基于传递函数法的非局部弹性直杆扭转振动研究  

Research on Torsional Vibration of Nonlocal Elastic Bar Using Transfer Function Method

作　　者：李立群[1] 段静波[1] 李家文[1] 雷勇军[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：《力学季刊》2012年第2期181-187,共7页Chinese Quarterly of Mechanics

基　　金：教育部新世纪优秀人才支持计划资助项目(NCET-08-0148);国防科技大学科研计划项目

摘　　要：基于Eringen提出的非局部理论研究了具有宏观尺度的非局部弹性直杆的扭转振动问题。运用非局部弹性本构关系模型,选择幂指数型衰减核函数,推导了非局部弹性直杆纯扭转振动的动力学控制方程,并采用传递函数法对常见边界条件下的非局部弹性直杆的扭转振动问题进行求解,获得了杆扭转振动的固有频率及振型。算例分析中考虑了非局部影响尺度、附加质量圆盘几何参数等因素对杆的扭转振动固有频率的影响。通过传递函数解与非局部解析解、局部解析解的对比分析,得到了一些有益的结论。Nonlocal theory, originally proposed by Eringen, was used to study torsional vibration of nonlocally elastic bar of macroscopic dimension. Based on the nonlocally elastic constitutive relation, the dynamic governing equations of a nonlocally torsional elastic bar were derived with the exponential attenuation kernel function which was frequently used. The transfer function method was used to obtain the natural frequencies and modes of the bar under common boundary conditions. The influences of nonlocal dimension and geometrical parameter of the attached circular plate on the bar＇s natural frequencies were researched. At last, the present solutions of transfer function method were compared with the analytic solutions of the nonlocally torsional elastic bar and locally one, respectively. A couple of useful conclusions were obtained.

关 键 词：非局部弹性体 传递函数法 扭转 直杆 固有频率 

分 类 号：O343.5[理学—固体力学]