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Vol. 5, Special Issue, March 2009, pp.53-68





A Study on Dynamic Stiffening of a Rotating Beam with a Tip Mass


1Shengjian BAI, 2Pinhas BEN-TZVI, 1Qingkun ZHOU, 1Xinsheng HUANG

1 College of Mechatronics Engineering and Automation, National University of Defense Technology,

Changsha Hunan 410073, P. R. China

2 Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science,

The George Washington University, 801 22nd St., NW, Washington, DC 20052

Tel.: (202) 994-6149

E-mail: zqkhome@gmail.com, bentzvi@gwu.edu



Received: 29 January 2009   /Accepted: 23 February 2009   /Published: 23 March 2009


Abstract: This paper presents a dynamic model of a rotating beam with a tip mass undergoing large angle, high speed maneuvering. This type of model may also be useful in modeling, analysis and development of various inertial sensors and transducers with similar operating principles. With the consideration of the second-order term of the coupling deformation field, the complete first-order approximated model (CFOAM) of a flexible spacecraft system is developed by using assumed mode method (AMM) and Lagrangian principle. A first-order approximated model (FOAM) is obtained by neglecting the high order terms of the generalized coordinates in CFOAM. A lower order simplified first-order approximated model (SFOAM) is derived by deleting the terms related to the axial deformation. Numerical simulations and theoretical analysis show that: (i) the second-order term has a significant effect on the dynamic characteristics of the system and the dynamic stiffening is accounted for, while the traditional linear approximated model (TLAM) presents invalid simulation results; (ii) the end mass has a ‘stiffening’ effect on the flexible system in FOAM, but a ‘softening’ effect in TLAM; and (iii) the SFOAM describes the dynamic behavior well and can be used for controller design.


Keywords: Flexible structure, Dynamic stiffening, Assumed mode method, Flexible beam


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