三跨有粘结预应力连续梁自振频率解析解  

Analytical solution for natural frequency of three-span bonded prestressed continuous beam

作　　者：石鲁宁 闫维明[1] 李勇[1,2] 马裕超[1] 

机构地区：[1]北京工业大学工程抗震与结构诊治北京市重点实验室,北京100124 [2]清华大学土木工程系,北京100084

出　　处：《长安大学学报（自然科学版）》2015年第4期69-75,共7页Journal of Chang’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(50878010;50978009)

摘　　要：为了研究三跨有粘结预应力连续梁的动力特性,建立了基于Bernoulli-Euler梁理论的有粘结预应力钢筋布置形式的连续梁分析模型。通过建立有粘结预应力与位移的函数关系,将连续梁视为满足弯矩、转角和位移条件的多个单跨梁,采用分段联立法建立三跨预应力连续梁的振动方程组,获得了频率方程的解析解。通过求解频率方程得到自振频率,以三跨有粘结预应力连续梁为例,分别将本文方法计算结果与有限元法计算结果及实桥测试结果进行对比。研究结果表明:本文方法所得预应力梁的基频与有限元法计算结果的相对误差仅为0.6%,与实桥测试结果的误差为-1.18%;前四阶频率与有限元法计算结果的最大误差在3%以内;前三阶自振频率与实桥测试结果的平均误差在3%以内,结果吻合较好。通过本文公式可以较准确地求得三跨有粘结预应力连续梁的自振频率等动力参数。In order to study the dynamic characteristics of three-span bonded prestressed continuous beam, the paper established the analysis model of prestressed tendon layout based on the Bernoulli-Euler beam theory. Through establishing the relationship between prestress force and displacement and taking the continuous beam as the multiple single beams satisfying with the moment, angle and displacement boundary conditions, the vibration equation of beam using piecewise simultaneous method was established and the analytical solution of the frequency equation was obtained. Then the frequency equation was solved to get natural frequency. Taking a three-span bonded prestressed continuous beam as example, the natural frequencies obtained by this method was compared with those calculated by finite element method （FEM） and actual bridge test. The results show that relative error of fundamental frequency is only 0. 6 % and the maximum error of the first four frequencies is within 3 % when this method and finite element method are adopted. The relative error of fundamental frequency is --1.18% and the average error of the first three frequencies is within 3% when this method and actual bridge test are adopted. It is found the results calculated by the formulas are in good agreement with the results of FEM and actual bridge tests. Thus by adopting this method, the dynamic parameters such as natural frequencies of three-span bonded prestressed continuous beams can be obtained accurately. 2 tabs, 10 figs, 15 refs.

关 键 词：桥梁工程 三跨有粘结预应力连续梁 自振频率 频率方程 振动方程 动力特性 

分 类 号：U448.21[建筑科学—桥梁与隧道工程]