基于DQM的曲梁平面外固有振动特性及参数分析  

OUT-OF-PLANE NATURAL VIBRATION CHARACTERISTIC AND PARAMETER ANALYSIS OF CURVED GIRDERS BASED ON DQM

作　　者：孙广俊[1,2,3] 李鸿晶[2] 王通[4] 邢浩洁 

机构地区：[1]北京工业大学建筑工程学院,北京100022 [2]南京工业大学土木工程学院,南京210009 [3]东南大学混凝土及预应力混凝土结构教育部重点实验室,南京210096 [4]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《工程力学》2013年第12期220-227,共8页Engineering Mechanics

基　　金：江苏省高校自然科学研究重大项目(10KJA560012);中国博士后科学基金项目(2012M520133);东南大学混凝土及预应力混凝土结构教育部重点实验室开放课题基金项目(CPCSME2011-04)

摘　　要：基于DQM(Differential Quadrature Method,微分求积法),对曲线梁的频率方程和边界条件进行离散,通过采用不等分网点划分和替换法边界处理,求解了单跨圆形曲线梁和单跨回旋缓和曲线梁的平面外固有振动特性,并将结果与精确解进行对比,验证了微分求积法的高效性,讨论了网点数对求解精度的影响。在此基础上,研究了弯扭刚度比、翘曲系数以及边界约束形式等因素对曲线梁振动频率的影响,分析对比了圆形和回旋缓和曲线梁振动特性的参数影响规律。研究表明,采用微分求积法可以方便、高效地求解曲线梁的固有动力特性;弯扭刚度比、翘曲系数以及边界约束条件对曲线梁振动频率有着较为显著的影响,随着边界约束的减少,两种形式曲线梁的基本频率均随之减小,对于多数约束情况,两种形式曲线梁振动特性的参数影响规律相类似,唯有一种悬臂形式下的回旋缓和曲线梁振动特性的参数影响规律表现出与其他约束情况下相反的规律。Based on the DQM （Differential Quadrature Method）, the frequency equations and boundary conditions of curved girder are discretized respectively. By the choice of the unequal spacing form of the sampling grid points and the replaced equation approach of boundary conditions, the out-of-plane natural vibration characteristic of the one-span circular curved girder and the one-span cyclotron transition curved girder are computed respectively. Through a comparison with the exact solutions, the high effectiveness of DQM is verified and the influence of grid point quantity on the solving precision is discussed. Based on the solution of natural vibration characteristic of curved girder, the influences of stiffness ratio of bending and torsion, warping coefficient and boundary constraint form on natural vibration frequency of curved girder are studied respectively and the parameter influence laws of circular curved girder and cyclotron transition curved girder are compared. The research shows that the natural vibration characteristic of curved girder can be computed conveniently andefficiently by the DQM and the stiffness ratio of bending and torsion, warping coefficient and boundary constraint form have obvious influence on the vibration frequency of curved girder. The computation results show that the fundamental frequencies of the two types of curved girders are both reduced with the decrease of boundary constraint conditions and the parameter influence laws are similar in most boundary constraint conditions; however, the parameter influence of the cantilever type cyclotron transition curved girder reflects a reversed law compared to the most boundary constraint conditions.

关 键 词：曲线梁 固有振动 微分求积 圆曲梁 缓和曲梁 

分 类 号：U448.21[建筑科学—桥梁与隧道工程] U448.42[交通运输工程—道路与铁道工程]