圆弧形波纹膜片的矩阵联乘解法

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The Method of Matrices Conjoint Multiplication for the Problem of Circular Arc Corrugated Diaphragm

摘要: 将圆弧形波纹膜片看作几段圆环壳和中心圆板的组合构件,本文利用钱伟长教授的圆环壳一般解^[1]及圆薄板小参数振动理论^[2],导出环壳和板的传递矩阵和连接矩阵,用矩阵联乘法求得线性精确解和非线性解,计算结果同W.A.Wildhack的实验^[3]是吻合的.

Abstract: The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang's general the ring shell^[1] and perturbation theory of the circular thin plates^[2]. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The results agree with that of the experiments presented by W. A. Wildhack^[3].

[1]	钱伟长、郑思梁,轴对称圆环壳的一般解.应用数学和力学.1,3(1980),287-300.
[2]	钱伟长,Large deflection of a circular clamped plate under uniform pressure,中国物理学报,7,2(1947),102-113.
[3]	Wildhack,W.A.,R.F.Dressler,E.C.Lloyd,Investigations of the Properties of Corrugated Diaphragms,Trans.ASME.79,(1957),65-82.
[4]	Андрееве Л.Е.,Расчт гофрированных мембран,как анизптропных пластинок,Инженерныu Сборнuк,ХХI(1955),128-15-41.
[5]	樊大钧、黄黔,圆弧波纹膜片的理论分析和工程设计方法,《第二届仪器仪表学术年会论文集》,北京(1982).
[6]	钱伟长、樊大钧、黄黔.环壳理论与直交异性版理沦在计算三圆弧波纹膜片上的比较,应用数学和力学,5, 1 (1984), 41-48.