Multi-degree-of-freedom Lumped Parameter Systems: Matrix representation, forced vibration using normal mode analysis, principal coordinates, coordinate transformations, orthogonality, dealing with damping, Lagrangian dynamics. Continuous Systems: Longitudinal and torsional vibration of rods, lateral vibration of beams.

4 lectures per week

Vibration M4 ENG4137

None

75% Degree examination

25% Written report

The aims of this course are to:

■ provide a good grounding in vibration fundamentals in order to intelligently use Finite Element (FE) packages to obtain a meaningful and reliable result;

■ introduce vibration testing as a fundamental part of troubleshooting and demonstrate that much analysis can be performed using models based on experimental measurements;

■ provide enough theoretical background to understand the two powerful tools of FE and experimental modal analysis;

■ demonstrate how experimental modal analysis and FE analysis can be used as a troubleshooting tool or a design tool.

By the end of this course students will be able to:

■ model and analyse simple lumped mass systems by hand;

■ model and analyse rods and beams by hand;

■ appreciate the principles of FE analysis and other approximation techniques;

■ appreciate the principles of and be able to perform experimental modal analysis;

■ have detailed knowledge and be able to use experimental modal analysis techniques for troubleshooting and design;

■ use FE packages for design and troubleshooting;

■ appreciate the principles of random vibration and some of the problems of nonlinear vibration.