## 留言板

 引用本文: 关玉铭，戈新生. 基于非约束模态的中心刚体-Timoshenko梁动力学建模与分析 [J]. 应用数学和力学，2022，43（2）：156-165
GUAN Yuming, GE Xinsheng. Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes[J]. Applied Mathematics and Mechanics, 2022, 43(2): 156-165. doi: 10.21656/1000-0887.420089
 Citation: GUAN Yuming, GE Xinsheng. Dynamic Modeling and Analysis of the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes[J]. Applied Mathematics and Mechanics, 2022, 43(2): 156-165.

## 基于非约束模态的中心刚体-Timoshenko梁动力学建模与分析

##### doi: 10.21656/1000-0887.420089

###### 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 the Central Rigid Body-Timoshenko Beam Model Based on Unconstrained Modes

• 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的广义刚度造成影响。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。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-Timoshenko梁系统结构图

Figure  1.  The structural diagram for the central rigid body-Timoshenko beam system

图  2  梁上微元质量变形

Figure  2.  The mass deformation of an infinite simal element on the beam

Figure  3.  The generalized stiffness at a constant speed of 0.1 rad /s

Figure  4.  The generalized stiffness at a constant speed of 0.5 rad /s

Figure  5.  The generalized stiffness at a constant speed of 1 rad /s

Figure  6.  The generalized stiffness at a constant speed of 5 rad /s

Figure  7.  The generalized stiffness at a constant speed of 0.1 rad /s

Figure  8.  The generalized stiffness at a constant speed of 0.5 rad / s

Figure  9.  The generalized stiffness of the model with centrifugal forces at a constant speed of 10 rad / s

Figure  10.  The generalized stiffness of the model without centrifugal forces at a constant speed of 10 rad / s

Figure  11.  Vibration responses of the beam end at a constant speed of 0.1 rad / s

Figure  12.  Vibration responses of the beam end at a constant speed of 0.5 rad / s

Figure  13.  Vibration responses of the beam end at a constant speed of 10 rad / s

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##### 出版历程
• 收稿日期:  2021-04-07
• 修回日期:  2022-01-06
• 网络出版日期:  2022-01-11
• 刊出日期:  2022-02-01

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