基于精确算法的单跨曲线梁结构模态分析  

Modal Analysis of Single-Span Curved Beam Structure Based on Precise Algorithm

作　　者：李晓飞 陈鸣东 尹赫男 孙宗光 LI Xiaofei;CHEN Mingdong;YIN Henan;SUN Zongguang(School of Transportation Engineering,Dalian Maritime University,Dalian 116026,China)

机构地区：[1]大连海事大学交通运输工程学院,大连116026

出　　处：《结构工程师》2022年第2期8-15,共8页Structural Engineers

基　　金：国家自然科学基金(51808092)。

摘　　要：从常曲率单跨曲线梁的动力学离散模型出发,推导出剪、弯、扭耦合的曲线梁刚度矩阵。结合曲线梁集中质量矩阵和多自由度系统运动方程的特征方程进行算法编写,计算出各阶固有频率及振型。通过对比所得到的刚度矩阵与有限元刚度矩阵各自的集成方法,直观展示了曲线梁结构刚度矩阵的分布形式,并论述了两种刚度矩阵的特征。并将刚度矩阵参与模态分析的计算结果与有限元数值仿真结果进行了对比分析,结果表明:前者逼近真解速度快于后者,虽然在中低阶时所求解的各阶固有频率吻合较好,但有限单元法在高阶转动振型求解精度方面存在一定误差。所编写的计算程序可为实际工程中精确求解曲线梁结构模态提供参考。The stiffness matrix of the curve beam coupled by shear,bending and torsion was derived based on the dynamic discrete model of a single-span curve beam with constant curvature.The algorithm was written with reference to the concentrated mass matrix of the curved beam and the characteristic equation of the motion equation of the multi-degree-of-freedom system,and the natural frequencies and modes of each order were calculated.By comparing the respective integration methods of the stiffness matrix and the finite element stiffness matrix,the distribution form of the stiffness matrix of curved beam structure is intuitively shown.the characteristics of the two stiffness matrices were discussed.The calculation results of the stiffness matrix of this article involved in the modal analysis and the finite element numerical simulation results were compared and analyzed.The results demonstrated that the former approaches the true solution faster than the latter,though the calculated natural frequencies of the middle and low orders were in good agreement.However,the finite element method has certain errors in the accuracy of solving high-order rotational modes.The written calculation program could provide reference for accurately solving the modal of curved beam structure in actual engineering.

关 键 词：单跨曲线梁 刚度矩阵 频率和振型 有限元 

分 类 号：U441[建筑科学—桥梁与隧道工程]