In this paper, the nonlinear vibration of railway track systems resting on elastic foundation has been studied. An axially loaded simply supported Euler–Bernoulli beam resting on a flexible foundation has been considered to provide a mathematical representation of the railway track system. Winkler springs have been used to model the elastic foundation. Nonlinear partial differential equation of the system has been presented and solved. A new approximate analytical solution called Improved Amplitude–Frequency Formulation (IAFF) is proposed to obtain nonlinear frequency of the system and an accurate analytical solution for the whole domain. The first iteration of the IAFF leads to a highly accurate solution in comparison with the exact frequency of the problem. The exact frequency of the problem is also presented, and the results of IAFF are compared and verified. Sensitive analysis of the soil stiffness and loading condition is studied for different parameters. A full comparison of the IAFF and exact solution results are illustrated. It has been proved that the IAFF can be potentially extended to highly nonlinear conservative problems.

本文研究了基于弹性地基的铁路轨道系统的非线性振动。考虑将轴向受力的简单支撑的Euler–Bernoulli梁置于柔性基础上，以提供铁路轨道系统的数学表示。温克勒（Winkler）弹簧已用于对弹性基础建模。提出并求解了系统的非线性偏微分方程。为了获得系统的非线性频率和整个域的精确解析解，提出了一种新的近似解析解，称为改进的振幅-频率公式（IAFF）。与问题的确切频率相比，IAFF的第一次迭代可提供高度准确的解决方案。还列出了问题的确切发生频率，并比较了IAFF的结果。研究了不同参数对土壤刚度和荷载条件的敏感性分析。说明了IAFF和精确解决方案结果的完整比较。已经证明，IAFF可以潜在地扩展到高度非线性的保守问题。