A linearization scheme for vibrations due to combined deterministic and stochastic loads

Abstract Nonlinear vibrations due to combined deterministic and stochastic loads are investigated through a novel linearization scheme. The steady-state motion is expressed as a sum of an ensemble mean (deterministic) part and a zero-mean stochastic part. Further, harmonic averaging is used to account for the mean response, while statistical linearization is used to determine the standard deviation of the random part. This solution scheme involves coupling of the two procedures since the elements of the linear system depend both on the standard deviation of the response, and on the amplitude of its periodic mean. Good agreement is observed, for several sets of parameter values, between the results derived by the proposed scheme and a suite of relevant Monte Carlo studies.