Nonsmooth dynamics of disc brake systems and aeroelastic panels

Contact forces and boundary conditions relaxation play an important role in the dynamic behaviors of mechanical systems such as disc brake systems, jointed structures, and aeroelastic panels. Contact forces between sliding surfaces are strongly nonlinear, non-smooth, and random; and thus can result in complex dynamic characteristics. In addition, boundary conditions relaxation causes stiffness and damping variations, and thus affects structural reliability and integrity. The main objectives of this study are to uncover the complex dynamic behavior associated with these two problems.; A novel data processing technique based on wavelet transform is adopted for statistical characterization of contact forces in addition to the analysis of transient signal of brake squeal in the time-frequency domain. In particular, the investigation is focused on the characterization of random component of the friction coefficient. A nonlinear analytical model describing the interaction between a flexible disc and flexible pads has been developed. The analytical model includes nonlinear contact stiffness, non-uniform distribution of contact forces, as well as random friction coefficient based on experimental measurements. The influence of nonlinearity and randomness of contact forces on generating low and high frequencies noise is investigated.; The second problem deals with the relaxation of boundary conditions in a two-dimensional aeroelastic panel exposed to supersonic air flow. The boundary value problem of the panel involves time-dependent boundary conditions that are converted into autonomous form using a special coordinate transformation. The model accounts for the structural and aerodynamic nonlinearities as well as structural and aerodynamic damping.; The study includes stability analysis, boundaries of panel flutter, and limit cycle oscillations (LCO) in terms of aerodynamic pressure, in-plane load, relaxation parameter, and damping factor. Stochastic stability boundaries under random in-plane loading, random pressure differential and combined effect of both random in-plane load and pressure differential are estimated below and above the critical aerodynamic pressure. It is found that, during relaxation, the panel experiences complex dynamic characteristics such as symmetric and asymmetric LCO, quasi-periodic, multi-periodic and chaotic oscillations. Non-stationary panel flutter caused by the time dependent boundary conditions is examined using short time Fourier transform and continuous wavelet transform. The results of this part have direct impact on the aging of aircraft.