Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2021-22
Module Leader
Lecturers
Prof AA Seshia and Prof \R Langley
Lab Leader
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Dr A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor R S Langley)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Coursework on non-linear vibrations. This involves a short lab, numerical modelling and simulation exercise, and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 8 1 Dec [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 28/09/2021 07:24
Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2020-21
Module Leader
Lecturers
Prof AA Seshia and Prof D Cebon
Lab Leader
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Dr A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor R S Langley)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Coursework on non-linear vibrations. This involves a short lab, numerical modelling and simulation exercise, and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 8 2 Dec [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 04/05/2021 14:25
Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2017-18
Module Leader
Lecturers
Prof R Langley and Dr A Seshia
Lab Leader
Dr A Seshia
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Dr A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor R S Langely)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Experiment on non-linear vibrations. This involves about 4 hours in the laboratory and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 9 29 Nov [15/60] |
Booklists
Please see the Booklist for Group C 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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 05/10/2017 07:55
Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2023-24
Module Leader
Lecturers
Prof AA Seshia and Prof D Cebon
Lab Leader
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Prof A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor D Cebon)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Coursework on non-linear vibrations. This involves a short lab, numerical modelling and simulation exercise, and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 8 29 Nov [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 03/10/2023 13:45
Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2019-20
Module Leader
Lecturers
Prof R Langley and Prof AA Seshia
Lab Leader
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Dr A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor R S Langely)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Experiment on non-linear vibrations. This involves about 4 hours in the laboratory and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 8 4 Dec [15/60] |
Booklists
Please see the Booklist for Group C 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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 11/10/2019 06:51
Engineering Tripos Part IIB, 4C7: Random & Non-Linear Vibrations, 2022-23
Module Leader
Lecturers
Prof AA Seshia and Prof D Cebon
Lab Leader
Timing and Structure
Michaelmas term. 12 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 useful.
Aims
The aims of the course are to:
- analyse the effects of random vibrations on machines and structures and the effects that occur as a result of non-linearities.
- describe the characteristics of random and non linear vibrations, deriving the effects of a system's dynamic response on the input and giving methods of determining resulting deflections or stresses.
- describe some of the characteristics of self excited vibrations.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify and describe random processes.
- predict the output from a system subjected to random forcing.
- predict how frequently output levels will be exceeded.
- apply the correct windows and filters for analysis.
- assess the reliability of frequency analyses.
- understand the effects of non-linearities on system response.
- calculate and use describing functions and harmonic balance.
- predict phase-plane behaviour of second-order systems.
- understand some of the common self excited vibrations and their characteristics.
Content
Non-linear and self-excited vibration. (6L, Prof A A Seshia )
- Types of non-linearities in engineering systems and their major qualitative effects. Method of harmonic balance, describing functions;
- Representation of second-order nonlinear systems in the phase plane. Stationary points and their classification. Periodic orbits;
- Introduction to self-excited vibration. Examples of systems which are excited by instability and dry friction. Self excited oscillations in micro electromechanical systems.
Random vibration. (6L, Professor D Cebon)
- Characteristics of random vibrations and the use of probability distributions and spectral densities to describe such vibration:
- Auto and cross spectra. Transmission of random vibration through linear systems and derivation of output statistics and spectral densities;
- Narrow-band processes and determination of level-crossing frequency, distribution of peaks and frequency of maxima;
- Spectral analysis. Fourier transforms. Problems with sampling and relevance of aliasing. Calculation of spectra for sampled points;
- Basic lag and use of windows and smoothing. Coherence. Accuracy of measurements.
Coursework
Coursework on non-linear vibrations. This involves a short lab, numerical modelling and simulation exercise, and 4 hours writing-up.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Nonlinear vibration of a clamped beam Learning objective: (i) To explore nonlinear effects due to high forcing amplitudes about resonance in mechanical structures. (ii) To construct a model to explain the nonlinear behaviour of the mechanism provided and use this model to simulate the behaviour of the system under specified conditions. (iii) Demonstrate use of the sonogram (time-varying spectrum) as an analytical tool to distinguish both frequency and temporal characteristics of a transient record. |
Individual Report Anonymously marked |
Weds Week 8 30 Nov [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
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: 27/09/2022 10:59
Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2023-24
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 13 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework. This course will be delivered in-person in 2021-22.
