Application of complex stochastic averaging to non-linear random vibration problems |
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| Affiliation: | 1. Purdue University, USA;2. Mitsubishi Electric Research Labs, Cambridge, MA, USA;3. Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Hungary;1. Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, Tianjin University of Technology, Tianjin 300384, PR China;2. National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, PR China;3. College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, PR China;4. School of Science, Tianjin Chengjian University, Tianjin 300384, PR China;1. Aerospace and Mechanical Engineering Department, University of Arizona, Tucson, AZ 85721, United States;2. Laboratoire de Mécanique et d''Acoustique, CNRS, Marseille 13453, France |
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| Abstract: | The stochastic averaging procedure in a complex-variable setting, used previously by Ariaratnam and Tarn to analyze a linear system under random parametric excitation, is extended to non-linear systems under both parametric and external random excitations. It is shown that equations for the moments of the system response, while still constituting an infinite hierarchy, form a simpler pattern compared with the corresponding equations obtained from the usual amplitude and phase formulation. From this simpler pattern, it is possible to identify those moments which tend to zero at the stationary state. Furthermore, a much smaller number of equations needs to be solved when the infinite hierarchy is truncated to calculate approximately the non-zero moments. |
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