Dynamic analysis of a deployable/retractable damped cantilever beam
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2650-6
Dynamic analysis of a deployable/retractable damped cantilever beam∗ Ming LIU1 ,
Zhi LI2 , Xiaodong YANG3,† , Wei ZHANG3 ,
C. W. LIM4,5
1. Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China; 2. China Academy of Launch Vehicle Technology, Beijing 100076, China; 3. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China; 4. City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057, China; 5. Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong, China (Received Feb. 15, 2020 / Revised Jun. 4, 2020)
Abstract Deployable/retractable damped cantilever beams are a class of time-varying parametric structures which have attracted considerable research interest due to their many potential applications in the intelligent robot field and aerospace. In the present work, the dynamic characteristics of a deployable/retractable damped cantilever beam are investigated experimentally and theoretically. The time-varying damping, as a function of the beam length, is obtained by both the enveloped fitting method and the period decrement method. Furthermore, the governing equation of the deployable/retractable damped cantilever beam is derived by introducing the time-varying damping parameter, and the corresponding closed-form solution and vibration principles are investigated based on the averaged method. The theoretical predictions for transient dynamic responses are in good agreement with the experimental results. The dynamic mechanism analysis on time-varying damping offers flexible technology in mechanical and aerospace fields. Key words time-varying damping, vibration, experimental method, transient response, deployable/retractable damped cantilever beam Chinese Library Classification O321 2010 Mathematics Subject Classification
74H45
∗ Citation: LIU, M., LI, Z., YANG, X. D., ZHANG, W., and LIM, C. W. Dynamic analysis of a deployable/retractable damped cantilever beam. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2650-6 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (Nos. 11672007 and 11832002) and the Graduate Technological Innovation Project of Beijing Institute of Technology (No. 2017CX10037) ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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Ming LIU, Zhi LI, Xiaodong YANG, Wei ZHANG, and C. W. LIM
Introduction
The manipulation of axially deployable/retractable damped cantilever beams is of great importance for a broad range of applications from mechanical devices[1–5] for robot arms[6–7] to aerospace systems[8–11] for the deployment of appendages[12] , which are typical time-varying parametric structures wi
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