Prerequisites
3C6 assumed.
Aims
The aims of the course are to:
- teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- be familiar with the theory and practice of modal analysis and its application to engineering structures.
- apply experimental modal techniques.
- understand the vibration behaviour of idealised system components, and be able to draw implications from this for complex coupled systems.
- appreciate the physical principles of vibration damping.
- analyse simple damped vibrating systems.
Content
Introduction (1L, Dr JP Tabot)
Outline of course and introduction to the laboratory experiment.
Measurement methods and modal analysis (4L, Dr JP Talbot)
- Instrumentation for vibration measurement;
- Review of modal analysis; General properties of vibration response;
- Introduction to experimental modal analysis; Modelling the bounce of a hammer;
- Applications.
Analysis of damped systems (4L, Dr Tore Butlin)
- Mechanisms of damping: complex modulus, boundary dissipation, lumped dissipative elements;
- Adding damping to structures, constrained and unconstrained layers;
- Viscous damping, complex modes.
System components and coupling (4L Dr Tore Butlin)
- The Helmholtz resonator and its uses;
- Review of beam, membrane and plate governing equations;
- The circular membrane, Bessel functions, mode shapes and frequencies;
- Coupling of subsystems, constraints and the interlacing theorem.
Further notes
Coursework
One laboratory experiment on experimental modal analysis, to be performed in pairs, essentially unsupervised. A booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. Total time commitment will be comparable to a Part IIA experiment plus FTR.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Lab experiment: modal analysis Measure vibration transfer functions over a grid of points covering a simple structure, then use modal analysis techniques explained in the lectures to infer the first few mode shapes. Learning objective:
|
Individual/pair Report Anonymously marked |
Completed reports should be submitted via Moodle as a PDF file by 4pm on Mon 27 Nov [15/15] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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: 04/10/2023 16:42
Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2020-21
Module Leader
Lecturers
Dr JP Talbot, Dr HEM Hunt, Dr T Butlin
Lab Leader
Timing and Structure
Michaelmas term. 13 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 assumed.
Aims
The aims of the course are to:
- teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- be familiar with the theory and practice of modal analysis and its application to engineering structures.
- apply experimental modal techniques.
- understand the vibration behaviour of idealised system components, and be able to draw implications from this for complex coupled systems.
- appreciate the physical principles of vibration damping.
- analyse simple damped vibrating systems.
Content
Introduction (1L, Dr JP Tabot)
Outline of course and introduction to the laboratory experiment.
Measurement methods and modal analysis (4L, Dr JP Talbot)
- Instrumentation for vibration measurement;
- Review of modal analysis; General properties of vibration response;
- Introduction to experimental modal analysis; Modelling the bounce of a hammer;
- Applications.
Analysis of damped systems (4L, Dr HEM Hunt)
- Mechanisms of damping: complex modulus, boundary dissipation, lumped dissipative elements;
- Adding damping to structures, constrained and unconstrained layers;
- Viscous damping, complex modes.
System components and coupling (4L Dr T Butlin)
- The Helmholtz resonator and its uses;
- Review of beam, membrane and plate governing equations;
- The circular membrane, Bessel functions, mode shapes and frequencies;
- Coupling of subsystems, constraints and the interlacing theorem.
Further notes
Coursework
One laboratory experiment on experimental modal analysis, to be performed in pairs, essentially unsupervised. A booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. Total time commitment will be comparable to a Part IIA experiment plus FTR.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Lab experiment: modal analysis Measure vibration transfer functions over a grid of points covering a simple structure, then use modal analysis techniques explained in the lectures to infer the first few mode shapes. Learning objective:
|
Individual/pair Report Anonymously marked |
Before final lecture slot, which is a feedback session on the lab Wed week 8 [15/15] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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: 15/09/2020 15:07
Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2017-18
Module Leader
Lecturers
Lecturers
Lab Leader
Prof J Woodhouse
Timing and Structure
Michaelmas term. 13 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3C6 assumed.
