This is an introduction to the theories of complex dynamics with application to engineering problems. In particular, this course introduce some basic concepts of nonlinear dynamics, stability analysis and nonlinear vibrations.

2 lectures per week

None

None

80% Written Exam

20% Report (report on nonlinear vibration measurements)

The aims of this course are to:

■ provide an introduction to theories of nonlinear dynamics with practical applications to problems in engineering;

■ introduce concepts of nonlinear vibration analysis;

■ provide the analytical and numerical tools to solve complex dynamical systems;

■ establish an advanced vectorial description of the kinematics of a rigid body for generalised motion with applications to multiple link machines and rotating bodies.

By the end of this course each student will be able to:

■ apply rigorously the Newton-Euler equations to a rigid rotor for purposes of machine design;

■ identify sources and categories of nonlinearity in models of vibrating systems;

■ explain the limitation of the linear modal analysis and describe some techniques to overcome such limitations;

■ set up reduced order models which lend themselves to the analysis of complex dynamical systems;

■ analyse the response of a nonlinear system and recognise the type of nonlinearity from the characteristics of the response;

■ use the most common numerical and analytical tools for the study of dynamical systems;

■ discuss issues of stability analysis in certain dynamical systems encountered in engineering;

■ explain the principles of signal analysis and processing in order to understand the operation of digital spectrum analysers;

■ use sufficient vector algebra to model kinematic systems relating to real engineering machines to a significant degree of complexity;

■ evaluate complete vector analytical solutions to multiple link systems and rotating links with slider couplings.

Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.

Students should attend at least 75% of the timetabled classes of the course.

Note that these are minimum requirements: good students will achieve far higher participation/submission rates.  Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.