旋转柔性悬臂梁的固有频率分析  

NATURAL FREQUENCIES ANALYSIS OF A ROTATING FLEXIBLE CANTILEVER BEAM

作　　者：方建士[1,2] 章定国[2] 王宏伟[1] 

机构地区：[1]南京工程学院材料工程学院,南京211167 [2]南京理工大学理学院,南京210094

出　　处：《机械强度》2013年第3期242-248,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金(11132007;10772085);江苏省"333工程"项目(BRA20111172);南京工学院校级科研基金(QKJB201203)资助~~

摘　　要：在精确描述柔性梁非线性变形基础上,利用Lagrange方程推导出考虑动力刚化项的一次近似刚柔耦合动力学方程。忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型作无量纲化处理,首先分析模态截断数对固有频率的影响,其次研究一次近似简化模型和零次近似简化模型的振动特性。研究发现,梁固有频率与模态截断数有关,合理的模态截断数应随无量纲角速度的增大而适当增加;一次近似简化模型的固有频率随无量纲角速度和系统径长比的增大而增大,零次近似简化模型的固有频率随无量纲角速度增大而减小;一次近似简化模型下梁横向弯曲振动不存在物理意义上的共振失稳现象。现有典型文献的相关结论值得商榷。Based on the accurate description of non-linear deformation of the flexible beam, the governing equations of motion with the dynamic stiffening terms （referred as the first-order approximation coupling （FOAC） model） are derived from Lagrange＇s equations. The first-order approximation simplified（FOAS） model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dependence of natural frequency of a flexible beam on number of modes is analyzed. Then, the vibration characteristics of the first-order approximation simplified model and the zero-order approximation simplified （ZOAS） model are investigated. Generally, as the dimensionless angular speed increases, the used number of modes should increase properly to obtain the adequate accuracy. As the dimensionless angular speed and hub radius ratio increase, the natural frequencies of the FOAS model increase monotonically. As the dimensionless angular speed increase, the natural frequencies of the ZOAS model decrease. There is no resonant unstable phenomenon of a cantilever beam in the FOAS model. The results in the typical existing references are arguable.

关 键 词：柔性梁 刚柔耦合 固有频率 一次近似简化模型 零次近似简化模型 

分 类 号：O313.7[理学—一般力学与力学基础] O326[理学—力学]