This study investigates the dynamical attitude of a nonlinear elastic circular rod’s longitudinal oscillation with lateral inertia and finite radius. This model was derived in 1986 by Wei and Gui-tong with a fourth-order nonlinear mixed derivative. The axial symmetry of this model has been thought through by using cylindrical coordinates. Furthermore, the strain and kinetic energy in the length unit of the rod have been determined. Two recent computational (extended Fan-expansion (EFE) and generalized rational (GR)) techniques are employed to construct some novel solitary wave solutions. The soliton wave solutions are obtained using Mathematica 13 software and are given with the distinct physical properties of trigonometric, hyperbolic and rational solution species. The stability of the investigated model and the obtained solutions through the suggested two analytical schemes are tested. Putting different values of the parameters explains these solutions through some numerical simulations in two-dimensional, three-dimensional and contour plots.

本研究研究了具有横向惯性和有限半径的非线性弹性圆杆纵向振荡的动力学姿态。该模型由 Wei 和 Gui-tong 于 1986 年使用四阶非线性混合导数导出。该模型的轴对称性已通过使用柱坐标进行了思考。此外，还确定了杆长度单位的应变和动能。两种最新的计算（扩展扇形展开（EFE）和广义有理（GR））技术被用来构建一些新颖的孤立波解决方案。孤子波解是使用 Mathematica 13 软件获得的，并具有三角、双曲线和有理解种类的独特物理性质。测试了所研究模型的稳定性和通过建议的两种分析方案获得的解决方案。将不同的参数值通过二维、三维和等高线图中的一些数值模拟来解释这些解决方案。