A fundamental course in nonlinear vibrations and stability. Basic concepts about linear and nonlinear systems; Routh-Hurwitz and Liapunov’s stability criteria; systems with periodic coefficients and Floquet theory; effects of nonlinearities; limit cycles, jump, saturation, nonlinear resonances, modal energy exchange, etc.; perturbation methods: straightforward perturbations, Lindstedt-Poincare, harmonic balancing, multiple time scales; steady-state and transient responses of nonlinear systems. Applications to discrete and structural systems. Use of symbolic manipulation to analyze problems.
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