考虑附加质量的中心刚体-柔性梁系统的动力学特性研究
|
摘要
对有附加质量的中心刚体-柔性梁系统的动力学特性进行了研究。柔性梁为等截面的Euler Bernoulli梁,针对柔性梁变形场使用假设模态法进行了离散,并运用第二类拉格朗日方程推导出系统的动力学方程后,采用Matlab编制了动力学仿真软件。首先讨论了附加质量对系统的固有频率与振型的影响,其次讨论了在大范围运动已知和未知的条件下,不同位置附加质量的中心刚体-柔性梁系统的刚柔耦合动力学特性,对带有附加质量的中心刚体-柔性梁系统的中心刚体转角、梁末端位移响应以及中心刚体角速度的仿真结果进行了分析。结果表明:附加质量从柔性梁固定端向自由端移动时,柔性梁前五阶固有频率近似地呈现周期性变化;附加质量所处位置的不同,对于系统的刚柔耦合动力学响应以及系统振型的影响十分明显。
The current research is focused on the study of the dynamic characteristics of a rigid body-flexible beam system with the added mass. The flexible beam is a uniform section of the Euler-Bernoulli beam. By using assumed mode method to disperse the deformation field of flexible beam and using Lagrange second kind equations to deduce the kinetic equations of the system, as well as using Matlab software to carry out the numerical simulation. Firstly, influence of the added mass on the natural frequency and vibration mode of the system is discussed. Secondly, in the large-scale movement of known and unknown conditions, the rigid-flexible coupling dynamics characteristics of added mass at different position of the flexible beam system are focused on. The simulation results ofthe rigid body corner, the tip responses of the beam and the rigid body angular velocity of the rigid body-flexible beam system with added mass are analyzed. Results obtained show that when the added mass moves from the fixed end of the flexible beam to the free end, the natural frequencies of the first-five orders of the flexible beam are approximate periodically changed. Not only this, the different positions of added mass can bring significant impact for the rigid-flexible coupling dynamical responses of the system and the vibration modes of the system.
The current research is focused on the study of the dynamic characteristics of a rigid body-flexible beam system with the added mass. The flexible beam is a uniform section of the Euler-Bernoulli beam. By using assumed mode method to disperse the deformation field of flexible beam and using Lagrange second kind equations to deduce the kinetic equations of the system, as well as using Matlab software to carry out the numerical simulation. Firstly, influence of the added mass on the natural frequency and vibration mode of the system is discussed. Secondly, in the large-scale movement of known and unknown conditions, the rigid-flexible coupling dynamics characteristics of added mass at different position of the flexible beam system are focused on. The simulation results ofthe rigid body corner, the tip responses of the beam and the rigid body angular velocity of the rigid body-flexible beam system with added mass are analyzed. Results obtained show that when the added mass moves from the fixed end of the flexible beam to the free end, the natural frequencies of the first-five orders of the flexible beam are approximate periodically changed. Not only this, the different positions of added mass can bring significant impact for the rigid-flexible coupling dynamical responses of the system and the vibration modes of the system.
引文
[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]杨辉,洪嘉振,余征跃.刚柔耦合建模理论的实验验证[J].力学学报,2003,35(2):253-256.(YANG Hui,HONG Jiazhen,YUZhengyue.Experiment validation on modeling theory for rigid-flexible coupling systems[J].Chinese journal of theoretical and applied mechanics,2003,35(2):253-256(in Chinese)).
[3]杨辉,洪嘉振,余征跃.动力刚化问题的实验研究[J].力学学报,2004,36(1):118-124.(YANG Hui,HONG Jiazhen,YUZhengyue.Experimental investigation on dynamic stiffening phenomenon[J].Chinese journal of theoretical and applied mechanics,2004,36(1):118-124(in Chinese)).
[4]吴胜宝,章定国.大范围运动刚体-柔性梁刚柔耦合动力学分析[J].振动工程学报,2011,24(1):1-7.(WU Shengbao,ZHANGDingguo.Rigid-flexible coupling dynamic analysis of hub-flexible beam with large overall motion[J].Journal of vibration engineering,2011,24(1):1-7(in Chinese)).
[5]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):313-319.(FANG Jianshi,ZHANG Dingguo.Analysis of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam[J].Acta physica sinica,2013,62(4):313-319(in Chinese)).
[6]刘锦阳,洪嘉振.柔性梁的刚-柔耦合动力学特性研究[J].振动工程学报,2002,15(2):74-78.(LIU Jinyang,HONG Jiazhen.Rigid-flexible coupling dynamic analysis of flexible body[J].Journal of vibration engineering,2002,15(2):74-78(in Chinese)).
