Study on Motion Stability of Variable CrossSection Flexible Beams
 Based on the Absolute Nodal Coordinate Formulation

doi:10.16183/j.cnki.jsjtu.2017.10.004

Abstract

Abstract: The boundary features of the variable crosssection beams are taken into consideration and the stiffness matrix is derived based on the nonlinear continuum mechanics. A dynamic model of the beam is established by using the absolute nodal coordinate formulation. The statespace equation of the beam during motion is developed. Based on the Lyapunov theory a criterion of the motion stability of the flexible beams is proposed, and the effects of material properties and variable crosssections are investigated. The results indicate that with a small elastic modulus, the variable crosssection beam shows a better stability than the constant crosssection beam. As the elastic modulus increases, the stability of the constant crosssection becomes better than that of the variable crosssection beam. When the elastic modulus reaches a certain value, the motion of constant crosssection beam becomes stable.

Key words: variable crosssection beams; large deformation; kinematic stability; Lyapunov theory

CLC Number:

TH 113.2

LUO Jingjinga,YU Haidonga,ZHAO Chunzhanga,b,WANG Haoa,b. Study on Motion Stability of Variable CrossSection Flexible Beams
Based on the Absolute Nodal Coordinate Formulation[J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1174-1180.

References

［1］SHABANA A A. Flexible multibody dynamics: Review of past and recent developments［J］. Multibody System Dynamics, 1997, 1(2): 189222.
［2］OMAR M A, SHABANA A A. A twodimensional shear deformable beam for large rotation and deformation problems［J］. Journal of Sound and Vibration, 2001, 243(3): 565576.
［3］SHABANA A A, YAKOUB R Y. Three dimensional absolute nodal coordinate formulation for beam elements: Theory［J］. Journal of Mechanical Design, ASME, 2001, 123(4): 606613.
［4］赵春璋, 余海东, 王皓, 等. 基于绝对节点坐标法的变截面梁动力学建模与运动变形分析［J］. 机械工程学报, 2014, 50(17): 3845.
ZHAO Chunzhang, YU Haidong, WANG Hao, et al. Dynamic modeling and kinematic behavior of variable crosssection beam based on the absolute nodal coordinate formulation［J］. Journal of Mechanical Engineering, 2014, 50(17): 3845.
［5］ZHAO Chunzhang, YU Haidong, LIN Zhangqin, et al. Dynamic model and behavior of viscoelastic beam based on the absolute nodal coordinate formulation［J］. Proceedings of the Institution of Mechanical Engineers. Part K: Journal of MultiBody Dynamics, 2014, 229(1): 8496.
［6］李彬, 刘锦阳. 大变形柔性梁系统的绝对坐标方法［J］.上海交通大学学报, 2005, 39(5): 827831.
LI Bin, LIU Jinyang. Application of absolute nodal coordination formulation in flexible beams with large deformation［J］. Journal of Shanghai Jiao Tong University, 2005, 39(5): 827831.
［7］刘铖, 田强, 胡海岩. 基于绝对节点坐标的多柔体系统动力学高效计算方法［J］. 力学学报, 2010, 42(6): 11971205.
LIU Cheng, TIAN Qiang, HU Haiyan. Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate［J］. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(6): 11971205.
［8］SHEN Z, LI P, LIU C, et al. A finite element beam model including crosssection distortion in the absolute nodal coordinate formulation［J］. Nonlinear Dynamics, 2014, 77(3): 10191033.
［9］ORZECHOWSKI G, SHABANA A A. Analysis of warping deformation modes using higher order ANCF beam element［J］. Journal of Sound and Vibration, 2016, 363: 428445.
［10］李俊峰, 王照林. 航天器柔性伸展附件非线性振动稳定性研究［J］.宇航学报, 1998, 19(3): 9396.
LI Junfeng, WANG Zhaolin. Study on the stability of nonlinear vibrations of a deploying flexible appendage of a spacecraft［J］. Journal of Astronautics, 1998, 19(3): 9396.
［11］李凤明, 王日新, 汪越胜, 等. 柔性压电梁结构运动稳定性分析［C］∥2006年压电声波和设备应用研讨会论文集. 新加坡: 世界科学出版社, 2007: 2630.
［12］刘屿, 黄浩维, 邬依林, 等. 基于Lyapunov直接法的柔性梁振动控制［J］.华南理工大学学报(自然科学版), 2013, 41(2): 2430.
LIU Yu, HUANG Haowei, WU Yilin, et al. Vibration control of lexible beam based on Lyapunov direct method［J］. Journal of South China University of Technology (Natural Science Edition), 2013, 41(2): 2430.
［13］刘延柱. 高等动力学［M］. 北京: 高等教育出版社, 2001: 7982.
［14］张凯之. 盾构机冗余驱动回转系统动态特性研究［D］.上海: 上海交通大学机械与动力工程学院, 2011.

