径向压力作用下夹层圆板自由振动理论解  

Analytical Solution of Free Vibration of Sandwich Circular Plate Subjected to Radial Compression

作　　者：廖明建[1] 李映辉[2] 

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621999 [2]西南交通大学力学与工程学院,成都610031

出　　处：《噪声与振动控制》2014年第3期11-14,共4页Noise and Vibration Control

基　　金：国家自然科学基金(11072204);中央高校业务费专项(SWJTU11ZT15);中国工程物理研究院科学技术发展基金重点资助项目(2010A0203007)

摘　　要：基于小挠度薄板理论,建立径向均布压力作用下夹层圆板的振动控制方程。采用分离变量法导出夹层圆板的固有频率及振型解析式,计算径向均布压力作用下周边固支夹层圆板固有频率和振型,讨论径向均布压力和夹心层比率对固有频率的影响。研究表明夹层圆板的固有频率随径向压力增大而减小,临界压力随阶次的增大而增大;作用径向压力的夹层圆板固有频率随夹心层比率增大,先缓慢增大,到峰值后减小,该趋势与无径向压力时相同。Based on the basic assumptions of elastic thin plates, the vibration control equation of a sandwich circular plate subjected to uniform radial compression is established. The analytical expressions of natural frequencies and vibration modes are derived by employing the method of separate variables. The natural frequencies and modes of a clamped sandwich circular plate are calculated. The influence of radial compression and core ratio on natural frequency is discussed. It is concluded that the natural frequency decreases with the radial compression increasing, the critical compressive force increases with the increase of orders, and the natural frequency of the plate increases at first and then decreases with the increase of core ratio.

关 键 词：振动与波 夹层圆板 固有频率 径向均布压力 

分 类 号：O326[理学—一般力学与力学基础]