Different types of solitary waves in a thermo-hyperelastic neo-Hookean cylindrical shell
Different types of solitary waves in a thermo-hyperelastic neo-Hookean cylindrical shell
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热超弹性新胡克圆柱壳中不同类型的孤立波
DOI：
10.1016/j.compstruct.2020.112178
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发表时间：
2020
影响因子：
6.3
通讯作者：
Chen Li-Qun
中科院分区：
文献类型：
--
作者：
Wang Ran;Ding Hu;Yuan Xuegang;Lv Na;Chen Li-Qun
基于超弹性材料模型，研究了非线性行波在圆柱杆中的传播。这里，确定了热超弹性新胡克圆柱壳中不同类型的非线性行波。利用变分原理，推导出描述壳轴对称运动的复杂微分动力系统。考虑了温度场的影响。而且，结构从一维的杆延伸到三维的圆柱壳。然后根据分岔理论对系统进行了详细的定性分析，对于分岔参数，确定了其对应的临界分岔值。结合不同参数下相图中的轨道，发现壳层中存在孤立波和周期波。值得指出的是，谷形孤立波可能出现在壳的径向方向。给出了这些行波的隐式解析解和轮廓。强非线性行波的传播在检测结构缺陷和确定材料参数方面具有广阔的前景。
Based on the hyperelastic material models, the propagation of nonlinear travelling waves in cylindrical rods has been studied. Here, different types of nonlinear travelling waves in a thermo-hyperelastic neo-Hookean cylindrical shell are determined. By using the variational principle, a complex differential dynamical system describing the axisymmetric motion of the shell is derived. The effect of the temperature fields is considered. Moreover, the structure is extended from a one-dimensional rod to a three-dimensional cylindrical shell. Then in terms of the bifurcation theory, a detailed qualitative analysis of the system is carried out, and for the bifurcation parameters, their corresponding critical bifurcation values are determined. Combining with the orbits in phase diagrams under different parameters, solitary waves and periodic waves are found in the shell. It is worth pointing out that the solitary waves with the valley form may appear in the radial direction of the shell. The implicit analytical solutions and profiles of these travelling waves are given. There is a promising prospect for the propagation of strongly nonlinear travelling waves to detect structural defects and determine material parameters.