Online Course Catalog

This course provides an introduction to the basic concepts and methods of the qualitative and quantitative theory of Nonlinear Dynamics and Vibrations. After discussing theorems on the existence and uniqueness of solutions for general classes of nonlinear oscillators described by ordinary differential equations, the course proceeds to a description of the dynamics in phase space. It introduces the definitions of dynamical flow, equilibrium points, and periodic, quasiperiodic and chaotic orbits. Students then examine basic asymptotic methods for analyzing the free and forced responses of single- and multi-degree-of-freedom nonlinear oscillators, including the methods of Lindsted-Poincare’, averaging and multiple-scales. Students then proceed to a systematic examination of forced (fundamental, subharmonic and superharmonic), internal and combination resonances in dynamical systems, together with a discussion of linearized stability analysis. This leads to a detailed study of Floquet theory, of the theory of linear parametrically excited systems, and of the notion of parametric resonance.

4 hours

Basic theory of ordinary differential equations and linear algebra, basic linear dynamics and vibrations.

• Mechanical Science and Engineering