[7]蔡国平,洪嘉振.中心刚体-柔性悬臂梁系统的动力特性研究[J].航空学报,2004,25(3):248-253.(CAI Guoping,HONG Jiazhen.Dynamic analysis of a flexible hub-beam system[J].Acta aeronautica et astronautica sinica,2004,25(3):248-253(in Chinese)).
[8]范纪华,章定国.旋转柔性悬臂梁动力学的Bezier插值离散方法研究[J].物理学报,2014,63(15):255-265.(FAN Jihua,ZHANGDingguo.Bezier interpolation method for the dynamics of rotating flexible cantilever beam[J].Acta physica sinica,2014,63(15):255-265(in Chinese)).
[9]范纪华,章定国.旋转悬臂梁动力学的B样条插值方法[J].机械工程学报,2012,48(23):59-64.(FAN Jihua,ZHANG Dingguo.B-spline interpolation method for the dynamics of rotating cantilever beam[J].Journal of mechanical engineering,2012,48(23):59-64(in Chinese)).
[10]章孝顺,章定国,洪嘉振.考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真[J].力学学报,2016,48(3):692-701.(ZHANG Xiaoshun,ZHANG Dingguo,HONG Jiazhen.Rigid-flexible coupling dynamic modeling and simulation with the longitudinal deformation induced curvature effect for a rotating flexible beam under large deformation[J].Chinese journal of theoretical and applied mechanics,2016,48(3):692-701(in Chinese)).
[11]蔡国平,洪嘉振.旋转运动柔性梁的假设模态方法研究[J].力学学报,2005,37(1):48-56.(CAI Guoping,HONG Jiazhen.Assumed mode method of a rotating flexible beam[J].Chinese journal of theoretical and applied mechanics,2005,37(1):48-56(in Chinese)).
[12]范纪华,章定国.基于变形场不同离散方法的柔性机器人动力学建模与仿真[J].力学学报,2016,48(4):843-856.(FAN Jihua,ZHANGDingguo.Dynamic modeling and simulation of flexible robots based on different discretization method[J].Chinese journal of theoretical and applied mechanics,2016,48(4):843-856(in Chinese)).
[13]CHOI S B,SHIN H C.A hybrid actuator scheme for robust position control of a flexible single-link manipulator[J].Journal of robotic systems,1996,13(6):359-370.
[14]陈思佳.刚-柔耦合问题与空间多杆柔性机械臂的动力学建模理论研究[D].南京:南京理工大学,2012.(CHEN Sijia.Researches on the rigid-flexible coupling problem and the dynamic modeling theory of multi-link spatial flexible manipulator arms[D].Nanjing:Nanjing University of Science and Technology,2012(in Chinese)).
[15]靳红玲,陈建军,郭康权.考虑附加质量的旋转柔性梁的随机动力学分析[J].振动工程学报,2015,28(6):960-965.(JIN Hongling,CHEN Jianjun,GUO Kangquan.Stochastic dynamic analysis of rotating flexible beam with tip mass[J].Journal of vibration engineering,2015,28(6):960-965(in Chinese)).
[16]蔡国平,洪嘉振.考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性研究[J].机械工程学报,2005,41(2):33-40.(CAI Guoping,HONG Jiazhen.Dynamics study of hub-beam system with tip mass[J].Journal of mechanical engineering,2005,41(2):33-40(in Chinese)).
[17]滕悠优,蔡国平.具有附加质量的中心刚体-柔性梁的频率特性[J].力学季刊,2005,26(4):623-628.(TENG Youyou,CAI Guoping.Frequency characteristics of a flexible hub-beam system with an attached mass[J].Chinese quarterly of mechanics,2005,26(4):623-628(in Chinese)).
[2]杨辉,洪嘉振,余征跃.刚柔耦合建模理论的实验验证[J].力学学报,2003,35(2):253-256.(YANG Hui,HONG Jiazhen,YUZhengyue.Experiment validation on modeling theory for rigid-flexible coupling systems[J].Chinese journal of theoretical and applied mechanics,2003,35(2):253-256(in Chinese)).
[3]杨辉,洪嘉振,余征跃.动力刚化问题的实验研究[J].力学学报,2004,36(1):118-124.(YANG Hui,HONG Jiazhen,YUZhengyue.Experimental investigation on dynamic stiffening phenomenon[J].Chinese journal of theoretical and applied mechanics,2004,36(1):118-124(in Chinese)).
