预应力效应对预应力混凝土简支梁动力特性的影响  

Influence of Prestressing Force on Dynamic Characteristics of Simply Supported Prestressed Concrete Beam

作　　者：董长军[1] 刘世忠[1] 李爱军[1,2] DONG Chang-jun;LIU Shi-zhong;LI Ai-jun(School of Civil Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Journal Editorial Department,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学土木工程学院,甘肃兰州730070 [2]兰州交通大学学报编辑部,甘肃兰州730070

出　　处：《兰州交通大学学报》2018年第5期13-17,共5页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(51368032;51568036);兰州交通大学优秀平台支持(201606)

摘　　要：为研究预应力对简支梁竖向基频的影响,以预应力混凝土简支梁为研究对象,运用能量变分法与Hamilton原理推导出简支梁在预应力作用下的竖向振动微分方程,并求出预应力对频率影响的解析解公式,从理论上证明了预应力可以提高简支梁的竖向自振频率.预应力混凝土简支梁竖向自振频率的影响因素主要有阶数、预应力大小和预应力筋截面面积.采用DOE实验设计方法对影响竖向自振频率因素的优先级进行分析,结果表明,阶数的影响大于预应力大小以及预应力筋截面面积的影响.最后利用ANSYS建立有限元模型与本文理论计算结果进行比较,结果表明预应力引起的轴向效应在计算竖向一阶自振频率时是不能忽略的.In order to study the influence of prestressing force on the vertical fundamental frequency of simple supported beam,with the prestressed concrete beam as the research object,the vertical vibration differential equation of beam under prestressing force was derived based on energy variation principle and Hamilton's principle.Analytical solution formula of the influence of prestressing force on frequency was achieved.It was proved theoretically that simply supported beam with prestressing force can improve the vertical natural frequency of vibration.The influence factors of vertical self vibration frequency of prestressed concrete beam include order of frequency,prestressing force and prestressed tendon cross sectional area.Analysis of the priority of the factors by the DOE design method shows that the influence of order number is more significant than that of the prestressing force and the area of prestressed tendon.Finally,the results of ANSYS finite element calculation were compared with the results of the theoretical calculation.Results show that the axial effect caused by prestress shall not be ignored in calculating the vertical vibration frequency.

关 键 词：预应力 自振频率 简支梁 变分法 

分 类 号：TU378.1[建筑科学—结构工程]