signal processing

Nonlinear Vibration

Course Description

This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. In mechanical vibration systems components such as springs, masses and dampers are conveniently supposed to behave linearly, resulting in linear vibration theory. Since all vibration systems tend to behave nonlinearly with increasing amplitude of oscillation, a knowledge of nonlinearly vibrations theory is desirable for a mechanical engineer, as specific important nonlinear phenomena can only be explained by this theory.

Course Objective

linear and nonlinear systems, conservative and non-conservative systems; potential well, Phase planes, types of forces and responses, fixed points, periodic, quasi-periodic and chaotic responses; Local and global stability; commonly observed nonlinear phenomena: multiple response, bifurcations, jump phenomena.

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