圆弧形波纹膜片的矩阵联乘解法
The Method of Matrices Conjoint Multiplication for the Problem of Circular Arc Corrugated Diaphragm
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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].
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[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. -
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