Vibration analysis of axially deploying cantilever beam based on ANCF with length-varying beam element

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (3) : 186-191.

WANG Zhongmin,WU Liguo

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Abstract

A deploying cantilever beam system has rigid body motion and large deformation motion, so its vibration problem is time-varying and rigid-flexible coupled nonlinear dynamic one.Here, the absolute node coordinates formulation (ANCF) proposed by Shabana was adopted to establish a length-varying Euler-Bernoulli beam element model.Starting from the accurate curvature under the condition of large deformation and Green-Lagrangian normal strain, based on the virtual work principle considering inertia force, nonlinear dynamic equations of a beam element, and those of a deploying cantilever beam system after element-assembling were derived.Finally, the effects of material characteristic parameters including elastic modulus and mass density and deploying laws including constant speed deploying and constant acceleration one on nonlinear deflection response at free end of the deploying cantilever beam system were analyzed through numerical examples.

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WANG Zhongmin,WU Liguo. Vibration analysis of axially deploying cantilever beam based on ANCF with length-varying beam element[J]. Journal of Vibration and Shock, 2019, 38(3): 186-191

References

1. Sivakumar S K. Tadikonda and Haim Baruh. Dynamics and control of a translating flexible beam with a prismatic joint[J]. Journal of Dynamic Systems, Measurement, and Control, 1992, 114(3):422-427.
2. Stylianou M, Tabarrok B. Finite element analysis of an axially moving beam, Part I: Time integration[J]. Journal of Sound and Vibration, 1994,178(4):433-453.
3. Stylianou M, Tabarrok B. Finite element analysis of an axially moving beam, Part II: Stability analysis[J]. Journal of Sound and Vibration, 1994,178(4):455-481.
4. Al-Bedoor B O, Khulief Y A. Finite element dynamic modeling of a translating and rotating flexible link[J]. Computer Methods in Applied Mechanics & Engineering, 1996, 131(1-2):173-189.
5. Piovan M T, Sampaio R. Vibrations of axially moving flexible beams made of functionally graded materials[J]. Thin-Walled Structures, 2008, 46(2):112-121.
6. Rogers K S, Ferguson N S, Perryman A A, et al. Modelling axially moving beams of varying length using the finite element method[C]. 7th Euromech Solid Mechanics Conference, 2009: 7-11.
7. Wang L H, Hu Z D, Zhong Z, et al. Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length[J]. Acta Mechanica, 2010, 214(3):225-244.
8. Chang J R, Lin W J, Huang C J, et al. Vibration and stability of an axially moving Rayleigh beam[J]. Applied Mathematical Modelling, 2010, 34(6):1482-1497.
9. 罗炳华, 高跃飞, 刘荣华，等. 轴向运动梁受移动载荷作用的横向动力响应[J]. 振动与冲击, 2011, 30(12): 59- 63. LUO Bing-hua, GAO Yue-fei, LIU Rong-hua, et al. Lateral dynamic response of an axially moving beam under a moving load[J]. Journal of Vibration and Shock, 2011, 30(12): 59- 63.
10. Downer J D, Park K C. Formulation and solution of inverse spaghetti problem: application to beam deployment dynamics[J]. Aiaa Journal, 2012, 31(2):339- 347.
11. Park S, Hong H Y, Chung J. Vibrations of an axially moving beam with deployment or retraction[J]. AIAA Journal, 2013, 51(51):686-696.
12. Yang X D, Liu M, Zhang W, Roderick V N Melnik. Invariant and energy analysis of an axially retracting beam[J]. Chinese Journal of Aeronautics, 2016, 29(4): 952–961.
13. 赵亮，胡振东. 轴向运动功能梯度悬臂梁动力学分析[J]. 振动与冲击，2016, 35 (2): 124-128. ZHAO Liang，HU Zhen-dong. Dynamic analysis of an axially translating functionally graded cantilever beam[J]. Journal of Vibration and Shock, 2016, 35 (2): 124-128.
14. 杨鑫，陈海波. 热冲击作用下轴向运动梁的振动特性研究[J]. 振动与冲击，2017, 36 (1): 8-15. YANG Xin，CHEN Hai-bo. Vibration characteristics of an axially moving beam under thermal shocks[J]. Journal of Vibration and Shock, 2017, 36 (1): 8-15.
15. 谭霞, 丁虎, 陈立群. 超临界轴向运动Timoshenko梁横向受迫振动[J]. 振动与冲击, 2017, 36 (22): 1-5. TAN Xia，DING Hu，CHEN Li-qun. Transverse forced vibration of an axially moving Timoshenko beam at a supercritical speed[J]. Journal of Vibration and Shock, 2017, 36 (22): 1-5.
16. Shabana A A. Definition of the slopes and the finite element absolute nodal coordinate formulation[J]. Multibody System Dynamics, 1997, 1(3): 339-348.