A New Method for Accounting for Dynamic Stiffening/Softening Effect of Flexible Beams in Dynamics Modeling
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摘要: 提出柔性梁的动力刚化/软化效应的本质是柔性梁的大范围运动所导致的梁内轴向力对于梁的横向弹性振动所产生的影响效应。给出了柔性梁动力学建模中计入动力刚化/软化效应的一种新方法:通过考虑大范围运动所导致的梁内轴向力对于梁的横向弹性振动所产生的影响,来达到动力学建模中计入柔性梁动力刚化/软化效应的目的。这种方法同目前已有的计入柔性梁动力刚化/软化效应的方法相比,具有直观、简单、物理概念清晰和符号运算简便的优点。通过对一旋转柔性梁的横向弹性振动的动力学建模和计算为例,具体演示了如何应用本文的方法计入柔性梁的动力刚化效应,同时也说明了本文方法在应用实施上的便捷性。最后,将本文的计算结果同相关文献的对应结果相比较,验证了本文方法的正确性。Abstract: The essence of the dynamic stiffening/softening effect of flexible beams is the influence of the axial internal force caused by the large overall motion on the transverse vibration of the beams. A new method for accounting for the effect is presented. The central idea of this method is that the dynamic stiffening/softening effect of flexible beams is accounted for in the dynamic model by taking into consideration the influence of the axial internal force on the transverse vibration of the beams. Compared with other methods for accounting for the dynamic stiffening/softening effect of flexible beams, this method is more intuitive, clearer in physical concept, and simpler in symbol operation. A flexible beam clamped to a rotating rigid hub is taken as an example to show how to use the method to account for the dynamic stiffening effect of the beam. The dynamic modeling and numerical simulation of the beam confirm the validity and simplicity of the method.
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Key words:
- flexible beam /
- dynamic stiffening/softening effect /
- axial internal force /
- vibration
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[1] Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base[J]. Journal of Guidance, Control, and Dynamics, 1987,10(2):139-151 [2] Mayo J, Domínguez J, Shabana A A. Geometrically nonlinear formulations of beams in flexible multibody dynamics[J]. Journal of Vibration and Acoustics, 1995,117(4):501-509 [3] Mayo J, García-Vallejo D, Dom? nguez J. Study of the geometric stiffening effect:comparison of different formulations[J]. Multibody System Dynamics, 2004,11(4):321-341 [4] Mayo J, Domínguez J. A finite element geometrically nonlinear dynamic formulation of flexible multibody systems using a new displacements representation[J]. Journal of Vibration and Acoustics, 1997,119(4):573-581 [5] Lugrís U, Naya M A, Pérez J A, et al. Implementation and efficiency of two geometric stiffening approaches[J]. Multibody System Dynamics, 2008,20(2):147-161 [6] Cai G P, Lim C W. Dynamics studies of a flexible hub-beam system with significant damping effect[J]. Journal of Sound and Vibration, 2008,318(1-2):1-17 [7] 吴胜宝,章定国,康新.刚体-微梁系统的动力学特性[J].机械工程学报,2010,46(3):76-82 Wu S B, Zhang D G, Kang X. Dynamic properties of hub-microbeam system[J]. Journal of Mechanical Engineering, 2010,46(3):76-82(in Chinese) [8] 郑彤,章定国,廖连芳,等.航空发动机叶片刚柔耦合动力学分析[J].机械工程学报,2014,50(23):42-49 Zheng T, Zhang D G, Liao L F, et al. Rigid-flexible coupling dynamic analysis of aero-engine blades[J]. Journal of Mechanical Engineering, 2014,50(23):42-49(in Chinese) [9] Wu S C, Haug E J. Geometric non-linear substructuring for dynamics of flexible mechanical systems[J]. International Journal on Numerical Methods in Engineering, 1988,26(10):2211-2226 [10] Liu A Q, Liew K M. Non-linear substructure approach for dynamic analysis of rigid-flexible multibody systems[J]. Computers Methods in Applied Mechanics and Engineering, 1994,114(3-4):379-396 [11] Shabana A A. computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics[J]. Nonlinear Dynamics, 1998,16(3):293-306 [12] Kwon S, Chung J, Yoo H H. Structural dynamic modeling and stability of a rotating blade under gravitational force[J]. Journal of Sound and Vibration, 2013,332(11):2688-2700 [13] Li Q, Wang T S, Ma X R. A note on the foreshortening effect of a flexible beam under oblique excitation[J]. Multibody System Dynamics, 2010,23(2):209-225 [14] Gerstmayr J, Sugiyama H, Mikkola A. Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems[J]. Journal of Computational and Nonlinear Dynamics, 2013,8(3):031016 [15] Xiao S F, Chen B. Dynamic Characteristic and stability analysis of a beam mounted on a moving rigid body[J]. Archive of Applied Mechanics, 2005,74(5-6):415-426 [16] 方建士,章定国.旋转内接悬臂梁的刚柔耦合动力学特性分析[J].物理学报,2013,62(4):044501 Fang J S, Zhang D G. Analyses of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam[J]. Acta Physica Sinica, 2013,62(4):044501(in Chinese) [17] Magrab E B. Vibrations of elastic systems[M]. New York:Springer, 2012 [18] 倪振华.振动力学[M].西安:西安交通大学出版社,1989 Ni Z H. Mechanics of vibration[M]. Xi'an:Xi'an Jiaotong University Press, 1989(in Chinese)
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