Abstract 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.

中文翻译：

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热超弹性新胡克圆柱壳中不同类型的孤立波

摘要 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。在这里，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微分动力系统。考虑了温度场的影响。此外，该结构从一维杆扩展到三维圆柱壳。然后根据分岔理论对系统进行详细的定性分析，并针对分岔参数确定其对应的临界分岔值。结合不同参数下相图中的轨道，在壳中发现孤立波和周期波。值得指出的是，具有谷形的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剖面。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。