含横向导支端Euler-Bernoulli梁弯曲振动的固有特性分析  

Analysis of natural properties for bending vibration of Euler-Bernoulli beams with transverse sliding support

作　　者：王秀[1] 刘初升[1] 彭利平[1] 杨志勇[1] 李珺[1] 

机构地区：[1]中国矿业大学机电工程学院,江苏徐州221116

出　　处：《机械设计》2014年第2期81-85,共5页Journal of Machine Design

基　　金：国家自然科学基金资助项目(11372071);中国博士后科学基金资助项目(2013M541139);国家科技支撑计划资助项目(2012BAH28F03);黑龙江省科技攻关资助项目(GZ11A405)

摘　　要：分析了起重机抗倾覆稳定性动态设计过程中,将起重机结构抽象成具有横向导支端的Euler-Bernoulli梁结构的必要性,计算并研究了此类梁在简单边界条件——两端导支(S-S)、导支-自由(S-F)、导支-简支(S-SS)和导支-固支(SC)下的弯曲振动固有频率和振型函数。用数值算法计算发现:一端导支另一端自由或导支横梁存在横向刚体模态;一端导支一端自由或导支及一端导支一端简支或固定的两种横梁的振动特性十分相似;导支端将引起振型函数凹凸性的变化。最后,对近工况复杂导支-弹性支撑与约束下的横梁模态参数进行了求解。In view of the anti-overturning stability of a crane structure, the paper firstly discussed the necessity of mathematically modeling the structure to be an Euler-Bernoulli beam with transverse sliding support in the dynamic design. Then, natural frequency and mode function of the bending vibration with simple boundary conditions（i.e.,both two endswith sliding support（S-S）, a sliding end and a free end （S-F）,a sliding end and a simply support end （S-SS）, a sliding end and a fixed end （S-C））were cal- culated respectively. Finally, we solved the modal parameters of the beam with a complex sliding support end and elastic support and restraint end, which is similar to the practice. By numerical examples, conclusions can be drawn that the horizontal rigid mode exists in the beams of S-S and S-F supports. Besides,the beams with S-S and S-F supports as well as the beams with S-SS and S-C supports share the similar vibratory characteristics. In addition,the sliding support causes the concavity and convexity change of vibration mode function.

关 键 词：导支 弯曲振动 EULER-BERNOULLI梁 模态参数 

分 类 号：TH2[机械工程—机械制造及自动化] O32[理学—一般力学与力学基础]