ME 669 Nonlinear Vibration
This course includes derivation of nonlinear equations of motion for large amplitude mechanical vibrations (such as of beams and plates) but focuses on the analysis of the dynamics of nonlinear oscillators (such as Duffing, Van der Pol, and Mathieu/Hill equations). Topics considered include phase-plane analysis and stability, asymptotic and perturbation methods such as Lindstedt-Poincaré, multiple scales, and Krylov-Bogoliubov-Mitropolsky, the harmonic balance method, external excitation, primary and secondary resonances; parametric excitation, Floquet theory, and multi-degree of freedom systems including nonlinear normal modes and center manifold theory.