Stationary response of colored noise excited vibro-impact system* *Project supported by the National Natural Science Foundation of China (Grant No. 11772149), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, China (Grant No. MCMS-I-19G01), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

Abstract

The generalized cell mapping (GCM) method is used to obtain the stationary response of a single-degree-of-freedom. Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, the stochastic averaging method is also presented. Both of the two methods are tested through concrete examples and verified by the direct numerical simulation. It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band, while the stochastic averaging method is valid only for the wide-band noise.