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基于非约束模态的中心刚体-Timoshenko动力学建模与分析

关玉铭 戈新生

关玉铭,戈新生. 基于非约束模态的中心刚体-Timoshenko动力学建模与分析 [J]. 应用数学和力学,2022,43(X):1-10 doi: 10.21656/1000-0887.420089
引用本文: 关玉铭,戈新生. 基于非约束模态的中心刚体-Timoshenko动力学建模与分析 [J]. 应用数学和力学,2022,43(X):1-10 doi: 10.21656/1000-0887.420089
GUAN Yuming, GE Xinsheng. Dynamic modeling and analysis of center rigid body Timoshenko beam model based on unconstrained mode[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420089
Citation: GUAN Yuming, GE Xinsheng. Dynamic modeling and analysis of center rigid body Timoshenko beam model based on unconstrained mode[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420089

基于非约束模态的中心刚体-Timoshenko动力学建模与分析

doi: 10.21656/1000-0887.420089
基金项目: 国家自然科学基金(重点项目)(11732005)
详细信息
    作者简介:

    关玉铭(1989—),男,硕士生(E-mail:gym15142027759@163.com

    戈新生(1957—),男,教授,博士(通讯作者。 E-mail:gebim@vip.sina.com

  • 中图分类号: V231.92;O342

Dynamic modeling and analysis of center rigid body Timoshenko beam model based on unconstrained mode

  • 摘要: 梁的横向变形会导致梁纵向缩短,建模过程中考虑梁横纵变形二次耦合项则存在动力刚化现象,这说明梁的纵向变形会对模型广义刚度造成影响。对于做旋转运动的梁结构,旋转运动时还会受到离心力的作用而产生轴向拉力,轴向拉力同样也会引起梁的轴向变形,这种影响对粗短梁更加明显。现以大范围运动中心刚体-Timoshenko梁模型为研究对象:首先,运用Timoshenko梁理论以及Hamilton原理建立含离心力的动力学模型;其次,引入非约束模态概念,采用Frobenius方法求解非约束模态振型函数以及固有频率;最后,通过数值仿真探究不同恒定转速时非约束模态与约束模态广义刚度的差异和非约束模态条件下离心力对模型的影响。
  • 图  1  中心刚体-铁木辛柯梁系统结构图

    Figure  1.  Structural diagram of central rigid body Timoshenko beam system

    图  2  梁上微元质量变形

    Figure  2.  Micro element mass deformation on beam

    图  3  恒定转速为0.1 rad/s的广义刚度

    Figure  3.  Generalized stiffness at constant speed of 0.1 rad /s

    图  4  恒定转速为0.5 rad/s的广义刚度

    Figure  4.  Generalized stiffness at constant speed of 0.5 rad /s

    图  5  恒定转速为1 rad/s的广义刚度

    Figure  5.  Generalized stiffness at constant speed of 1 rad /s

    图  6  恒定转速为5 rad/s的广义刚度

    Figure  6.  Generalized stiffness at constant speed of 5 rad /s

    图  7  恒定转速为0.1 rad/s的广义刚度

    Figure  7.  Generalized stiffness at constant speed of 0.1 rad /s

    图  8  恒定转速为0.5 rad/s的广义刚度

    Figure  8.  Generalized stiffness at constant speed of 0.5 rad / s

    图  9  恒定转速为10 rad/s含离心力模型的广义刚度

    Figure  9.  Generalized stiffness of model with centrifugal force at constant speed 10 rad / s

    图  10  恒定转速为10 rad/s不含离心力模型的广义刚度

    Figure  10.  Generalized stiffness of model without centrifugal force at constant speed 10 rad / s

    图  11  恒定转速为0.1 rad/s时梁末端振动响应

    Figure  11.  Vibration response of beam end at constant speed of 0.1 rad / s

    图  12  恒定转速为0.5 rad/s时梁末端振动响应

    Figure  12.  Vibration response of beam end at constant speed of 0.5 rad / s

    图  13  恒定转速为10 rad/s梁末端振动响应

    Figure  13.  Vibration response of beam end at constant speed of 10 rad / s

    表  1  Timoshenko 梁参数

    Table  1.   Parameters of Timoshenko beam

    Beam parametersLength L / mCross sectional
    area Ab / m−2
    Moment of inertia of
    cross section I / m4
    Young's modulus
    E/GPa
    Area density
    $\rho /({\rm{kg}}/{{\rm{m}}^{ - 3}})$
    Poisson's
    ratio $\upsilon $
    Shear
    coefficient $\kappa $
    value0.5m1.6e−32.56e−6163.878500.35/6
    下载: 导出CSV
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  • 收稿日期:  2021-04-07
  • 修回日期:  2022-01-06
  • 网络出版日期:  2022-01-11

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