Aims
The aims of the course are to:
- teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- be familiar with the theory and practice of modal analysis and its application to engineering structures.
- apply experimental modal techniques.
- understand the vibration behaviour of idealised system components, and be able to draw implications from this for complex coupled systems.
- appreciate the physical principles of vibration damping.
- analyse simple damped vibrating systems.
Content
Introduction (1L, Prof J Woodhouse)
Outline of course and introduction to the laboratory experiment.
Measurement methods and modal analysis (4L, Dr HEM Hunt)
- Instrumentation for vibration measurement;
- Review of modal analysis; General properties of vibration response;
- Introduction to experimental modal analysis; Modelling the bounce of a hammer.
Analysis of damped systems (4L, Prof J Woodhouse)
- Mechanisms of damping: complex modulus, boundary dissipation, lumped dissipative elements;
- Adding damping to structures, constrained and unconstrained layers;
- Viscous damping, complex modes.
System components and coupling (4L Prof J Woodhouse)
- The Helmholtz resonator and its uses;
- Review of beam, membrane and plate governing equations;
- The circular membrane, Bessel functions, mode shapes and frequencies;
- Coupling of subsystems, constraints and the interlacing theorem.
Coursework
One laboratory experiment on experimental modal analysis, to be performed in pairs, essentially unsupervised. A booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. Total time commitment will be comparable to a Part IIA experiment plus FTR.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Lab experiment: modal analysis Measure vibration transfer functions over a grid of points covering a simple structure, then use modal analysis techniques explained in the lectures to infer the first few mode shapes. Learning objective:
|
Individual/pair Report Anonymously marked |
Before final lecture slot, which is a feedback session on the lab Wed week 8 [15/15] |
Booklists
Please see the Booklist for Group C 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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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: 01/09/2017 10:01
Engineering Tripos Part IIB, 4C6: Advanced Linear Vibrations, 2022-23
Module Leader
Lecturers
Lab Leader
Timing and Structure
Michaelmas term. 13 lectures + 2 examples classes + coursework. Assessment: 75% exam/25% coursework. This course will be delivered in-person in 2021-22.
Prerequisites
3C6 assumed.
Aims
The aims of the course are to:
- teach some essential tools for the understanding, analysis and measurement of vibration in engineering structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- be familiar with the theory and practice of modal analysis and its application to engineering structures.
- apply experimental modal techniques.
- understand the vibration behaviour of idealised system components, and be able to draw implications from this for complex coupled systems.
- appreciate the physical principles of vibration damping.
- analyse simple damped vibrating systems.
Content
Introduction (1L, Dr JP Tabot)
Outline of course and introduction to the laboratory experiment.
Measurement methods and modal analysis (4L, Dr JP Talbot)
- Instrumentation for vibration measurement;
- Review of modal analysis; General properties of vibration response;
- Introduction to experimental modal analysis; Modelling the bounce of a hammer;
- Applications.
Analysis of damped systems (4L, Dr Tore Butlin)
- Mechanisms of damping: complex modulus, boundary dissipation, lumped dissipative elements;
- Adding damping to structures, constrained and unconstrained layers;
- Viscous damping, complex modes.
System components and coupling (4L Dr Tore Butlin)
- The Helmholtz resonator and its uses;
- Review of beam, membrane and plate governing equations;
- The circular membrane, Bessel functions, mode shapes and frequencies;
- Coupling of subsystems, constraints and the interlacing theorem.
Further notes
Coursework
One laboratory experiment on experimental modal analysis, to be performed in pairs, essentially unsupervised. A booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. Total time commitment will be comparable to a Part IIA experiment plus FTR.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
Lab experiment: modal analysis Measure vibration transfer functions over a grid of points covering a simple structure, then use modal analysis techniques explained in the lectures to infer the first few mode shapes. Learning objective:
|
Individual/pair Report Anonymously marked |
Completed reports should be submitted via Moodle as a PDF file by 4pm on Tues 29 Nov [15/15] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
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.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
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: 22/11/2022 17:30
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