white noise excitation. This expressionreveals that the PSD of the nonlinear system can be expressed as polynomialfunction of the input intensity. This expression provides an efficient wayto study the effect of the input intensity of a Gaussian white noiseexcitation on the PSD of nonlinear system output.