This study deals with the impact of cylindrical eigenstrains on the traveling wave solutions of a neo-Hookean cylindrical rod. For this purpose, we consider an isotropic, incompressible neo-Hookean rod with the symmetrical distribution of radial, circumferential and longitudinal eigenstrains. To establish the momentum balance equations, we construct a Riemannian manifold as the reference configuration, and then place it in Euclidean space. Assuming that the rod has an axisymmetric region with uniform eigenstrains, we extend and simplify the governing equations to come up with the final nonlinear differential equation. After thorough analysis of this equation, we introduce a traveling wave which is not observed in an eigenstrain-free rod and also explain how the cylindrical eigenstrains affect the velocities. In addition, we propose an important solution, stating that with special quantities of the eigenstrains, any arbitrary function can be a traveling wave in the rod (provided that it is physically acceptable). To substantiate this claim, we find those eigenstrain parameters by which the equilibrium equation is satisfied automatically. Proving that these waves are of equal velocities, we can say that this solution is similar to d’Alembert’s solution in linear approaches.

这项研究处理圆柱特征应变对新霍克式圆柱棒的行波解的影响。为此，我们考虑了各向同性，不可压缩的新霍克杆，该杆具有径向，周向和纵向特征应变的对称分布。为了建立动量平衡方程，我们构造了黎曼流形作为参考配置，然后将其放置在欧几里得空间中。假设杆具有一个具有均匀特征应变的轴对称区域，我们可以扩展和简化控制方程，以得出最终的非线性微分方程。经过对该方程的彻底分析，我们引入了在无本征应变的杆中未观察到的行波，并解释了圆柱本征应变如何影响速度。此外，我们提出了一个重要的解决方案，指出如果使用特殊数量的本征应变，则任意函数都可以是杆中的行波（只要它在物理上是可以接受的）。为了证明这一点，我们找到了自动满足平衡方程的那些特征应变参数。证明这些波具有相同的速度，可以说该解与线性方法中的d'Alembert解类似。