竖直方向弹性约束悬臂梁的固有频率分析  

Nature Frequency Analysis of a Cantilever Beam with Elastic Restraint in Vertical Direction

作　　者：杨帅[1] 王太勇[1] 

机构地区：[1]天津大学机械工程学院,天津300072

出　　处：《天津大学学报》2011年第1期18-22,共5页Journal of Tianjin University(Science and Technology)

基　　金：国家高技术研究发展计划(863计划)资助项目(2007AA042005);教育部高等学校博士学科点专项科研基金资助项目(20060056016)

摘　　要：针对固定端部竖直方向为弹性约束的悬臂梁结构进行了模态分析.用欧拉-伯努利梁模型,推导出前3阶固有频率方程和振型函数.针对不同刚度,采用数值方法求解固有频率方程,得到固有频率随约束刚度变化的关系曲线.运用最小二乘法对该曲线进行函数拟合.以不同尺度梁为例,通过有限元方法对该拟合函数的正确性进行了验证,其误差小于2%.应用该函数,通过固有频率对端部刚度进行识别,其误差小于6%.Modal analysis of a cantilever beam with elastic support in vertical direction was conducted.With Ber-noulli-Euler beam model,the first three nature frequency equations and the vibration mode functions were obtained.With different stiffness,the nature frequency equations were solved using numerical method.The relationship curves between support stiffness and nature frequency were acquired,and the corresponding functions were fitted with least square method.To beams in different scales,the accuracy of the functions was validated using finite element method,and the relative error was less than 2%.Based on the functions and nature frequency,the support stiffness was identified and the relative error was less than 6%.

关 键 词：悬臂梁 弹性约束 固有频率 模态 有限元 

分 类 号：TH113.1[机械工程—机械设计及理论]