[4]吴胜宝,章定国.大范围运动刚体-柔性梁刚柔耦合动力学分析[J].振动工程学报,2011,24(1):1-7.(WU Shengbao,ZHANGDingguo.Rigid-flexible coupling dynamic analysis of hub-flexible beam with large overall motion[J].Journal of vibration engineering,2011,24(1):1-7(in Chinese)).
[5]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):313-319.(FANG Jianshi,ZHANG Dingguo.Analysis of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam[J].Acta physica sinica,2013,62(4):313-319(in Chinese)).
[6]刘锦阳,洪嘉振.柔性梁的刚-柔耦合动力学特性研究[J].振动工程学报,2002,15(2):74-78.(LIU Jinyang,HONG Jiazhen.Rigid-flexible coupling dynamic analysis of flexible body[J].Journal of vibration engineering,2002,15(2):74-78(in Chinese)).
[7]蔡国平,洪嘉振.中心刚体-柔性悬臂梁系统的动力特性研究[J].航空学报,2004,25(3):248-253.(CAI Guoping,HONG Jiazhen.Dynamic analysis of a flexible hub-beam system[J].Acta aeronautica et astronautica sinica,2004,25(3):248-253(in Chinese)).
[8]范纪华,章定国.旋转柔性悬臂梁动力学的Bezier插值离散方法研究[J].物理学报,2014,63(15):255-265.(FAN Jihua,ZHANGDingguo.Bezier interpolation method for the dynamics of rotating flexible cantilever beam[J].Acta physica sinica,2014,63(15):255-265(in Chinese)).
[9]范纪华,章定国.旋转悬臂梁动力学的B样条插值方法[J].机械工程学报,2012,48(23):59-64.(FAN Jihua,ZHANG Dingguo.B-spline interpolation method for the dynamics of rotating cantilever beam[J].Journal of mechanical engineering,2012,48(23):59-64(in Chinese)).
[10]章孝顺,章定国,洪嘉振.考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真[J].力学学报,2016,48(3):692-701.(ZHANG Xiaoshun,ZHANG Dingguo,HONG Jiazhen.Rigid-flexible coupling dynamic modeling and simulation with the longitudinal deformation induced curvature effect for a rotating flexible beam under large deformation[J].Chinese journal of theoretical and applied mechanics,2016,48(3):692-701(in Chinese)).
[11]蔡国平,洪嘉振.旋转运动柔性梁的假设模态方法研究[J].力学学报,2005,37(1):48-56.(CAI Guoping,HONG Jiazhen.Assumed mode method of a rotating flexible beam[J].Chinese journal of theoretical and applied mechanics,2005,37(1):48-56(in Chinese)).
[12]范纪华,章定国.基于变形场不同离散方法的柔性机器人动力学建模与仿真[J].力学学报,2016,48(4):843-856.(FAN Jihua,ZHANGDingguo.Dynamic modeling and simulation of flexible robots based on different discretization method[J].Chinese journal of theoretical and applied mechanics,2016,48(4):843-856(in Chinese)).
[13]CHOI S B,SHIN H C.A hybrid actuator scheme for robust position control of a flexible single-link manipulator[J].Journal of robotic systems,1996,13(6):359-370.
[14]陈思佳.刚-柔耦合问题与空间多杆柔性机械臂的动力学建模理论研究[D].南京:南京理工大学,2012.(CHEN Sijia.Researches on the rigid-flexible coupling problem and the dynamic modeling theory of multi-link spatial flexible manipulator arms[D].Nanjing:Nanjing University of Science and Technology,2012(in Chinese)).
[15]靳红玲,陈建军,郭康权.考虑附加质量的旋转柔性梁的随机动力学分析[J].振动工程学报,2015,28(6):960-965.(JIN Hongling,CHEN Jianjun,GUO Kangquan.Stochastic dynamic analysis of rotating flexible beam with tip mass[J].Journal of vibration engineering,2015,28(6):960-965(in Chinese)).
[16]蔡国平,洪嘉振.考虑附加质量的中心刚体-柔性悬臂梁系统的动力特性研究[J].机械工程学报,2005,41(2):33-40.(CAI Guoping,HONG Jiazhen.Dynamics study of hub-beam system with tip mass[J].Journal of mechanical engineering,2005,41(2):33-40(in Chinese)).
[17]滕悠优,蔡国平.具有附加质量的中心刚体-柔性梁的频率特性[J].力学季刊,2005,26(4):623-628.(TENG Youyou,CAI Guoping.Frequency characteristics of a flexible hub-beam system with an attached mass[J].Chinese quarterly of mechanics,2005,26(4):623-628(in Chinese)).