多参数多状态变量离散型有势非线性稳定问题的活化方法*
The Activation Method for Discretized Conservative Nonlinear Stability Problems with Multiple Parameter and State Variables
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摘要: 本文针对多参数变量和多状态变量的离散型有势系统的非线性稳定问题,提出了活化方法,导出了活化势函数和活化平衡方程.活化方法是弹性稳定理论中Liapunov-Schmidt方法的改进和提高,它比通常的摄动方法更加一般化、规范化.活化势函数可变换成标准突变势函数,活化平衡方程可作为分岔方程.本文的研究将促进弹性稳定理论与突变理论和分岔理论的结合.Abstract: For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory.
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[1] Thompson,J.M.T.and G.W.Hunt,A General Theory of Elastic Stability,Wiley(1973). [2] Thompson,J.M.T.,Elastic Instability Phenomena,Wiley(1984). [3] Poston,T.and I.Stewart,Catastrophe Theory and Its Applications,Pitman(1978). [4] Chow,S.N.and J.K.Hale,Methods of Bifurcation Theory,Springer-Verlag(1982). [5] 邓长根,加权残值法和突变理论的结合,《第四届全国加权残值法会议论文集》(1992). [6] 邓长根,突变理论在结构稳定分析中的应用,结构工程学报,2(3-A) (1991). -
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