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Several state of the art papers and even books on brake vibration and/or noise have been presented in the literature. Many of them have analytically and sharply accounted for the impressive amount of research undertaken on this topic. This state of the art review focuses on the still-open questions that appear crucial from the perspective of a leading brake manufacturer. The paper deals with the phenomena of brake vibration and/or noise, the experimental and theoretical methods for studying such phenomena, and the actions that are identified to be necessary to definitely solve the addressed problem. Key topics are the modelling of friction, the modelling of the dynamics of the brake as a non-linear system subjected to deterministic or random (parametric) excitation, the proper modelling of the contact between the disc and the pad, and the experimental validation of the mathematical models.

The paper deals with the bifurcation analysis of a rather simple model describing an automobile negotiating a curve. The mechanical model has two degrees of freedom and the related equations of motion contain the nonlinear tyre characteristics. Bifurcation analysis is adopted as the proper procedure for analysing steady-state cornering.Two independent parameters referring to running conditions, namely steering angle and speed, are varied. Ten different combinations of front and rear tyre characteristics (featuring understeer or oversteer automobiles) are considered for the bifurcation analysis. Many different dynamical behaviours of the model are obtained by slightly varying the parameters describing the tyre characteristics. Both simple and extremely complex bifurcations may occur. Homoclinic bifurcations, stable and unstable limit cycles (of considerable amplitude) are found, giving a sound and ultimate interpretation to some actual (rare but very dangerous) dynamic behaviours of automobiles, as reported by professional drivers. The presented results are cross-validated by exploiting handling diagram theory. The knowledge of the derived set of bifurcations is dramatically important to fully understand the actual vehicle yaw motions occurring while running on an even surface. Such a knowledge is a pre-requisite for robustly designing the chassis and for enhancing the active safety of vehicles

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Often at the earliest stage of an engineering project, a preliminary optimization could be useful, in order to allow the designer to ascertain the envisaged performance of the system under development.Providing an efficient (analytical) tool to quickly define the Pareto-optimal set could be an extremely valuable chance to make the right design decision at the right time.The procedure proposed here to obtain the Pareto-optimal set in analytical form refers mostly to design problems described by a limited number of design variables and a limited number of objective functions and constraints.In the first part of the paper, the analytical derivation of the expression of the Pareto-optimal set for multi-objective optimization problems is dealt with.According to the knowledge of the authors, in the literature, very few papers exist on this topic and related issues. A survey of current continuous multi-objective optimization concepts and methods is presented in Ref. [19]. Some relevant contributions are given in Ref. [17] and Ref. [20] in which some new formulations of the Fritz John first order conditions are proposed and analyzed. In Ref. [30] first and second order conditions are proposed for a convex multi-objective problem via scalarization and in Ref.[1] some second order conditions are analyzed in detail. In Refs. [17,20,30,1,32,26] necessary and/or sufficient conditions are discussed but