Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions  

复杂边界条件下含圆形通孔的矩形板振动特性建模及分析

作　　者：TANG Tianyi HE Yijie WU Jiajun DONG Menglong WANG Gang NI Junfang 唐天逸;何逸杰;吴佳俊;董梦龙;王刚;倪俊芳(苏州大学机电工程学院,苏州215131)

机构地区：[1]School of Mechanical and Electrical Engineering,Soochow University,Suzhou 215131,P.R.China

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2024年第4期515-525,共11页南京航空航天大学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.51805341);the Science and Technology Major Project of Ningbo City(No.2021Z098)。

摘　　要：This paper presents a method to study the free vibration of a plate with circular holes.The circular hole is regarded as a virtual small plate in which the mass density and Young's modulus are zero.Therefore,the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness.The model is derived from the spectral geometry method(SGM),and the displacement of the plate with circular holes is expanded by the modified Fourier series.Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports.The accuracy of this method is verified by comparison with the finite element calculation results.The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied.提出了一种研究带圆孔弹性约束平板自由振动的方法。该方法将圆孔视为一个虚拟小板,其密度和杨氏模量为零,则带圆孔板的自由振动问题可以转化为非均匀厚度等效矩形板的自由振动问题。该模型基于谱几何法(Spectral geometry method,SGM)导出,用修正的傅里叶级数展开带圆孔板的位移;在板的边界加入虚拟弹簧以模拟板的简支和固支边界条件。通过与有限元计算结果的对比,验证了该方法的准确性。同时本文还研究了带圆孔板模态数值解与边界条件和板的几何尺寸的关系。

关 键 词：round hole plate spectral geometry method(SGM) energy method virtual spring 

分 类 号：TB31[一般工业技术—材料科学与工程]