Course Websites

TAM 416 - Intro to Nonlinear Dyn & Vib

Last offered Fall 2024

Official Description

Single- and multi-degree-of-freedom oscillators; asymptotic methods; forced, internal and combination resonances; time-discrete dynamical systems (maps); complex dynamics; parametric vibrations and resonances; introduction to nonlinear localization and nonlinear targeted energy transfer; nonlinear vibrations of elastic continua; application in mechanics and engineering. Course Information: Same as AE 452. 4 undergraduate hours. 4 graduate hours. Prerequisite: TAM 412, ME 340, or AE 352.

Related Faculty

Subject Area

  • Mechanical Science and Engineering

Course Description

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.

Credit Hours

4 hours


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

Intro to Nonlinear Dyn & VibGR462710LCD41300 - 1450 M W  410C1 Engineering Hall Alex Vakakis
Intro to Nonlinear Dyn & VibONL73427ONL4 -    Alex Vakakis
Intro to Nonlinear Dyn & VibUG473566LCD41300 - 1450 M W  410C1 Engineering Hall Alex Vakakis