张文福, 杜娟, 刘迎春, 计静, 任亚文. 空间桁架梁固有振动的能量变分解析解[J]. 工程力学, 2014, 31(7): 106-111. DOI: 10.6052/j.issn.1000-4750.2013.01.0064
引用本文: 张文福, 杜娟, 刘迎春, 计静, 任亚文. 空间桁架梁固有振动的能量变分解析解[J]. 工程力学, 2014, 31(7): 106-111. DOI: 10.6052/j.issn.1000-4750.2013.01.0064
ZHANG Wen-fu, DU Juan, LIU Ying-chun, JI Jing, REN Ya-wen. THE ENERGY VARIATION ANALYTICAL SOLUTION FOR THE NATURE VIBRATION OF THE SPACE TRUSS GIRDER[J]. Engineering Mechanics, 2014, 31(7): 106-111. DOI: 10.6052/j.issn.1000-4750.2013.01.0064
Citation: ZHANG Wen-fu, DU Juan, LIU Ying-chun, JI Jing, REN Ya-wen. THE ENERGY VARIATION ANALYTICAL SOLUTION FOR THE NATURE VIBRATION OF THE SPACE TRUSS GIRDER[J]. Engineering Mechanics, 2014, 31(7): 106-111. DOI: 10.6052/j.issn.1000-4750.2013.01.0064

空间桁架梁固有振动的能量变分解析解

THE ENERGY VARIATION ANALYTICAL SOLUTION FOR THE NATURE VIBRATION OF THE SPACE TRUSS GIRDER

  • 摘要: 目前人们对空间桁架梁的振动特性研究得较少,该文首先采用Timoshenko梁的连续化模型来模拟空间桁架梁,推导得到了空间桁架梁的等代抗弯刚度和等代抗剪刚度,并采用能量变分法对空间桁架梁的固有振动进行分析,给出空间桁架梁的竖向振动频率和振型的解析解。然后采用有限元软件ANSYS对几种不同算例进行模拟,通过模态分析得到空间桁架梁的频率与振型。将能量变分法求得的频率解析解与有限元分析求得的频率数值解进行对比,结果基本上是一致的,将两种方法得到的振型对比,结果吻合良好。该文所提出的能量变分解析解可供空间桁架梁的工程设计参考。

     

    Abstract: The vibration characteristics of the space truss girder has been less studied. The continuous Timoshenko beam model is adopted to simulate the space truss girder and the equivalent bending stiffness and equivalent shear stiffness are obtained. The nature vibration of the space truss beam is analyzed based on the energy variational method, and the analytical solutions of vertical vibration frequency and the vibration mode of the space truss beam can be derived. Then the finite element software ANSYS is adopted to simulate different cases, and the frequency and the vibration mode of the space truss beam can be obtained. The frequency obtained by the energy variational method is compared with that obtained by the finite element analysis, and consistent results are found. The vibration modes obtained by those two methods are compared, and good agreement is found. The analytical solutions of energy variational method can be used as a reference for engineering design of the space truss beam.

     

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