Nonlinear Vibrations

Course content

Introduction to nonlinear systems, phase plane analysis, bifurcations. Averaging and perturbation methods. Forced response in frequency domain. Solution of systems of nonlinear algebraic equations, Newtons method, path following methods for nonlinear equations. Describing functions, Describing Function Method (DFM). Harmonic Balance Method (HBM), multi harmonic HBM. Nonlinear forced response of structures having many degrees of freedom, receptance methods, model summation methods. Modeling dry fiction, one and two dimensional dry fiction models, mixed frequency and time domain methods. Vibrations of systems with dry fiction.