Disc brake squeal is a manifestation of friction-induced, self-excited instability in disc brake systems. This paper investigates the nonsmooth bifurcations and chaotic dynamics associated with braking systems. In most situations, decreasing squealing is a means to suppress chaotic disturbances, which would otherwise compromise the comfort of passengers. The proposed method begins with an estimation of the largest Lyapunov exponent using synchronization to differentiate between periodic and chaotic motions. We then observe complex nonlinear behaviors associated with a range of parameters and plot them in a bifurcation diagram. Rich dynamics of disc brake systems are examined using the bifurcation diagram, phase portraits, Poincaré maps, frequency spectra, and Lyapunov exponents. Finally, state feedback control is used to overcome chaotic behaviors and prevent squealing from occurring during braking. Finally, the effectiveness of the proposed control method is examined through numerical simulations.
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