关于压杆屈曲载荷及自振基频的计算分析  

Calculation and Analysis of Buckling Load and Natural Frequency of Compression Bar

作　　者：刘意中 吴晓 肖珍 LIU Yi-zhong;WU Xiao;XIAO Zhen(School of Intelligent Building,Changde College,Changde 415000,China)

机构地区：[1]常德学院智能建筑学院,常德415000

出　　处：《湖南师范大学自然科学学报》2025年第1期130-136,共7页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(52008164)。

摘　　要：研究了压杆屈曲载荷及自振基频的计算问题。基于高阶剪切变形理论,针对圆形和矩形截面压杆,假设杆轴向位移为沿杆截面高方向的高阶函数,利用剪切应变、轴向位移和弯曲挠度的几何关系,推导出了压杆弯曲挠曲线表达式。结合Galerkin原理,利用有限元法和相关实验,探讨了压杆屈曲载荷及自振基频的计算。研究结果表明:采用高阶剪切变形理论研究压杆自振基频,取指数n=9时计算得到的自振基频值精度最高。用振动法做测试压杆屈曲载荷的实验时,建议采用高阶剪切变形理论研究压杆屈曲载荷。在实际工程中,可以采用高阶剪切变形理论研究压杆的屈曲载荷及自振基频。The study investigated the calculation issues of buckling load and natural frequency of compression bars.Based on the high-order shear deformation theory,for circular and rectangular cross-section compression bars,assuming the axial displacement of the bar as a high-order function along the height direction of the section,the expression of the bending deflection curve of the compression bar was derived using the geometric relationships between shear strain,axial displacement,and bending deflection.By combining the Galerkin principle with finite element method and relevant experiments,the calculation of buckling load and natural frequency of compression bars was explored.The research results indicate that using the high-order shear deformation theory to study the natural frequency of compression bars,with the exponent n=9,yields the highest accuracy in calculating the natural frequency value.When conducting experimental tests on the buckling load of compression bars using vibration methods,it is recommended to use the high-order shear deformation theory to study the buckling load of compression bars.In practical engineering applications,the high-order shear deformation theory can be fully employed to study the buckling load and natural frequency of compression bar.

关 键 词：压杆 屈曲载荷 自振 基频 高阶剪切 

分 类 号：O341[理学—固体力学]