功能梯度开孔平行四边形板的等几何振动分析  

Isogeometric vibration analysis of functionally graded perforated parallelogram plates with holes

作　　者：钟锐 胡双卫 秦斌 王青山 ZHONG Rui;HU Shuangwei;QIN Bin;WANG Qingshan(State Key Laboratory of High-Performance Complex Manufacturing,Central South University,Changsha 410083,China;School of Traffic&Transportation Engineering,Central South University,Changsha 410083,China)

机构地区：[1]中南大学高性能复杂制造国家重点实验室,湖南长沙410083 [2]中南大学交通运输工程学院,湖南长沙410083

出　　处：《哈尔滨工程大学学报》2022年第7期999-1005,共7页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(51705537);湖南省自然科学基金项目(2021JJ30841)。

摘　　要：针对功能梯度开孔平行四边形板的自由振动问题,本文基于一阶剪切变形层合理论,利用等几何法研究开矩形孔的功能梯度平行四边形板的振动特性。结构位移变量采用具备高阶连续性的非均匀有理B样条函数表征,并引入边界弹簧和坐标映射技术建立一般边界下功能梯度开孔板的自由振动模型。数值算例中,通过等几何法结果与有限元结果间的对比验证等几何法模型的正确性,进而分析梯度指数、边界约束、几何角度等对开孔板振动特性的影响。结果表明:板的频率参数随铝基成分增加而减小,边界刚度增大会使结构频率增大,角度对结构频率的影响与模态阶次、边界条件相关联。The vibration characteristics of functionally graded(FGM)parallelogram plates with rectangular holes are studied using an isogeometric approach to address the free vibration problem based on the lamination theory of first-order shear deformation(IGA).Nonuniform rational B-spline(NURBS)functions with high-order continuity are used to characterize the structural displacement variables,and boundary springs and coordinate mapping techniques are used to establish the free vibration model of a functionally graded perforated plate with general boundaries.The correctness of the IGA model is demonstrated in the numerical example by comparing the IGA and finite element results.The effects of gradient index,boundary constraints,and geometric angles on the perforated plate vibration characteristics are investigated.Results reveal the following:the frequency parameter of the plate decreases with increasing aluminum composition;the increase in the boundary stiffness increases the structural frequency;the influence of the angle on the structural frequency is related to the modal order and boundary condition.

关 键 词：功能梯度结构 平行四边形板 矩形孔 等几何法 自由振动 非均匀有理样条 边界弹簧 坐标映射 

分 类 号：TU311.3[建筑科学—结构工程] TU352.1