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 In ibis paper, we proved the existence of infinite many solutions and nodal character of the solutions for singular quasilinear boundary value problems(1), (2). From our result, we can get the existence of infinite many radial solutions and the nodal character of solutions for pLaplace equations(3), (4) if we take ρ(t)=t~(N1) in(1), (2).  本文证明了R~+上含奇性拟线性边值问题(1),(2)的无穷多解的存在性及其波节性质。当(1),(2)中ρ(t)=t~(N1)时则可得到关于pLaplace方程(3),(4)的相应结论。  With the help of the concept of virtual regions and the character of solution curve, a practical algorithm is presented for finding the multiple solutions of DC canonical piecewiselinear resistive networks. The advantage of this algorithm is that there is no repeatedly noneffective iterative procedure throughout the complete operation. Regardless of how many solutions being in the network, the total number of iterative steps is only dependent on the number of the regions made up of the hyperplanes... With the help of the concept of virtual regions and the character of solution curve, a practical algorithm is presented for finding the multiple solutions of DC canonical piecewiselinear resistive networks. The advantage of this algorithm is that there is no repeatedly noneffective iterative procedure throughout the complete operation. Regardless of how many solutions being in the network, the total number of iterative steps is only dependent on the number of the regions made up of the hyperplanes in the Rn. This algorithm is simple in concept and easy in programing. It can be used to find all solutions of piecewiselinear resistive netvvorks with a common microcomputer.  本文采用虚区域的概念和解曲线的基本性质,提出了求规范化分段线性化电阻钢络多解的实用算法。它的特点是整个求解过程没有重复无效的迭代步骤,不论网络有多少个解,求出全部解的总迭代步骤数仅取决于定义域R~n由超平面分割而成的区域总数。它所依据的概念简单,易编程序,在一般微机上能解多个非线性元件的网络,比较实用。  In this paper, a new mathematical model of the shaft crack opening and closing is developed. In the model, the time of open close lasting and the procedure between the two states are considered. The open crack, the' square wave' and the cosine model are the particular cases of this model. This model is not limited by the relationship of dynamic deflection and static deflection when being used. The stiffness coefficients of the cracked shaft calculated with this model are more approaching the experiment results... In this paper, a new mathematical model of the shaft crack opening and closing is developed. In the model, the time of open close lasting and the procedure between the two states are considered. The open crack, the' square wave' and the cosine model are the particular cases of this model. This model is not limited by the relationship of dynamic deflection and static deflection when being used. The stiffness coefficients of the cracked shaft calculated with this model are more approaching the experiment results than those with the' square wave' and the cosine model. In the numerical example of Jeffcott cracked rotor, the models are used and some comparison results is given. When unsynchronous vibration being studied, the solutions of our model are quite different from those of the' square wave' and the cosine model; the change of vector direction of shaft displacement near the static balance position has some effects on the character of solution. When synchronous vibration being studied, the differences and the effects are very little.  本文提出了一种新的描述转轴裂纹开闭状态的数学模型,此模型描述了裂纹开、闭及过渡状态的持续过程,它将开裂纹、方波和余弦模型统一于同一模型中,它的使用不受动、静挠度关系的限制.用这个模型算得的裂纹轴刚度变化曲线与实验结果吻合程度比余弦和方波模型好.文中还以Jeffcott裂纹转子为例,对各模型进行了理论探讨.结果表明:当研究非同步运动时,本文模型与方波和余弦模型所得的解差别较大,且轴心位移矢量的方向角在静平衡位置处的波动,影响到所得响应的特性.而对同步运动,这种差别及影响都很小.   << 更多相关文摘 
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