自然弯扭梁的耦合振动分析  

Analysis of coupled vibrational behavior of naturally curved and twisted beams

作　　者：虞爱民[1] 杨昌锦[2] 郝颖[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092 [2]苏州大学城市轨道交通学院,苏州215021

出　　处：《振动与冲击》2009年第8期175-179,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10572105);上海市重点学科建设资助项目(B302)

摘　　要：以空间曲梁理论为基础对具有一般横截面形状自然弯扭梁的耦合振动特性进行了研究,分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响。通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式,精确的固有频率则可用搜索的方法来确定。为了证明理论的有效性,对两端固支椭圆截面曲梁的固有频率和振型进行了求解,并把数值计算结果同PATRAN梁单元的有限元结果进行了比较。Coupled vibrational behavior of spatial curved beams with general cross-sectional shapes was theoretically investigated. In the governing equations of motion of the beams, all displacement functions and the generalized warping coordinate were defined on the centroid axis and the effects of rotary inertia, transverse shear deformations and torsion-related warping were considered in the present formulations. The explicit analytical expressions which give the vibrating mode shapes of the beams were derived by rigorous application of the computing package MATHEMATICA and a process of searching was used to determine the exact natural frequencies. In order to demonstrate the validity of the present theory, the natural frequencies and vibration modes of a curved beam with elliptic cross section under clamped-clamped boundary condition were evaluated and compared with the FE-results using PATRAN’s beam elements.

关 键 词：自然弯扭梁 广义翘曲坐标 耦合振动 固有频率 振型 

分 类 号：O326[理学—一般力学与力学基础] TU323[理学—力学]