一种多层组合梁自由振动分析的混合有限元法  

A mixed finite element method for free vibration analysis of multilayer composite beams

作　　者：蒋佳卿 王云[3] 陈伟球[4] 徐荣桥[1,2] JIANG Jia-qing;WANG Yun;CHEN Wei-qiu;XU Rong-qiao(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,China;Center for Balance Architec-ture,Zhejiang University,Hangzhou 310007,China;School of Mechanical Engineering,Hangzhou Dianzi University,Hangzhou 310018,China;School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江大学平衡建筑研究中心,浙江杭州310007 [3]杭州电子科技大学机械工程学院,浙江杭州310018 [4]浙江大学航空航天学院,浙江杭州310027

出　　处：《振动工程学报》2024年第5期856-863,共8页Journal of Vibration Engineering

基　　金：浙江省尖兵领雁研发攻关计划项目(2022C01143);国家自然科学基金资助项目(12072097)。

摘　　要：基于截面等效,提出了多层组合梁的二维分析模型。使用混合能变分原理,以包含频率函数的节点位移及其能量对偶的应力分量为单元节点未知量,引入混合元对梁长方向进行离散,建立动力学状态空间控制方程;接着引入微分求积法(Differential Quadrature Method,DQM)对控制方程进行梁高度方向的离散,求得组合梁在不同轴力与边界条件下的动力学方程。以混凝土-木材组合梁、波形钢腹板梁和钢-混组合梁为例进行验证。该方法基于二维理论,可为梁理论提供假设依据和误差分析的基准。In this paper,a two-dimensional analytical model for composite beams is first proposed through the equivalent transformation of the cross-section.Based on the mixed variational principle,the dynamic state equations are derived through finite element meshing and interpolation along the length of the beam,with frequency contained nodal displacements and their energy-conjugated stresses as element nodal variables.The differential quadrature method(DQM) is introduced to discretize the equations along the height of the beam,and natural frequencies of composite beams under different axial forces and boundary conditions are obtained.This method was verified by numerical examples about natural frequencies of three beams,i.e.a concrete-wood composite beam,a concrete beam with a corrugated steel web and steel-concrete composite beam.Since the proposed method is based on the two-dimensional theory,it can provide benchmarks for beam theories and error analyses.

关 键 词：自由振动 组合梁 混合有限元 DQM 状态空间法 

分 类 号：O327[理学—一般力学与力学基础]