Timoshenko梁运动方程的修正及其影响  

Modification of Motion Equation of Timoshenko Beam and Its Effect

作　　者：陈镕[1] 万春风[1] 薛松涛[1] 唐和生[1] 

机构地区：[1]同济大学结构工程与防灾研究所

出　　处：《同济大学学报（自然科学版）》2005年第6期711-715,共5页Journal of Tongji University:Natural Science

基　　金：国家杰出青年科学基金资助项目(59925820)

摘　　要：在Timoshenko梁的基础上,考虑剪切变形所引起的转动惯量,对传统的Timoshenko梁的运动方程进行了修正,分析了这种修正对梁的运动特性所带来的影响,并论证了Timoshenko梁实际上只存在一个相速度系,一个群速度系,以及一个固有频谱.这种修正在低频段影响很小,而在高频段影响比较显著,因此在诸如冲击等高频影响占重要地位的动力分析中必须加以考虑.Based on the Timoshenko beam theory,the rotary inertia caused by the shear deformation of the beam is considered in this paper,and the motion equation of the Timoshenko beam theory is then modified.The dynamic characters of this new model has been discussed and it can be concluded that in the beam only one set of phase velocity series,one set of group velocity series and one natural frequency spectrum exist,respectively.The effect of this modification is very small when the frequency is very low,but when the frequency is much high,the effect is very evident and should be considered,(especially) for the dynamic transient response analysis,such as impact analysis,in which high frequencies have important effect.

关 键 词：修正Timoshenko梁 运动方程 波速 群速度 固有频率 

分 类 号：O347.1[理学—固体力学]