均匀热环境下四边固支矩形PCB薄板的自由振动  

Free vibration of a PCB rectangular thin plate with 4-side clamped support under thermal environment

作　　者：高军[1] 黄再兴[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《振动与冲击》2014年第12期75-79,共5页Journal of Vibration and Shock

基　　金：航空科学基金(20080252)资助项目;江苏高校优势学科建设工程资助项目

摘　　要：表面贴装形式中PCB板可简化为四边固支矩形薄板。基于刚性板的小挠度理论,推导了热载下四边固支矩形PCB薄板的自由振动微分方程。从微分方程中得出,热载下的PCB薄板等效于面内受均布张力的薄板,进而通过结构力学方法将热载下四边固支薄板振动问题转换为受面内均布张力固支薄板振动问题。利用虚位移理论,得出了温度沿厚度均匀线性变化的热载下四边固支矩形PCB薄板固有频率和自由振动的挠度值的计算方法。讨论了热载下温度、薄板的几何尺寸对矩形PCB薄板自由振动固有频率的影响。结论可为矩形PCB薄板在热载下的振动分析以及固有频率计算提供方法上的参考。PCB board in SMT （surface mount technology） can be simplified as a rectangular thin plate with 4-side clamped support.Based on the small deflection theory,the free vibration differential equation of a rectangular thin plate subjected to thermal load was derived.The differential equation showed that the thermal load applied on the PCB thin plate is equivalent to a uniform in-plane tension of the plate,so the clamped plate vibration under thermal environment can be converted into a clamped thin plate vibration with uniform in-plane tension.Using the virtual displacement theory,the methods to calculate natural frequencies and deflections of the plate were presented.The influences of geometric size and temperature on the natural frequencies of the plate were discussed.Some valuable conclusions were drawn.

关 键 词：PCB矩形薄板 热环境 四边固支 微分方程 固有频率 

分 类 号：O343[理学—固体力学]