传递函数法在非局部弹性梁动力学分析中的应用  

APPLICATION OF TRANSFER FUNCTION METHOD TO DYNAMIC ANALYSIS OF A NONLOCAL ELASTIC BEAM

作　　者：赵雪川[1] 雷勇军[1] 唐国金[1] 

机构地区：[1]国防科学技术大学航天与材料工程学院,长沙410073

出　　处：《振动与冲击》2007年第5期4-7,共4页Journal of Vibration and Shock

基　　金：国家杰出青年基金资助项目(19925209);国防科技大学校预研基金资助

摘　　要：采用传递函数方法进行了非局部弹性梁的动力学分析。非局部弹性梁内一点的应力与梁某一区域内任意一点的应变均有关系。本文基于Eringen的非局部弹性积分型本构关系,采用幂指数型核函数,利用Laplace变换导出梁的四阶偏微分形式振动方程,通过定义状态向量,将控制方程化为一阶微分方程组,并采用传递函数方法进行了求解,针对两种边界条件给出了非局部弹性梁的固有频率和固有振型。结果表明,同阶频率下,非局部弹性梁的频率比局部梁的频率低,振型基本一致。Dynamic analysis of a nonlocal elastic beam is studied by using transfer function method.The stress of a point of the beam is related with strain of any point in the certain domain of the beam which is so called the nonlocal elastic beam.Based on Eringen's nonlocal elastic constitutive relationship,adapting exponential attenuation kernel function,its four order differential governing equation is obtained with Laplace transformation.By defining a state vector the four order differential equation is transformed into a set of one order equations,and the solution is obtained by using transfer function method.For two different boundary conditions,the natural frequencies and modes of the nonlocal elastic beam are given.Compared with the results using local theory,the natural frequencies of the beam using nonlocal theory are lower than those of the same beam using local theory,and the corresponding modes are almost the same.

关 键 词：非局部弹性体 梁 固有频率 传递函数法 

分 类 号：O343.5[理学—固体力学]