# Influence of Material-Dependent Damping on Brake Squeal in a Specific Disc Brake System
## 4 Discussion  
In this study, we examined the effect of damping on the stability of a particular disc brake system to assess the importance of components damping in terms of stability and thus brake squeal. The analysis was performed using simplified (2 DoF) and complex (multiple DoF) models of a disc brake. Various authors as well as the classical theory of vibration of mechanical systems state that in nonconservative systems, damping can play both a stabilizing as well as a destabilizing role.  
Both analyzed models showed the dependence of stability on the degree of proportionality of damping. At low damping levels, the systems showed unstable behavior. Increasing the damping while maintaining its proportionality ultimately stabilized the system. However, this did not apply in the case of a deviation from proportional damping, where increasing the damping of one part of the structure at the expense of another led  
Figure 11: (**a**) Stability map with respect to \(\zeta_{d}\), \(\zeta_{p}\) damping ratios and (**b**) stability map in the \(\zeta_{d}\)–\(\zeta_{p}\) plane. Bold lines—stability boundary, dashed line—proportional damping line, and red circle—default damping ratio values.  
to destabilization. Since both models showed this action, regardless of the complexity, it implies that similar behavior can be anticipated in commercial disc brake systems. From the given observation, we concluded that an effective brake-squeal prediction process should account for damping.  
Concerning the questions defined in the Introduction, both can be answered positively. Nonproportional damping can significantly influence the stability of disc brake systems. Our findings demonstrate that disc brake systems can contain unstable modes, which are, for common material properties, prone to being destabilized by dissipation-induced instability. However, from the scope of this research, we cannot conclude that all unstable modes are sensitive in this manner for physically reasonable material properties, especially damping propensity.  
Nonproportional damping can be modeled in modern FEM tools using material-dependent damping models. By definition of specific material-dependent damping, for single components, this leads to a nonproportional damping matrix relative to the mass and stiffness matrices of a system. This allows appraising unstable system modes' sensitivity to damping.  
Here, we experimentally confirmed hypotheses from previous research [12; 20]. Two coalescent patterns in the brake system can have different modal damping ratios, potentially leading to dissipation-induced instability. In this research, the damping matrix was not synthesized artificially using the coefficients to change the structure of the damping matrix to achieve general damping, as was done by [PERSON] et al. [12]; the damping matrix was constructed directly from the definition of material-dependent damping properties, making the resulting matrix nonproportional to the mass and stiffness matrices. This approach is effective since the desired damping model can be defined directly from the experimental measurement of components damping properties.  
The novelty of this research is supporting the hypothesis of possible dissipation-induced instability occurrences in disc brake systems through analyses of a real experimental brake system with measured and justified damping properties.This paper shows a possible method of including material-dependent damping into modern FEM tools and performing analyses leading to a prediction of dissipation-induced instability in disc brake systems.