Abstract The axisymmetric longitudinal waves propagating in the long infinite cylindrical rod composed of material and structural constants, combinedly called as general incompressible materials, are derived using the perturbation reduction method as the far-field equation in the form of KdV equation in Dai and Huo (2002). In this work, the F expansion method is applied to the far-field equation and the properties of longitudinal strain waves travelling in the cylindrical rod are studied. The behaviour of the strain waves is analysed with the material and structural constants. To support the study, the graphs are drawn in the two and three dimensional surfaces. The obtained longitudinal strain waves are in the form of Jacobi elliptic function and necessary condition for the existence of each wave is provided.

中文翻译：

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在由一般不可压缩材料组成的无限长圆柱杆中传播的纵向应变波及其雅可比椭圆函数解

摘要 轴对称纵波在由材料常数和结构常数组成的无限长圆柱杆中传播，合称为一般不可压缩材料，采用微扰约减法作为远场方程推导出KdV方程形式的Dai和Huo ( 2002）。在这项工作中，将 F 展开方法应用于远场方程，并研究了在圆柱杆中传播的纵向应变波的特性。应变波的行为通过材料和结构常数进行分析。为了支持这项研究，在二维和三维曲面上绘制了图形。得到的纵向应变波为雅可比椭圆函数形式，并给出了各波存在的必要条件。