Novozhilov环壳方程的新解
New Solutions of Novozhilov’s Equation of Toroidal Shells
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摘要: 当环壳的细度比α(=α/R)取一般值时0<α<1求得Novozhilov方程的新解.与连分法的结果相比,这里级数解的指标和展开系数全是封闭的显式.直接验证,此级数解满足方程.给出收敛性证明.边缘效应的范围和单值群的指标也都用显式表述.最后讨论本法适用于求解旋成薄壳的基本方程组.Abstract: New solutions are obtained for Novozhilov's equation of toreidal shells having general slenderness ratio 0<a<1(a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.
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[1] Novozhilov,V,V.,Theory of Thin Shells(1951),(俄文),第四章(及其中引用的文献). [2] 钱伟长、郑思棵,轴对称圆环壳的一般解,应用数学和力学,(1980),287-300. [3] 钱伟长、郑思裸,半圆弧波纹管的计算—环壳一般解的应用,应用数学和力学,2,1(1981),97-111. [4] 董明德,Poincar非正则积分问题(讲义,待出版). [5] Dong Ming-de,(a)Non-perturbative solutions of Bloch-Mathieu Hamiltonian system. [6] Physics Letters,97A,7,Sep,(1983),275一279.(b)The problem of secular terms:Non-perturbative analysis of the Hill-Bloch system,ibid.,98A,4 Oct,(I983),156-160. -
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