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On the simulation technique of stochastic processes and nonlinear vibrations

In this paper the procedure and program for simulation of stochastic processes are represented. The program is applied to nonlinear mechanical systems subjected to stochastic stationary excitation. The results obtained are compared with the ones from other methods which are used for estimating the exactitude of simulation technique. | Journal of Mechanics, NCNST of Vietnam T. XVI, 1994, No 3 (23 - 31) ON THE SIMULATION TECHNIQUE OF STOCHASTIC PROCESSES AND NONLINEAR VIBRATIONS NGUYEN CAO MENH, TRAN DUONG TRI Institute of Mechanics, Hanoi SUMMARY. In this paper the procedure and program for simulation of stochastic processes are represented. The program is applied to nonlinear mechanical systems subjected to stochastic stationary excitation. The results obtained are compared with the ones from other methods which are used for estimating the exactitude of simulation technique. §1. INTRODUCTION The investigation of random vibration of non-linear dynamical systems is usually carried out by some following methods: the method of Fokker-Planck-Kolmogorov equation(FPK) gives equations for the probability density function of solutions of the systems, which are excited directly or indirectly by white noises. In proper cases it is possible to find stationary solutions of FPK equation. Therefore, it is diffieult to apply this method to general dynamical systems [3]. The statistiCal linearization method is widely used for nonlinear dynamical system but at greater nonlin~arity tht; exactitude of this method is worse [3, 4]. The perturbation method is also used widely but in practice it is able to find solution in the first approximation order [1, 3, 4, 6]. In order to overcome above-mentioned difficulties for more general dynamic systems it is necessary to use numerical method for siiuulation of stochastic p~ocesses and looking for solutions of nonlinear stochastic systems. The main difficulties of the method are to create a reliable computer program for obtaining quite exact results. In this paPer the justification. and procedure of simulation: of stochastic processes are repre.sented. This is 'the basis of creating the program for simulation and solving random differential equation. §2. SIMULATION OF A STOCHASTIC PROCESS 2.1. Simulation formula Suppose that {x(t)} is a stationary Gaussian stochastic .