GPLs/Al复合材料阵列开口结构的自由振动  

Free vibration of GPLs/Al composite with an array cutouts

作　　者：颜建伟 江思岑 何陵辉[3] YAN Jianwei;JIANG Sicen;HE Linghui(State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,China;School of Civil Engineering and Architecture,East China Jiaotong University,Nanchang 330013,China;CAS Key Laboratory of Mechanical Behavior and Design of Materials,University of Science and Technology of China,Hefei 230027,China)

机构地区：[1]华东交通大学轨道交通基础设施性能监测与保障国家重点实验室,江西南昌330013 [2]华东交通大学土木建筑学院,江西南昌330013 [3]中国科学技术大学中国科学院材料力学行为和设计重点实验室,安徽合肥230027

出　　处：《振动工程学报》2025年第3期612-622,共11页Journal of Vibration Engineering

基　　金：国家重点研发计划资助项目(2023YFC3009400);国家自然科学基金资助项目(12072112);江西省自然科学基金资助项目(20232ACB204028)。

摘　　要：针对板经典解析解中不可避免的场函数假设依赖边界约束问题,提出一种具有高自由选择性的一般性场函数方法,研究GPLs/Al复合材料板阵列开口结构的自由振动特性。场函数由高自由度的基函数和待定权重系数求积后求和得到,其中权重系数具有线性相关性,其基础解系恰好由边界约束的位移函数线性方程组确定,因此边界约束的改变只需要修改边界位移函数线性方程组。由此建立的一般性场函数半解析法在处理边界约束上既解决了场函数依赖边界问题,又具备了快速转换边界条件的优点,同时在开口结构和阵列结构上以微分求和替代积分的计算方式具有更高的计算效率和鲁棒性。本文在GPLs/Al复合材料板单开口及阵列开口的自由振动研究中,从固有频率和模态分析发现,随着开口分布的均匀性增加,开口结构的质量矩阵和刚度矩阵同步减小,其自由振动特性趋于完整板的自由振动特性。In this paper,we propose a general displacement field function method,which consists of the highly freely chosen basic function and a series of undetermined weighted coefficients to study the free vibration characteristics of GPLs/Al composite plate with an array cutouts.This general displacement field function method can solve the boundary constraint dependence when choosing the displacement field function to obtain the analytical solution in classical plate theory.There is a linear correlation between the weight coefficients.The system of linear equations is constructed based on the boundary constraints,thus the fundamental system of solutions can then be determined.By changing the system of linear equations as well as the fundamental system of solutions,the type of boundary constraint can be easily transferred.This proposed semi-analytic method not only solves the problem of assumed field function dependence on boundary constraints in the classical solution,but also has the superiority of fast conversion of boundary conditions.Meanwhile,by introducing the scatter integral method,a much more efficient and robust method is obtained other than the continuous integral method on the study of free vibration for the structure with an array cutouts.In this paper,we study the free vibration of GPLs/Al composite plates with a single and array cutouts.From the natural frequency and modal analysis,it is found that the generalized mass matrix and stiffness matrix of the open structure decrease synchronously when the cutouts distributed uniformly,and its free vibration characteristics tend to that of the complete plate.

关 键 词：自由振动 GPLs/Al复合材料 阵列开口 一般性场函数法 

分 类 号：O323[理学—一般力学与力学基础] TB333[理学—力学]