Nonlinear Vibrations

3 units

In this course students are introduced to concepts in nonlinear dynamics and vibration and application of these concepts to nonlinear engineering problems. Specific topics include: modeling of lumped and continuous nonlinear systems (strings, beams, and plates); vibrations of buckled structures; perturbation and other approximate analytical methods; the use and limitations of local linearization; properties of nonlinear behavior, such as dimension and Lyapunov exponents; stability of limit cycles; bifurcations; chaos and chaotic vibrations; experimental methods and data analysis for nonlinear systems. Concepts will be reinforced with a number of examples from recently published research. Applications will include aeroelastic flutter, impact dynamics, machine-tool vibrations, cardiac arrhythmias, and control of chaotic behavior.