张拉整体结构外力与形变间关系分析及实验验证
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摘要
针对张拉整体结构中杆件只受轴向压力,绳索和弹簧等只受轴向拉力的情况,采用拉格朗日动力学和样机实验,对外力作用下张拉整体结构中弹簧变形量进行了分析和测量.首先,推导了张拉整体结构平衡状态的力学模型,对非保守力作用下张拉整体结构弹簧的变形量进行了计算;然后,通过三杆六索张拉整体结构样机实验,对弹簧变形量进行了测量.实验与计算结果的对比分析,验证了张拉整体结构力学模型的合理性,揭示了外力与形变间的内在数学关系.
The tensegrity structures suffer the axial pressure in struts and the axial tension in cables and springs,so they are widely used in many engineering fields such as architecture,biotechnology,aerospace and robotics.Based on the Lagrangian dynamics and prototype experiment,the spring deformation of the tensegrity structure under the action of external forces is analyzed and measured.First,the dynamic model of the equilibrium state of the tensegrity structure is derived.The spring deformation of the tensegrity structure under the action of external nonconservative forces is analyzed.Then,by means of the prototype experiment on the tensegrity structure with six struts and three cables,the spring deformation is measured.The comparison and analysis between the experimental and numerical results validate the dynamic model of the tensegrity structure and reveal the mathematical relation between external forces and deformation of the tensegrity structure.
The tensegrity structures suffer the axial pressure in struts and the axial tension in cables and springs,so they are widely used in many engineering fields such as architecture,biotechnology,aerospace and robotics.Based on the Lagrangian dynamics and prototype experiment,the spring deformation of the tensegrity structure under the action of external forces is analyzed and measured.First,the dynamic model of the equilibrium state of the tensegrity structure is derived.The spring deformation of the tensegrity structure under the action of external nonconservative forces is analyzed.Then,by means of the prototype experiment on the tensegrity structure with six struts and three cables,the spring deformation is measured.The comparison and analysis between the experimental and numerical results validate the dynamic model of the tensegrity structure and reveal the mathematical relation between external forces and deformation of the tensegrity structure.
引文
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[11]纪志飞,李团结,林敏.张拉整体并联机构波浪能采集研究[J].西安电子科技大学学报,2015,42(4):70-75.JI Zhifei,LI Tuanjie,LIN Min.Research on a Tensegrity Parallel Mechanism for Wave Energy Harvesting[J].Journal of Xidian University,2015,42(4):70-75.
[12]王征.张拉整体结构的找形和稳定性分析[D].西安:西安电子科技大学,2012.
[13]李团结,贾建援,胡雪梅.机械工程中两类非线性方程组的完全解[J].西安电子科技大学学报,2005,32(1):71-74.LI Tuanjie,JIA Jianyuan,HU Xuemei.Global Set of Solutions for Two Types of Systems of Nonlinear Equations in Mechanical Engineering[J].Journal of Xidian University,2005,32(1):71-74.
[2]OHSAKI M,ZHANG J Y.Nonlinear Programming Approach to Form-finding and Folding Analysis of Tensegrity Structures Using Fictitious Material Properties[J].International Journal of Solids and Structures,2015,69-70:1-10.
[3]MOTOR R.Tensegrity:Structural Systems for the Future[M].London:Butterworth-Heinemann,2006.
[4]纪志飞.3-SPS张拉整体并联机构的构型综合与运动性能分析及能量采集研究[D].西安:西安电子科技大学,2015.
[5]陆金钰,武啸龙,赵曦蕾,等.基于环形张拉整体的索杆全张力穹顶结构形态分析[J].工程力学,2015,32(6):66-71.LU Jingyu,WU Xiaolong,ZHAO Xilei,et al.Form Finding Analysis of Cable-strut Tensile Dome Based on Tensegrity Torus[J].Engineering Mechanics,2015,32(6):66-71.
[6]CALUWAERTS K,DESPRAZ J,I爦EN A,et al.Design and Control of Compliant Tensegrity Robots through Simulation and Hardware Validation[J].Journal of the Royal Society Interface,2014,11(98):20140520.
[7]纪红娜.张拉整体移动机器人动力学及运动性能分析[D].西安:西安电子科技大学,2011.
[8]SULTAN C,SKELTON R.A Force and Torque Tensegrity Sensor[J].Sensors and Actuators,A:Physical,2004,112(2/3):220-231.
[9]林敏,李团结,纪志飞.采用改进鱼群算法的张拉整体结构找形方法[J].西安电子科技大学学报,2014,41(5):112-117.LIN Min,LI Tuanjie,JI Zhifei.Form-finding of Tensegrity Structures Based on IAFSA[J].Journal of Xidian University,2014,41(5):112-117.
[10]孙国鼎.张拉整体结构的形态分析[D].西安:西安电子科技大学,2010.
[11]纪志飞,李团结,林敏.张拉整体并联机构波浪能采集研究[J].西安电子科技大学学报,2015,42(4):70-75.JI Zhifei,LI Tuanjie,LIN Min.Research on a Tensegrity Parallel Mechanism for Wave Energy Harvesting[J].Journal of Xidian University,2015,42(4):70-75.
[12]王征.张拉整体结构的找形和稳定性分析[D].西安:西安电子科技大学,2012.
[13]李团结,贾建援,胡雪梅.机械工程中两类非线性方程组的完全解[J].西安电子科技大学学报,2005,32(1):71-74.LI Tuanjie,JIA Jianyuan,HU Xuemei.Global Set of Solutions for Two Types of Systems of Nonlinear Equations in Mechanical Engineering[J].Journal of Xidian University,2005,32(1):71-74.