Impact of the initial conditions in time integration methods for self-excited nonlinear vibrations: the case of railway curve squeal

Time integration of the dynamic equations that model railway curve squeal phenomenon is a commonly used method to determine the nonlinear self-sustained vibrations associated to this disturbing tonal noise. Although it is well known that the solutions obtained with time integration depend on the initial conditions used, their choice is often overlooked, mostly because it is implicitly assumed that the final limit cycle is independent of them. Moreover, the use of a modal description of the rail and wheel introduces some challenges when it comes to a physical understanding of the initial conditions. This study investigates their impact on a curve squeal model based on a modal reduction of the wheel by using two types of initial conditions, namely the modal and physical-based ones. Two families of limit cycles were obtained: low-amplitude cycles with a periodic regime and high-amplitude cycles with a quasi-periodic regime, where a strong harmonic coupling between the wheel modes is found. These results stress the importance of a reasonable choice of the initial conditions in order to produce more reliable and robust simulations. Future developments involving direct nonlinear methods for limit cycle determination could help deepen the understanding of the problem treated in the present study.