摘要
仪器设备中大量使用了四点简支状态矩形电路板结构,电路板结构的动力学特性对于电路板结构设计的频率管理、疲劳寿命设计有着重要的意义。本文针对电路板结构设计阶段中一阶频率快速预示的需求,开展四点简支矩形板振动特性半解析求解方法研究。提出了一种四点简支状态矩形板试函数表示形式,采用迭代抽样计算方式代替泛函变分方式求解试函数中的待定系数,最后基于Rayleigh-Ritz法完成四点简支矩形板一阶频率及模态振型的求解。半解析求解方法与有限元计算结果对比表明:半解析计算方法对迭代次数、网格密度不敏感,收敛性较好。对于长宽比小于1.8的矩形板,计算误差不超过8%,且计算时间极短。该方法可以应用于四点简支电路板一阶频率及疲劳寿命估算中,为仪器设备电路板结构设计提供有力的支撑。
A large number of four point simply supported rectangular circuit board structures are used in instrument equipment,and the vibration characteristics of the circuit board structure are of great significance for frequency management and fatigue life design of the circuit board structure.This article focuses on the demand for fast prediction of resonance frequency in the design stage of circuit board structures,and conducts a semi analytical solution method for the vibration characteristics of four point simply supported rectangular plates.A four point simply supported rectangular plate trial function representation was proposed,which used iterative sampling calculation instead of functional variational method to solve the undetermined coefficients in the trial function.Finally,the resonance frequencies and modal shapes of the four point simply supported rectangular plate were solved based on Rayleigh Ritz method.The comparison between the semi analytical solution method and the finite element calculation results shows that the semi analytical calculation method is insensitive to the number of iterations and grid density,and has good convergence.For rectangular plates with an aspect ratio less than 1.8,the calculation error does not exceed 8%and the calculation time is extremely short.This method can be applied to the estimation of resonance frequency and fatigue life of four point simply supported circuit boards,providing strong support for the structural design of instrument and equipment circuit boards.
作者
李志强
闫兴
侯传涛
程昊
王博
LI Zhiqiang;YAN Xing;HOU Chuantao;CHENG Hao;WANG Bo(Science and Technology on Reliability and Environmental Engineering Laboratory,Beijing Institute of Structure and Environment Engineering,Beijing 100076,China;Beijing Institute of Structure and Environment Engineering,Beijing 100076,China)
出处
《强度与环境》
2025年第3期1-9,共9页
Structure & Environment Engineering
