均匀热环境下四边固支矩形PCB薄板的自由振动

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (12) : 75-79.

论文

均匀热环境下四边固支矩形PCB薄板的自由振动

高军，黄再兴

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Free Vibration of PCB Rectangular Thin Plate with Completed Clamped Support Subjected to Thermal Environment

GAO Jun，HUANG Zai-xing

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文章历史 +

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。本文结论可为矩形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。

Abstract

PCB board in SMT (surface mount technology) can be simplified as a rectangular thin plate with completed clamped support. Based on the small deflection theory, the differential equation of rectangular thin plate subjected to thermal load is derived. The differential equation shows that 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 simulated with a clamped thin plate with uniform in-plane tension. Using virtual displacement theory, the methods to calculate natural frequency and deflection are presented. The influences of geometry size and temperature on the natural frequencies of plate are discussed. Some valuable conclusions are given.

导出引用

高军;黄再兴. 均匀热环境下四边固支矩形PCB薄板的自由振动[J]. 振动与冲击, 2014, 33(12): 75-79

GAO Jun;HUANG Zai-xing. Free Vibration of PCB Rectangular Thin Plate with Completed Clamped Support Subjected to Thermal Environment[J]. Journal of Vibration and Shock, 2014, 33(12): 75-79