[1]	ZHAO Ziren1, DU Shichang1, HUANG Delin1, REN Fei2, LIANG Xinguang2. Modelling and Bottleneck Analysis of Product Quality in Transient Phase#br# of MultiStage Manufacturing Systems Based on Markovian Chains [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1166-1173.
[2]	ZHOU Penghui, MA Hongzhan, CHEN Dongping, CHEN Mengyue, CHU Xuening. Identification of Product Redesign Modules Based on#br# Fuzzy Random Failure Mode and Effects Analysis [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1189-1195.
[3]	LI Changxi1, 2, ZHOU Yan1, LIN Han3, LI Lingzhi1, GUO Ge1. TemporalSpatial Sequential Fusion Recognition Method of#br# Ballistic Missile Target Based on MIMOFNN Model [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1138-.
[4]	FENG Mingyue, HE Minghao, HAN Jun, YU Chunlai. High Resolution Direction of Arrival Estimation Based on#br# Covariance Fitting Estimation of Signal Parameters by#br# Rotational Invariance Technique Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1145-.
[5]	?YANG Ping1,SHENG Jie1,WANG Yucheng2,LI Zhuyong1,JIN Zhijian1,HONG Zhiyong1. Quench Propagation Characteristics Influenced by NonUniform Properties of YBa2Cu3O7δ High Temperature Superconducting Tape [J]. Journal of Shanghai Jiaotong University, 2017, 51(9): 1090-1096.
[6]	WANG Xing, ZHOU Yipeng, TIAN Yuanrong, CHEN You, ZHOU Dongqing, HE Jiyuan. Sparse Decomposition for Frequency Modulation Radar Signal Based on#br# Advanced Genetic Algorithm and SinChirplet Atom [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1124-1130.
[7]	ZHANG Liangjun1, 2, LI Xiaoci1, WU Jingyi1, CAI Aifeng1. ThermalStructure Coupling Analysis of #br# Microgravity Environment Simulation Suspension Structure for #br# Large Space Deployable Mechanisms [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 954-961.
[8]	XIA Hailiang1, 2, LIU Yakun1, 2, LIU Quanzhen3, LIU Baoquan3, FU Zhengcai1, 2. Metal Ablation Affected by Electrode Shapes Under#br# Long Continuing Lightning Current [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 903-908.
[9]	GU Jiayang, XIE Yulin, TAO Yanwu, HUANG Xianghong, WU Jie. Numerical Simulation and Experimental Study on VortexInduced#br# Motion of a New Type of Floating Drilling Production Storage Offloading [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 878-885.
[10]	LIN Da, ZHU Yijia, WEI Xiaodong, WANG Zhiyu, ZHANG Wugao. Combustion and Particle Emission Characteristics Affected by#br# Fuel Supply Parameters for a Diesel Engine Fuelled with#br# Polyoxymethylene Dimethyl Ethers/Diesel [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 787-795.
[11]	MENG Qingyang1, YAN Weiwu1, HU Yong1, CHENG Jianlin1, CHEN Shihe2, ZHANG Xi2. Model Identification Based on Subspace Model Identification of#br# Superheated Steam System in UltraSupercritical CoalFired Power Unit [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 672-678.
[12]	JIANG Huajuna, CAI Yana, b, LI Chaohaoa, LI Fanga, b, HUA Xueminga, b. Recognition Method for Gas Pores on XRay Image of Lap Joints#br# Based on the Improved Sobel Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 665-671.
[13]	DONG Guanhua,YIN Qin,YIN Guofu,XIANG Zhaowei. Identification and Modeling of Coupling Dynamic Stiffness in Joints of Machine Tool [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1263-1434.
[14]	XIE Qijiang,YU Haidong. Coupling Relationship Between Loads on Cutterhead of Tunnel Boring Machine and Contact Stiffness of Gripper Shoes and Rocks [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1269-1275.
[15]	ZHONG Jianlin1,MA Dawei1,REN Jie1,LI Shijun2,WANG Xu3. Static Compression Analysis of Rubber Hollow Cylinder Based on Plane Strain Assumption [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1276-1280.