## 1 Introduction
Furthermore, time integration methods (for curve squeal models), can be subdivided into those based on the condensation of the wheel and rail behavior at their contact degrees of freedom [9; 18], which involve computing impulse responses and solving integral-differential equations, and those based on spatial discretization of the vibration fields of the structures (mostly of modal type) [6; 19], which translates into solving second-order systems of differential equations. It is clear that the solution obtained with time integration methods (irrespective of their classification) depends on the initial conditions used. In spite of this, their choice is not generally discussed or is partially justified, mostly because the implicit but inaccurate hypothesis that the final limit cycle is independent of the initial conditions is accepted. However, previous works in the wider field of friction-induced vibrations have pointed out the existence of different limit cycles depending on the initial conditions. For example, [PERSON] et al. [20] were able to obtain different limit cycles for a simple sliding elastic layer and these limit cycles could be of periodic or quasi-periodic nature and have different fundamental frequencies, depending on the parameters of the model, the total number of unstable modes, and also the initial conditions used. For curve squeal in particular, [PERSON] [6] demonstrated that by favoring a particular mode in the initial conditions, by imposing a non-zero modal contribution to it, led to a different limit cycle than would be obtained with similar modal contributions for all unstable modes. The influence of harmonically-related modes on the frequencies that appeared in the final limit cycle was also highlighted in this study, where there is a factor of 2 between the natural frequencies of two specific wheel modes. [PERSON] et al. [21] also stated that initial conditions act on the limit cycle and dominant frequencies, although no further details were given. The types of initial conditions generally used on curve squeal models are a zero initial position at rest \((U_{0},U_{0})=(0,0)\)[22; 23], the quasi-static equilibrium \((U_{0},\dot{U}_{0})=(U_{st},0)\)[8], a static disturbance of the equilibrium \((U_{0},\dot{U}_{0})=(U_{st}(1\pm e),0)\)[24], a non-zero relative velocity and initial position at equilibrium \((U_{0},\dot{U}_{0})=(U_{st},V_{0})\)[6], and a progressive application of creepage and normal load [9]. These conditions are expressed in terms of physical quantities such as velocity or position, which means that they could be directly linked to the operating conditions, such as surface irregularities or the variation of the angle of attack during the curve. However, for time integration using a modal description of the structures, initial conditions in terms of the modal contributions \((q_{0,i},\dot{q}_{0,i})\) need to be imposed, as performed by [PERSON] et al. [20], but these initial conditions do not have a physical meaning per se, which limits their comprehension. Finally, in terms of noise levels, it is well established that squeal noise is primarily radiated by the wheel in axial vibrations [1]. Moreover, the spectrum of radiated noise is very close to the spectrum of self-sustained vibrations, since the sound radiation factors of the vibration modes involved in curve squeal are very close to each other. The calculation of these radiation factors is well controlled and can be carried out in the same way as for the prediction of rolling noise, using for instance numerical techniques such as Boundary Element Methods [21] or approximate analytical formulae [25]. Consequently, the main issue is the determination of the self-sustained vibrations. The objective of this article is thus to assess the impact of initial conditions on the final limit cycle obtained with numerical time integration for a curve squeal model based on the falling friction mechanism and using a modal description of the wheel.