Dynamic stability of pre-twisted beams with non-constant spin rates under axial random forces |
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| Institution: | 1. Department of Automatic Testing and Control, Harbin Institute of Technology, Harbin 150001, China;2. Department of Management and Information Systems, Prefectural University of Hiroshima, 1-1-71 Ujina-Higashi, Minami-ku, Hiroshima 734-8558, Japan;1. School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;2. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong;3. City University of Hong Kong Shenzhen Research Institute Building, Shenzhen Hi-Tech Industrial Park, Nanshan District, Shenzhen, China;4. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China;1. Univ. Bordeaux, Bordeaux INP, CNRS, IMS, UMR 5218, 33405 Talence, France;2. CNRS, GIPSA-lab, UMR 5216, F-38402 Saint Martin D’Hères, France |
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| Abstract: | This paper investigates the dynamic stability of a pre-twisted cantilever beam spinning along its longitudinal axis with a periodically varying speed and acted upon by an axial random force at the free end. The spin rate of the beam is characterized as a small periodic perturbation superimposed on a constant speed, and the axial force is assumed as the sum of a static force and a weakly stationary random process with a zero mean. Both the periodically varying spin rate and the axial random force may lead to parametric instability of the beam. In this work, the finite element method is applied first to get rid of the dependence on the spatial coordinate. The method of stochastic averaging is then adopted to obtain Ito’s equations for the system response under different resonant frequency combinations. Finally, the first-moment and the second-moment stability conditions of the beam are derived explicitly. Numerical results are presented for a simple harmonic speed perturbation and a Gaussian white noise axial force. |
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