## 留言板

 引用本文: 陈政清. 万因斯坦-钱伟长法的应用——简支与固支混合边界矩形板基频上下限[J]. 应用数学和力学, 1984, 5(3): 437-446.
Cheng Zheng-qing. The Application of Weinstein-Chien’s Method——The Upper and Lower Limits of Fundamental Frequency of Rectangular Plates with Edges Which Are a Mixture of Simply Supported Portions and Clamped Portions[J]. Applied Mathematics and Mechanics, 1984, 5(3): 437-446.
 Citation: Cheng Zheng-qing. The Application of Weinstein-Chien’s Method——The Upper and Lower Limits of Fundamental Frequency of Rectangular Plates with Edges Which Are a Mixture of Simply Supported Portions and Clamped Portions[J]. Applied Mathematics and Mechanics, 1984, 5(3): 437-446.

## The Application of Weinstein-Chien’s Method——The Upper and Lower Limits of Fundamental Frequency of Rectangular Plates with Edges Which Are a Mixture of Simply Supported Portions and Clamped Portions

• 摘要: 本文将边界条件放松法[1][2]应用于简支与固支混合边界矩形板,求得此类板的基频下限值.文中还设计了一种能满足位移边界条件的多项式作为振型试函数,从而用里兹法得到相应的上限值.具体算例得到了满意的结果.最后本文指出,通常用力法迭加法得到的此类板的所谓精确解,若考虑实际计算的级数截断误差,本质上是一种下限解.
•  [1] (1) Weistein,A.and W.Z.Chien,On the vibrations of a clamped plate under tension,Quart.Appl.Math.,Vol.1,(1943),pp.61-68. [2] (2) 钱伟长.《变分法与有限元》(上册),科学出版社(1980) [3] (3) Kurata.M.and H.Okamura,Natural vibrations of partially clamped plate,ASCE.EM.,(1963.3),p.3561. [4] (4) 徐芝纶,《弹性力学》(下册).人民教育出版社(1979).28.

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##### 出版历程
• 收稿日期:  1983-05-15
• 刊出日期:  1984-06-15

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