简支条件下单轴对称三角形管翼缘工字形梁弯扭振动理论与有限元验证  

Flexural and torsional vibration theory of uniaxially symmetric triangulartube flange I-beam and finite element verification

作　　者：张文福 江杨[1] 杨琴 ZHANG Wenfu;JIANG Yang;YANG Qin(College of Civil Engineering,Anhui Jianzhu University,Hefei 230000,China;College of Architecture Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]安徽建筑大学土木工程学院,安徽合肥230000 [2]南京工程学院建筑工程学院,江苏南京211167

出　　处：《苏州科技大学学报（自然科学版）》2023年第4期17-24,共8页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金项目(51578120,51178087,52178143)。

摘　　要：基于板-梁理论求出单轴对称三角形管翼缘工字形梁的弯扭变形应变能以及弯扭振动的动能,利用能量变分原理分析单轴对称三角形管翼缘工字形梁弯扭振动问题,同时利用Mathematica进行辅助求解,计算得到简支条件下弯扭振动各阶频率解,最后利用ANSYS软件进行验证并提取相对应频率解验证各阶频率解的正确性。结果表明:频率误差在-2.23%~2.36%之间。文章通过对单轴对称三角形管翼缘工字形梁的研究试图为工程应用提供参考。Based on the plate-beam theory,the flexural-torsional deformation strain energy and the kinetic energy of the flexural-torsional vibration of the I-shaped beam with a single axisymmetric triangular tube flange are obtained.The energy variational principle was used to analyze the flexural-torsional vibration of the I-shaped beam with a single axisymmetric triangular tube flange.Meanwhile,Mathematica was used to assist the calculation to obtain the frequency solutions of the flexural-torsional vibration of the simply supported beam.Finally,the finite element model was established using ANSYS software,and the corresponding frequency solutions were extracted for comparison and verification.The results show that the error between the theoretical solution and the finite element solution for the frequencies is between-2.23%and 2.36%,thus tentatively proving the correctness of the theory in this paper.The uniaxially symmetric triangular tube flange I-beam studied is attempted to provide a reference for engineering applications.

关 键 词：弯扭振动 振动频率解 简支梁 有限元 

分 类 号：U441[建筑科学—桥梁与隧道工程]