受移动质量作用的一类变截面梁横向振动分析  

TRANSVERSE VIBRATION ANALYSIS FOR A TYPE OF VARIABLE CROSS-SECTION BEAM SUBJECTED TO MOVING MASS

作　　者：刘雷[1] 杨国来[2] 

机构地区：[1]南京航空航天大学机电学院,南京210016 [2]南京理工大学机械工程学院,南京210094

出　　处：《工程力学》2015年第4期212-219,共8页Engineering Mechanics

基　　金：国家重点基础研究发展计划973项目(61311603)

摘　　要：采用半解析法计算了横截面积、横截面的惯性矩沿轴线方向以幂函数规律变化的一类变截面梁的固有频率和振型,通过与有限元法的计算结果比较说明了半解析解的精确性。在此基础上,考虑牵连惯性力、相对惯性力、科氏力和离心惯性力的影响,推导了变截面梁受移动质量作用的横向弯曲振动方程,并采用Newmark法进行数值求解。以某梁式结构受移动质量作用为例,将其简化为横截面积和惯性矩沿轴线按任意次幂函数变化的变截面梁,结果表明:该方法能够正确、有效地处理此类问题。The dynamic responses of a type of beam are investigated, the cross-section and inertia moment of which vary with power functions. Natural frequencies and vibration modes of the beam are calculated by semi-analytical method. Comparison of the solutions with finite element solutions is conducted to verify the accuracy. Considering convected inertial force, relative inertial force, Coriolis force and centrifugal inertial force, equations for transverse bending vibration of the beam under moving mass are derived and solved numerically using Newmark method. The dynamic response of a cantilever beam with variable cross-section and inertia moment is analyzed in a case study, which verifies the proposed approach.

关 键 词：变截面梁 移动质量 横向弯曲振动 形状参数 NEWMARK法 

分 类 号：TB535[理学—物理]