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Lecturers
Lab Leader
Timing and Structure
Lent term. Vibration of Continuous Systems: 2 lectures/week, weeks 1-4 Lent term (Dr T Butlin), Vibration of Lumped Systems: Rayleigh's method, 2 lectures/week, weeks 5-8 Lent term (Prof D Cebon). 16 lectures.
Prerequisites
3C5 useful (there is one particular result from the Lagrange section of 3C5 which will be quoted without proof)
Aims
The aims of the course are to:
- Introduce the central ideas and tools for the analysis of small (linear) vibration in mechanical systems.
- Introduce simple continuous systems which may be combined as components of larger systems.
- Introduce the general approach to lumped systems via mass and stiffness matrices, and the resulting properties of vibration modes and their frequencies.
Objectives
As specific objectives, by the end of the course students should be able to:
- Derive the partial differential equations governing the forced or free motion of uniform one-dimensional systems.
- Use these equations and appropriate boundary conditions to obtain vibration modes and natural frequencies.
- Be familiar with musical intervals and how these are useful in vibration diagnostics.
- Analyse continuous systems using modal methods.
- Compute impulse and harmonic response by modal and direct methods.
- Calculate the response of a coupled system from a knowledge of the responses of the separate subsystems.
- Apply Rayleigh's method to continuous sytems.
- Take advantage of the link between Lagrange's equations and small vibration.
- Explain the concept of a vibration mode, and be able to find the modes and their natural frequencies by an eigenvector/eigenvaluecalculation.
- Understand orthogonality of modes, modal damping, modal density and modal overlap factor.
- Express the frequency response functions or the impulse response functions of a system in terms of the normal modes, and be familiar with the concepts of resonances and antiresonances.
- Recognise and apply the reciprocal theorem for responses.
- Use the stationary property of normal mode frequencies to estimate frequencies given assumed mode shapes, using minimisation with respect to any free parameters.
Content
This course aims to present a systematic approach to the study of small vibration of engineering components and structures. The course picks up where Part IA Linear Systems and Vibration left off. Concepts which were barely discussed (e.g. reciprocity and the orthogonality of vibration modes) are important for building up qualitative insights into vibration behaviour. Alongside the mathematical tools for quantitative analysis the course offers vital ingredients for an engineer's education.
Vibration of Continuous Systems (8L)
- Vibration of strings; axial and transverse vibration of beams, torsional vibration of circular shafts;
- Modal analysis of simple systems;
- Response to impulse and harmonic excitation;
- Coupling of systems;
- Rayleigh's method for continuous systems.
Vibration of Lumped Systems (8L)
- Application of Lagrange's equations to small vibrations; undamped vibration of systems with N degrees of freedom;
- Matrix methods and modal analysis;
- Response functions in frequency and time domains; properties of frequency-response functions; reciprocal theorems;
- Modal damping and modal overlap;
- Rayleigh's method for discrete systems.
Coursework
A data-logging and FFT analysis system is used to measure the frequency response of a vibrating system by three different methods, to compare their merits and disadvantages.
[Coursework]
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
Full Technical Report:
Students [will/won't] have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 03/08/2017 15:27