Non-Linear Forced Response of Vibrating Mechanical Systems: The Impact of Computational Parameters

The harmonic balance method (HBM) is a widely used method for determining the forced response of non-linear systems such as bladed disks. This paper focuses on analyzing the sensitivity of this method to key computational parameters and its robustness. HBM and HBM coupled with pseudo arc length continuation are used in this paper to solve the equation of motion of a test case. The pseudo arc length continuation is necessary because when intermittent contact occurs, natural continuation cannot guarantee solver convergence. Intermittent contact, in addition to turning points, introduces further problems, which are caused by an infinite sequence of decaying, but not zero, Fourier coefficients. This results in the need to oversample the non-linear force time signal to avoid convergence problems. The computational parameters investigated in this paper are the samples per period, which determine the number of points in which the time signal is discretized, and the harmonic truncation order. In addition, the connection of contact parameters, such as friction and contact stiffness, with computational parameters is analyzed. This study shows that the number of time samples per period is the most limiting parameter when intermittent contact occurs; whereas, in the absence of intermittent contact convergence, problems can be avoided with a reasonable number of time points. Poor discretization of the signal leads to a bad computation of Fourier coefficients and thus a lack of convergence. Sensitivity analysis shows that the samples per period depend on the contact parameters, especially normal stiffness. To ensure the solver robustness, it is important to set the computation parameters appropriately to ensure the convergence of the solver while avoiding unnecessary computation effort.