^{1,2}and Pol. D. Spanos

^{3}

^{1}Department of Mechanical Engineering, Rice University, USA

^{2}School of Manufacturing Science and Engineering, Sichuan University, China

^{3}Ryon Chair in Engineering, Rice University, USA

Nonlinear vibrations due to combined deterministic and stochastic loadsare investigated through a novellinearization scheme. The steady-statemotion is expressed as a sum of an ensemblemean (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.