Dynamics of a nonlinear oscillator and a low-amplitude frequency-modulated wave |
| |
| Affiliation: | 1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China;3. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639798, Singapore;1. Acoustical and Mechanical Engineering Laboratory (LEAM), Universitat Politècnica de Catalunya (UPC), c/Colom, 11, 08222 Terrassa, Barcelona, Spain;2. Serra Húnter Fellow, Universitat Politècnica de Catalunya (UPC);1. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, PR China;2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China;3. Department of Mathematics, Swinburne University of Technology, Melbourne, VIC 3122, Australia;1. School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610000, China;2. Centre for New Energy Transition Research, Institute of Innovation, Science and Sustainability, Federation University Australia, Mount Helen, 3353 VIC, Australia;3. School of Mechanical and Power Engineering, Zhengzhou University, Zhengzhou 450000, China |
| |
| Abstract: | When the frequency of a small amplitude plane wave is varied slowly over a large enough bandwidth and this wave is incident upon a nonlinear oscillator, the resulting perturbed motion can exhibit stochastic behavior. Applications for the study of this system are wide and varied. We apply Lie-transform perturbation theory and mapping techniques in the analysis of the stochastic transition and the consequent induced diffusion in the oscillator phase space. A constant of the motion to the first order in a perturbation parameter is calculated, a mapping approximation is derived, and diffusion calculations from the mapping are given. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
