ENME 361 - Vibrations, Control, and Optimization I

3 Credits


B. Balachandran and E. B. Magrab, Vibrations, Second Edition, CENGAGE Learning, Toronto, ON, 2009.


ENES 220
ENES 221
ENME 271 or MATH 206
MATH 246


Fundamentals of vibration, controls and optimization. Analysis and design in time, Laplace and frequency domains. Mathematical description of system response, system stability, control and optimization. Optimal design of mechanical systems.


In this course, the student will develop and/or refine the following areas of knowledge:

  • Model linear and nonlinear systems as combinations of springs, dampers, and masses. 
  • Analyze and interpret the response of mechanical systems to various types of excitations.
  • Predict qualitatively the response of systems based on the spectral content of the excitation and the frequency response characteristics of the system.
  • Minimize the effects of transient and harmonic excitations on systems and their support structures.


Preliminaries from dynamics, modeling of vibratory systems, single degree-of-freedom systems: governing equations, free response, periodic excitations, and transient excitation. Multiple degree-of-freedom systems: natural frequencies, mode shapes, forced oscillations.

Learning Outcomes 

  • an ability to apply knowledge of mathematics, science, and engineering
  • an ability to identify, formulate, and solve engineering problems

Class/Laboratory Schedule 

  • Two 75 minute lectures each week

Last Updated By 
Miao Yu, June 2017