预应力圆弧曲梁振动微分方程推导及求解  

Derivation and solution of vibration differential equation of prestressed circular curved beam

作　　者：何文正[1,2] 陈晨[3] 文竞舟 

机构地区：[1]重庆广播电视大学重庆401520 [2]重庆市建筑科学研究院,重庆400015 [3]宜宾职业技术学院,四川宜宾644000 [4]云南省公路科学技术研究院,云南昆明650051

出　　处：《人民长江》2016年第17期88-92,共5页Yangtze River

基　　金：交通运输部建设科技项目(2013318791440);重庆电大重点项目(ZD2015-02)

摘　　要：曲梁的动力特性是曲梁结构设计所关注的重要内容。为了研究预应力圆弧曲梁的振动特性,以振动状态下的预应力圆弧曲梁微段为研究对象,考虑预加力对微段弯矩的影响,根据达朗贝尔原理推导了预应力圆弧曲线梁的振动微分方程并对方程进行求解。导出了预应力简支圆弧曲梁面内振动的一阶自振频率解析式。通过有限元数值解与本文解析解的比较,验证了所提出解析公式的正确性。Dynamic characteristic of a curved beam is an important part in curved beam structure design. In order to study the vibration characteristics of pre-stressed circular curved beams,we take an infinitesimal segment of a pre-stressed curved beam as a case,and by considering the influence of pre-forcing on bending moment,derive the vibration differential equations of arc-curved beam based on d’Alembert principle. The formula for the first order natural vibration frequency in plane of a pre-stressed simply supported circular curved beam is obtained. Finally,by comparing with numerical results of FEM,the proposed analytical formula is verified.

关 键 词：预应力 振动微分方程 自振频率 曲梁 

分 类 号：TV332.12[水利工程—水工结构工程]