旋转薄壳振动耦合转点问题的一致有效解

旋转薄壳自由振动转点问题具有弯曲解和无矩解的耦合特性.用3类广义函数族表示得到了该耦合转点问题的薄壳全域一致有效解,该解在低频段、转点频段和高频段均适用.所得解呈现出弯曲解和无矩解的对称耦合结构.

量子非线性谐振子的一致有效渐近解

使用两参量法求得了量子非线性谐振子的能量及波函数对于ε＿１为Ｎ阶和对ε＿２为Ｍ阶的一致的效渐近解。由该方程获得的能量中，由于（ｎ为偶数，ｍ≠０）不为零，使得其能量修正值具有更高的可靠性．

四边固定变厚度正交各向异性矩形板的非线性非对称弯曲问题的一致有效渐近解

利用"修正的两变量法"和"混合摄动法",引进4个小参数,对厚度线性变化的正交各向异性矩形板的非线性非对称弯曲问题进行了研究,得到了挠度函数W(x,y)和应力函数Φ(x,y)

群体多目标规划的群体一致Pareto有效存在性

本文对群体多目标规划(Group Multiobjective Programming)(GMP)的群体一致Pareto有效解和群体一致Pareto弱有效解的存在性进行了初步探讨,并引进了(GMP)的群体一致p—Pareto(弱)有效解定义.

旋转薄壳转点频段的轴对称振动解

用渐近方法求解了含转点频段的旋转薄壳自由振动方程,重新定义了第一和第二类广义相关函数,求得了一致有效解.该解的新颖之处在于具有对称的耦合结构,即转点一侧的奇异无矩解在另一侧含有快变弯曲解成分,同时转点一侧的1个弯曲解在另一侧含有慢变无矩解成分.数值计算表明,所得一致有效解与有限元计算结果吻合.

旋转薄壳自由振动中3类广义相关函数的求解

为求解旋转薄壳自由振动问题中起关键作用的3类广义相关函数,采用数值计算方法详尽研究这3类函数,得到其精确解答.通过此解答可以解决旋转薄壳自由振动一致有效解的求解问题.

The Uniformly Valid Solution for a Top System of Two Free Dimensions with Parameter

A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.

Singular Perturbation of a Class of Dirichlet Exterior Problems for Elliptic Equations

In this paper, we consider a class of singularly perturbed Dirichlet exterior problems for elliptic equations. Under the appropriate conditions we construct the formally asymptotic solution of the problem described. Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution.