Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk |
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| Affiliation: | 1. School of Science, Northeastern University, Shenyang 110819, PR China;2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, PR China;3. Northeastern University at Qinhuangdao, Qinhuangdao 066004, PR China;4. Shenyang Ligong University, Shenyang 110168, PR China;5. Shenyang Institute of Engineering, Shenyang 110136, PR China;1. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, China;2. Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China;3. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada;1. College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing, 210016, China;2. School of Mechanical Engineering and Automation, Northeastern University, Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Shenyang, 110819, China |
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| Abstract: | The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated. The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately large shell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-plane displacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed with commercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed. Both a perturbation approach and a direct numerical technique are used. The perturbation method allows to obtain instability boundaries by means of elementary formulae; the numerical approach allows to perform a complete analysis of the linear and nonlinear response. |
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