In this module you will be introduced to the analysis needed to understand the vibration of systems with Single, two and more than two degrees of freedom. You will also be introduced to the important concept of a mode shape and the method of modal analysis which is highly used when studying the response of multi-degree-of-freedom systems. Focus would be not only the modelling the complex vibration system but also looking into vibration control techniques. More specifically, you will cover the following topics:

1. Single degree of freedom systems: Free vibration, forced vibration, undamped vibration, damped vibration
2. Two-degree-of-freedom systems: Free vibration, forced vibration, frequency equation method, characteristic equation method
3. Multi-degree-of-freedom systems: Stiffness matrix, flexibility matrix, matrix iteration method
4. Vibration Control: Vibration isolator and Absorber, whirling motion and critical speed

You will be required to complete two elements of summative assessment as follows:

A report including research and simulation task on dynamic and vibration system weighted 50% consisting of 2500 words covering Learning Outcomes 3, and 4. Meeting AHEP 4 outcomes B3, and B4.

A report based on a range of laboratory activities focusing on dynamic and vibration system weighted 50% consisting of 2500 words covering Learning Outcomes 1, and 2. Meeting AHEP 4 outcomes B1, B2, and B3.

Formative assessment, guidance and feedback will be provided throughout the module.

This module will enable students to gain understanding, apply knowledge, analyse and evaluate problems and create solutions through a variety of activities, including problem-based lectures, tutorials, laboratories and independent study.

1. Solve a range of problems related to dynamics and vibration analysis, including multi-degree-freedom systems, making use of appropriate advanced concepts and principles (AHEP 4: B1, B2)

University Learning Outcome: Knowledge and Understanding, Learning, Problem Solving

2. Investigate the dynamic behaviour of mechanical systems through experimental methods, accurately collect and interpret vibration and motion data, and effectively communicate the results in relation to theoretical models and predicted system responses. (AHEP 4: B3)

University Learning Outcome: Communication, Analysis, Application

3. Critically analyse and interpret the vibration and dynamic behaviour of mechanical systems through the application of appropriate simulation and modelling tools, and critically evaluate and reflect on the accuracy, validity, and limitations of the simulated results against theoretical predictions or experimental data. (AHEP 4: B3)

University Learning Outcome: Reflection, Analysis, Application

4. Investigate and evaluate published research related to dynamics and vibration problems, drawing on evidence from academic and industrial sources to inform practical engineering solutions. (AHEP 4: B4)

University Learning Outcome: Learning, Knowledge & Understanding, Analysis

Library facilities
Standard office software
Engineering Laboratory Equipment (e.g 2DOF vibration rig(s))
Finite element analysis software of an industrial standard capable of performing static and dynamic analyses (e.g. ANSYS)

Singiresu, S. RAO, (2017) Mechanical vibrations. Sixth Edition. Pearson.

Inman, D.J., (2013) Engineering vibrations. Third Edition. Pearson.

Thomson, W.T. and Dahleh, M.D., (2013) Theory of vibrations with applications. Fifth Edition. Pearson.

Kelly, S.G. (2011) Mechanical vibrations: theory and applications. International Student Edition. CL Engineering.

Goncalves Salsa Junior, R. (2025) Fundamentals of the Theory of Mechanical Vibrations.Spinger

Must be registered on BEng (Hons) Mechanical Engineering with Manufacturing provision at Riverside College.

This module you will cover the analysis needed to understand the vibration of systems with Single, two and more than two degrees of freedom. You will also be introduced to the important concept of a mode shape and the method of modal analysis which is highly used when studying the response of multi-degree-of-freedom systems.