基于板-梁理论的三角形薄壁梁扭转振动能量方程与有限元验证  

Energy Equation and Finite Element Verification of Torsional Vibration of Triangular Thin-walled Beams Based on Plate Beam Theory

作　　者：张文福 俞文涛[1] 周季虎 黄斌 计静 刘迎春[3] ZHANG Wenfu;YU Wentao;ZHOU Jihu;HUANG Bin;JI Jing;LIU Yingchun(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215009,China;School of Architectural Engineering,Nanjing Institute of Technology,Nanjing 211167,China;School of Civil Engineering and Architecture,Northeast Petroleum University,Daqing 163318,China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215009 [2]南京工程学院建筑工程学院,江苏南京211167 [3]东北石油大学土木建筑工程学院,黑龙江大庆163318

出　　处：《南京工程学院学报（自然科学版）》2023年第4期85-90,共6页Journal of Nanjing Institute of Technology(Natural Science Edition)

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

摘　　要：以三角形薄壁梁作为研究对象,基于板-梁理论研究三角形薄壁梁扭转振动.依据Timoshenke梁和Kirchhoff板力学模型,求出三角形薄壁梁的总应变能和扭转刚度;把截面位移分量带入动能方程,建立三角形薄壁梁总势能方程,并求得两边简支的三角形薄壁梁扭转振动频率的理论解.采用ANSYS模拟相同条件下的三角形薄壁简支梁,求解得到扭转振动频率,并与本文理论公式进行对比分析,验证了本文理论公式的正确性.At present,Umanski's second theory predominantly governs the classical analysis of torsional behavior in thin-walled members with closed sections.This paper abandons the sectorial coordinates of classical theory and studies the torsional vibration of triangular thin-walled beams based on the plate-beam theory.By leveraging the mechanical models of Timoshenke beam and Kirchhoff plate,the total strain energy and torsional stiffness of triangular thin-walled beam are calculated.Introducing the cross-sectional displacement component into the kinetic energy equation,the paper establishes the total potential energy equation for a triangular thin-walled beam.The theoretical solution of the torsional vibration frequency of a triangular thin-walled beam simply supported on both sides is obtained.Through ANSYS simulation of a triangular thin-walled simply supported beam under the same conditions,the torsional vibration frequency is obtained and compared with the theoretical formula,which verifies the correctness of the theoretical formula in this paper.

关 键 词：扭转振动 板-梁理论 能量变分法 自由振动 薄壁构件 

分 类 号：TU391[建筑科学—结构工程]