摘要
针对正交各向异性梁的振动问题,本文基于卡雷拉定理建立了多种边界下正交各向异性梁结构的振动分析模型。将正交各向异性梁结构的位移函数分离为截面和轴向位移2部分。依据卡雷拉定理拟合梁结构的截面位移变形,利用有限元分段插值函数给出梁的轴向位移。结合三维弹性理论建立梁结构的能量表达式,并由最小势能原理推导梁结构3×3阶核心质量矩阵和刚度矩阵。采用划行化列、赋大数等有限元边界施加方法得到特定的动力学方程,进而获得正交各向异性梁的自由振动特性,并开展了多种边界条件下正交各向异性梁结构的数值算例。对比分析表明:本文方法具有较好的收敛速度,计算结果与文献数据和有限元商业软件仿真结果吻合良好。
Based on the Carrera unified formulation (CUF), this study established a dynamic model for orthotropic beams under various boundary conditions to solve the vibration problem. The displacement function of the orthotropic beam was divided into two parts: cross sectional and axial. The cross-sectional displacement deformation function was fitted with the CUF, and the axial displacement was obtained using the finite element piece wise interpolation function. The energy function of the beam structure was established using three-dimensional elasticity theory. Then, the 3×3 nuclear mass and rigid matrices of the beam were derived using the principle of minimum potential energy. The finite element boundary methods, such as delimited rows and columns, assigned large numbers, and so on, were used to obtain the specific dynamic equations, subsequently obtaining the free vibration characteristics of orthotropic beams. Lastly, numerical examples of orthotropic beams under various boundary conditions were given. Results show that the proposed method has a good convergence rate, and the calculation results are in good agreement with the data in the literature and the simulation results obtained by the commercial software of finite element.
作者
刘瑞杰
王雪仁
贾地
LIU Ruijie;WANG Xueren;JIA Di(92578 Troops,People′s Liberation Army,Beijing 100161,China;College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
北大核心
2020年第4期556-561,共6页
Journal of Harbin Engineering University
基金
海军预研基金项目(995-0204010706).
关键词
正交各向异性材料
自由振动
卡雷拉定理
有限元方法
梁结构
三维理论
最小势能原理
核心矩阵
orthotropic material
free vibration
Carrera unified formulation
finite element method
beam structure
three-dimensional theory
principle of minimum potential energy
nuclear matrices
