Model Reduction of a Coulomb Friction Damped System using Singular Perturbaion Theory

This paper presents an extension of singular perturbation theory for use on systems with dry (Coulombic) friction. The technique is developed for a particular example - that of a 4th order model commonly used to describe turbine and compressor blades. A zeroth order approximation is obtained yielding a reduced order model. An improvement to this approximation in the form of a first order correction term is also developed. The first order correction term is seen to greatly improve the approximation with no added cost to the numerical simulations. The accuracy and numerical efficiency of the zeroth order and the first order reduced order models are checked against numerical simulations of the full order model.