Effect of substructuring techniques on the simulation of friction-induced vibrations

The modeling, simulation, and analysis of friction-induced vibrations is a very challenging topic in science and technology. The method of complex eigenvalue analysis is the standard procedure used to analyze and judge the stability of the systems and the steady-state response of friction-induced vibrations. In this method, high-dimensional finite element models are linearized, and the circulatory and gyroscopic matrices of the equation of motion are first calculated assuming quasi-static conditions. Then, a projection onto the subspace of the undamped, non-circulatory system is performed, and finally, a quadratic eigenvalue problem is solved providing complex eigenvalues and eigenvectors. In this contribution, the effect of different substructuring techniques on a full brake system is analyzed. Substructuring of a model permits to reduce the number of degrees of freedom of the system matrices used in an analysis, and thus, savings on the simulation time can be achieved, which may be crucial when studying, for example, high-frequency vibrations or the influence of parameters variability.