FASTER SIMULATION METHODS FOR THE NONSTATIONARY RANDOM VIBRATIONS OF NONLINEAR MDOF SYSTEMS

In this paper semi-analytical forward-difference Monte Carlo simulatio n procedures are proposed for the determination of the lower order sta tistics and the Joint Probability Density Function (JPDF) of the stoch astic response of geometrically nonlinear multi-degree-of-freedom stru ctural systems subject to nonstationary Gaussian white noise excitatio n, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gauss ianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. All of the proposed proced ures yield the exact results as the time step goes to zero. The propos ed procedures are based on analytical convolutions of the excitation p rocess, hereby, reducing the generation of stochastic processes and nu merical integration to the generation of random vectors only. Such a t reatment offers higher rates of convergence, faster speed and higher a ccuracy. These procedures are compared to the direct Monte Carlo simul ation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The comparisons show that the so-called Ermark-Allen alg orithm developed for simulation applications in molecular dynamics is the most favourable procedure for MDOF structural systems.