The impact of the unsteadiness in the considered turbulence quantities on the numerical prediction of the aeroelastic behavior of a low-pressure turbine (LPT) rotor blade is evaluated by means of a numerical study. In this context, one of the main objectives of this work is to compare different nonlinear harmonic balance (HB) approaches—one neglecting and one considering the unsteadiness in the employed turbulence models—with a conventional nonlinear solver of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in the time domain. In order to avoid unphysical oscillations in the turbulence quantities caused by the Gibbs phenomenon in the chosen HB approach, a filter method based on the Lanczos filter is developed. The developed filter method is applied in the course of the HB simulations considering the unsteadiness in the underlying turbulence model. Furthermore, the impact of its application on the solution of the flow field and on the unsteady surface pressure of the rotor blade, in particular, is discussed in the context of this work.