Courses Detail Information

ME6402J – Mechanical Vibrations


Instructors:

Yanfeng Shen

Credits: 3 credits

Pre-requisites: This course will focus on conveying the fundamental concepts, advanced theories, and numerical computation algorithms of mechanical vibrations. Although pre-requisites such as VM440 (intermediate dynamics and vibrations) or equivalent undergraduate vibration courses are preferred, the instructor will carefully and systematically design the course material in the fashion of building blocks. The course is intended to be self-contained. Related fundamentals of vibrations will be introduced in each topic to help the students pave their progress.

Description:

Mechanical vibrations are widely found in engineering practice and various infrastructures. They are
sometimes useful and beneficial for us to make good use of, while they may become considerably
harmful and need to be avoided in other cases. Harnessing mechanical vibrations will allow engineers
to design more effective vibro-acoustic actuators and sensors, more comfortable automobile vehicles,
more durable civil infrastructures, and safer aerospace crafts.
In this class, a variety of aspects on mechanical vibrations will be covered. The students will learn the
analytical and numerical skills in solving structural vibration problems. Time and frequency domain
mathematical techniques for linear system vibrations. Detailed topics include undamped and damped
free and harmonic vibration of a single degree of freedom system; Fourier series and response to
periodic, unit impulse, and arbitrary excitations; time-stepping methods (central difference method);
multiple degree of freedom systems; natural frequencies and mode shapes; mode orthogonality and
normalization; modal expansion technique and modal analysis; response spectrum concepts and design
spectrum; introduction to vibrations of continuous structures.

Course Topics:

Introduction/Definition of a degree of freedom/Equation
of motion
Undamped free vibration (Section 2.1); Viscously damped
free vibration (Section 2.2)
Harmonic vibration of undamped systems (Section 3.1)
Harmonic vibration with viscous damping (Section 3.2)
Viscously damped systems: Applications (Chapter 3,
Section B)
Fourier Series (Section 3.12)
Response to periodic force (Section 3.13)
Response to unit impulse (Section 4.1)
Response to arbitrary force (Section 4.2)
Time-stepping methods (Sections 5.1 and 5.2)
Central difference method (Section 5.3)
Introduction to multiple degree of freedom systems
(Sections 9.1 and 9.10)
Natural frequencies and mode shapes (MDOF) (Sections
10.1 to 10.3)
Mode orthogonality and normalization modes
Modal expansion of displacements (Section 10.7)
Modal analysis (Chapter 12 Part B)
Response spectrum concepts (Sections 6.1 to
6.8); Design spectrum (Sections 6.9 to 6.12)
Introduction to vibrations of continuous structures