Asymptotics of cellular buckling close to the Maxwell load
Asymptotics of cellular buckling close to the Maxwell load
复制标题
接近麦克斯韦载荷的细胞屈曲渐近
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
R. Kuske
中科院分区：
文献类型：
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作者：
C. Budd;G. Hunt;R. Kuske
我们研究的变形的非线性Winkler基础上的弹性支柱进行轴向压缩载荷P.使用多尺度分析和数值方法，我们描述了本地化，细胞，后屈曲状态的系统时，P是从临界载荷P = 2。的解决方案，和他们的调制频率，显着不同的弱非线性分析预测非常接近P = 2。特别地，当P接近麦克斯韦负载PM时，局部化解接近未屈曲解和周期解之间的大振幅异宿连接。给出了PM关于系统参数的渐近描述。数值计算和渐近近似之间的协议是惊人的。
We study the deformation of an elastic strut on a nonlinear Winkler foundation subjected to an axial compressive load P. Using multi–scale analysis and numerical methods we describe the localized, cellular, post–buckled state of the system when P is removed from the critical load P = 2. The solutions, and their modulation frequencies, differ significantly from those predicted by weakly nonlinear analysis very close to P = 2. In particular, when P approaches the Maxwell load PM , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of PM in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.