Engineering and the Environment, University of Southampton

Knowledge and understanding
Having successfully completed the module, you will be able to demonstrate knowledge and understanding of:

• The basic principles underlying the behaviour of vibrating systems.
• The role of mass, stiffness and damping.
• The importance of resonance and consequences.
• Methods for deriving and solving the equations of motion for vibrating systems.
• The vibrational behaviour of lumped-mass and continuous systems.
• The modal behaviour of structures.
• The principles of wave motion in structures.
• The interpretation of the results of numerical models and of measured vibrational response.
• The measurement of basic vibration quantities (e.g. acceleration).
• Modern vibration transducers and their associated electronics.

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Read, understand and interpret the literature relating to analytical and numerical methods in vibrations.
• Recognise and select appropriate techniques for the solution of analytical and numerical problems in vibrations.
• Understand and interpret the vibrational behaviour of structures.

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Analyse straightforward vibration problems.
• Undertake measurement of vibration quantities.
• Measure modes of vibration on a simple structure.

Key transferable skills
Having successfully completed the module, you will be better able to:

• Develop the equations of motion of systems and structures.

The aims of this module are to:

• Introduce students with little or no previous experience of mechanical vibrations to the basic concept of vibrational behaviour.
• Provide a general introduction to vibration modelling, analysis and control.
• To give students some experience of vibration measurement.

• To introduce the student to the physical behaviour of vibrating systems.
• To introduce the main theoretical procedures used for the analysis of practical vibration problems.
• To demonstrate the influence of the various model parameters on vibrational behaviour.

Introduction

• Vibration problems in engineering.
• Terminology.
• Basic principles.

Single degree of freedom system

• Free vibration of mass-spring system: natural frequency.
• Free vibration with damping: damping factor.
• Energy methods.
• Time harmonic forced vibration: resonance.
• Isolation, base excitation and other applications.
• Structural damping.
• Transient vibration: response to transient excitation: impulse response; shock spectra.

Multiple degree of freedom systems

• Free vibration of two degree of freedom systems: modes of vibration, natural frequencies and mode shapes.
• Multiple degree of freedom systems: matrix methods.
• Time harmonic forced vibration with damping: modal decomposition.
• Introduction to vibration treatment; vibration absorbers.

Continuous systems

• Free vibrations of strings, bars and shafts: equation of motion, boundary conditions.
• Modes of vibration: natural frequencies and mode shapes.
• Bending vibration of beams.
• Forced vibration of continuous systems: modes and resonance.
• Introduction to structural wave motion in one dimension: propagation, reflection and transmission; coincidence.

Modelling methods

• Rayleigh’s method.
• Lagrange’s equations for free undamped vibration.
• Applications.

Vibration measurement and analysis

• Vibration transducers and measurement.
• Experimental modal analysis.

2 lectures a week.

1 laboratory class of up to 4 hours duration.

The students are provided with copies of the overheads. These include problems worked through in class to demonstrate problem formulation and solution, and the thought processes involved.

Students are encouraged to discuss difficulties informally with the lecturer.

Additional tutorials are provided towards the end of the course as preparation for the examination.

Laboratory "Beam Vibration Measurement".
The laboratory class will be supervised by a member of academic staff or a suitably qualified postgraduate student. The class will be restricted to no more than 6 students per rig.
Students need to work in their own time to complete the laboratory work and are able to go to the lecturer for assistance. Feedback on laboratory reports will be returned to the student normally within two weeks of the submission deadline.

Example sheets are provided to students in order to practise their analytical skills and the material covered in lectures. Worked solutions and solution notes are provided.

A laboratory sheet provides instructions, information and assistance with the experimental procedure.

Secondary text

Mechanical Vibrations
3rd Edition, S S Rao, Addison-Wesley

Fundamentals of Noise and Vibration, 1998, F J Fahy
J G Walker (eds), E&FN Spon
0419227008

Theory of Vibration with Applications
4th edition, 1993
3rd edition, 1988
2nd edition, 1972, WT Thomson, Unwin Hyman
0412546205
0044450699
0046200096