Determination of the natural frequencies of axially moving beams by the method of multiple scales  

作　　者：杨晓东 陈立群 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China [2]Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

出　　处：《Journal of Shanghai University(English Edition)》2007年第3期251-254,共4页上海大学学报（英文版）

基　　金：Project supported by the National Natural Science Foundation of China （Grant No.10472060）

摘　　要：The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

关 键 词：the method of multiple scales natural frequency axially moving beam 

分 类 号：TN011[电子电信—物理电子学]