Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2018-19
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- understand how to define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
- Note that this part of the 4C9 course is new for 2018-19.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
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: 03/08/2018 14:56
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2023-24
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
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: 30/05/2023 15:28
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2024-25
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
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: 31/05/2024 10:02
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2017-18
Module Leader
Lecturers
Prof VS Deshpande and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic, visco-elastic and plastic bodies.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of Cartesian tensor notation
- use the method of minimum potential energy to solve problems in linear elasticity
- understand how to solve viscoelastic problems in 1D and 3D for arbitrary loading time-histories
- know Drucker's stability postulate and understand the implications of convexity and normality
- understand the difference between deformation and flow theories of plasticity
- able to apply slip line field theory as well as upper and lower bound theorems for perfectly plastic solids
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic and plastic bodies.
Preliminaries (3L, Dr GJ McShane)
- Introduction to indicial notation
- Vectors, tensors and their manipulation
- Stress and equilibrium, strain and compatibility, constitutive relationships
Elasticity and Viscoelasticity (5L, Dr GJ McShane)
- Method of minimum potential energy
- Examples: application to elastic beams and plates in bending
- Deriving constitutive equations for linear viscoelasticity
- Solving viscoelastic problems in 1D for arbitrary loading time-histories
- Viscoelastic analysis in 3D
Plasticity (8L, Prof VS Deshpande)
- Constitutive relationships - Drucker's stability postulate, normality and convexity conditions, yield criteria, flow rules, strain-hardening materials, flow and deformation theories of plasticity;
- Limit analysis theorems;
- Slip-line field theory; the solution of boundary value problems - metal forming, contact problems, cracked bodies.
Examples papers
- Paper 1 - Preliminaries
- Paper 2 - Elastic and viscoelastic analysis
- Paper 3 - Plasticity 1
- Paper 4 - Plasticity 2
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.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
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: 31/05/2017 09:12
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, 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, 2018-19
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 8 28 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: 27/11/2018 15:24
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