| Citation: | JIN Xiaoling, WANG Yong, HUANG Zhilong. Response and stability of multi-degree-of-freedom nonlinear stochastic systems[J]. Advances in Mechanics, 2013, 43(1): 56-62. doi: 10.6052/1000-0992-12-026
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The response prediction and stability analysis are always hot topics of research in stochastic dynamics. Developing the method for response prediction of nonlinear stochastic systems and determining the qualitative behavior of the system response are of important significance and extensive application potential. This paper reviews response and stability of multi-degree-of-freedom nonlinear stochastic systems. Firstly, main methods for the response prediction of stochastic systems are outlined, such as Fokker-Planck-Kolmogorov equation, stochastic averaging method, equivalent linearization, equivalent nonlinear system procedure and Monte Carlo simulation. The advantages and disadvantages of these methods are discussed, respectively. The state-of-the-art of the exact stationary solutions and approximately nonstationary solutions is also illustrated for the multi-degree-of-freedom nonlinear stochastic systems. Then, two effective procedures to evaluate the stochastic stability, i.e., the Lyapunov function and Lyapunov exponent, are briefly presented. Based on these two methods, the stochastic stability of multi-degree-of-freedom nonlinear stochastic systems is outlined. Finally, some suggestions are given for further research on the response and stability of nonlinear stochastic systems.
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