Nonlinear Structural Dynamics
Lead Research Organisation:
University of Glasgow
Department Name: School of Engineering
Abstract
This work will continue the work of Cammarano, Hill, Neild and Wagg, conducting further studies into the behaviour of multi-degrees-of-freedom nonlinear oscillators. The research will initially be conducted theoretically, and then these theoretical findings will be applied and proven in a laboratory setting. In particular, focus will be given to the occurrence of bifurcations in the backbone curves of these oscillators, investigating the reason and conditions behind them and the influence of physical parameters on their size, nature and the frequency with which they occur.
The outcomes for this research are as follows:
1. To create mathematical models for nonlinear dynamic systems, using computational techniques to allow analysis of the solutions and models to completed
2. To conduct analysis of the behaviour of multi-degrees-of-freedom nonlinear oscillators using realistic values for the parameters in aforementioned mathematical models
3. To test the accuracy of these theoretical models using experimental techniques
The outcomes for this research are as follows:
1. To create mathematical models for nonlinear dynamic systems, using computational techniques to allow analysis of the solutions and models to completed
2. To conduct analysis of the behaviour of multi-degrees-of-freedom nonlinear oscillators using realistic values for the parameters in aforementioned mathematical models
3. To test the accuracy of these theoretical models using experimental techniques
People |
ORCID iD |
| Andrea Cammarano (Primary Supervisor) | |
| Alexander Elliott (Student) |
Publications
Elliott A
(2019)
Nonlinear Dynamics, Volume 1
Elliott AJ
(2018)
Comparing the direct normal form and multiple scales methods through frequency detuning.
in Nonlinear dynamics
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509668/1 | 30/09/2016 | 29/09/2021 | |||
| 1655916 | Studentship | EP/N509668/1 | 30/09/2015 | 04/07/2019 | Alexander Elliott |
| Description | The accuracy of the Method of Multiple Scales (MS) has been improved through the novel application of a detuning to the response frequency. This originated in a comparison between the accuracy of this method and the Direct Normal Forms (DNF) method; effectively, the DNF method assumes that the response frequency is close to the forcing frequency and adds a small term in the equations to account for this. The application of this step in the MS method led to more accurate results. A thorough investigation into the accuracy of ROMs, both using finite element software and analytical techniques, is currently being undertaken. Particular emphasis is being put on the way in which these methods develop the numerical coefficients and the extent to which this affects their accuracy. |
| Exploitation Route | In terms of the analytical approximation comparison, the final step is to complete the comparison into forced, continuous structures; this will be completed for a chapter in the thesis. By effectively creating an equivalence between some of the leading methods, the user will be left with a range of techniques which cover a broad scope of nonlinear behaviour with no reduction in accuracy from the use of a particular technique. A key aim of the investigation into reduced-order models is to develop the knowledge, and possibly a rigorous technique, that allows the size of the model to be optimised in terms of accuracy and performance. The investigation is something that has already been started as part of this project and will be completed as part of the thesis. It is currently unclear whether a rigorous technique will be achieved, but there is already scope to extend the current application of correlation coefficients into such a method. A final application for the investigations thus far is in nanoscale structures, which is something that is being planned as a final chapter of the thesis. |
| Sectors | Aerospace Defence and Marine Construction Digital/Communication/Information Technologies (including Software) Energy Environment Transport |
| Description | Extended collaboration with the University of Bristol and the University of Sheffield |
| Organisation | University of Bristol |
| Department | Faculty of Engineering |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This collaboration is effectively a continuation of the progress made in the EPSRC-funded Engineering Nonlinearity project, which has now come to a close. The work together has been primarily driven by the fact that both my first and second supervisors were part of this project, with the latter being based at the University of Bristol. The collaboration can be broadly separated into two parts: one project to investigate the relative accuracy of analytical approximation techniques (in further conjunction with the University of Sheffield), and the other into reduced-order models for nonlinear structures. For the analytical investigation, the vast majority of this work has been undertaken by myself, including the development of the symbolic mathematical and numerical codes, as well as writing the two publications that have been created. The first of these is the conference paper presented at the International Modal Analysis Conference, entitled "Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems". The second is a full journal paper in Nonlinear Dynamics, entitled "Comparing the direct normal form and multiple scales methods through frequency detuning", which is currently in the final stages of the review, with the response to the reviewer submitted. There is the further possibility of submitting a second journal paper looking into an extended comparison for continuous structures and forced responses, though this is dependent on the completion of some of the other sections in my thesis. The second part of the collaboration with the University of Bristol is primarily with another researcher and is concerned with assessing and developing reduced-order models (ROMs) for both lumped-mass and continuous nonlinear structures. In this collaboration, my contribution has been the investigation into continuous structures, including developing the existent code for producing the ROMs, as well as developing the code to generate the full-model responses; it should be noted that I am in the process of developing/refining my own ROM codes, but these were not used in the publication for reasons of consistency. The publication will be submitted to the Journal of Sound and Vibration and is in the final stages of development. My contribution to the paper was both the results and writing of the discussion for the investigation into continuous structures. I am further contributing to a second journal paper investigating a specific, more complex continuous structure, in which I will again develop the results for the full mode through the use of the code I have developed. |
| Collaborator Contribution | In the first part of the collaboration, the role of my collaborators has been an advisory role in the project, with the application of their expertise guiding the investigation and contributing to the discussion. In the second collaboration, the researcher at the University of Bristol has led the direction of the project and developed the code for creating the ROMs, which were then compared with the numerical results from my code. |
| Impact | ISBN 978-3-319-54403-8, future publications discussed above. |
| Start Year | 2015 |
| Description | Extended collaboration with the University of Bristol and the University of Sheffield |
| Organisation | University of Sheffield |
| Department | Department of Mechanical Engineering |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This collaboration is effectively a continuation of the progress made in the EPSRC-funded Engineering Nonlinearity project, which has now come to a close. The work together has been primarily driven by the fact that both my first and second supervisors were part of this project, with the latter being based at the University of Bristol. The collaboration can be broadly separated into two parts: one project to investigate the relative accuracy of analytical approximation techniques (in further conjunction with the University of Sheffield), and the other into reduced-order models for nonlinear structures. For the analytical investigation, the vast majority of this work has been undertaken by myself, including the development of the symbolic mathematical and numerical codes, as well as writing the two publications that have been created. The first of these is the conference paper presented at the International Modal Analysis Conference, entitled "Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems". The second is a full journal paper in Nonlinear Dynamics, entitled "Comparing the direct normal form and multiple scales methods through frequency detuning", which is currently in the final stages of the review, with the response to the reviewer submitted. There is the further possibility of submitting a second journal paper looking into an extended comparison for continuous structures and forced responses, though this is dependent on the completion of some of the other sections in my thesis. The second part of the collaboration with the University of Bristol is primarily with another researcher and is concerned with assessing and developing reduced-order models (ROMs) for both lumped-mass and continuous nonlinear structures. In this collaboration, my contribution has been the investigation into continuous structures, including developing the existent code for producing the ROMs, as well as developing the code to generate the full-model responses; it should be noted that I am in the process of developing/refining my own ROM codes, but these were not used in the publication for reasons of consistency. The publication will be submitted to the Journal of Sound and Vibration and is in the final stages of development. My contribution to the paper was both the results and writing of the discussion for the investigation into continuous structures. I am further contributing to a second journal paper investigating a specific, more complex continuous structure, in which I will again develop the results for the full mode through the use of the code I have developed. |
| Collaborator Contribution | In the first part of the collaboration, the role of my collaborators has been an advisory role in the project, with the application of their expertise guiding the investigation and contributing to the discussion. In the second collaboration, the researcher at the University of Bristol has led the direction of the project and developed the code for creating the ROMs, which were then compared with the numerical results from my code. |
| Impact | ISBN 978-3-319-54403-8, future publications discussed above. |
| Start Year | 2015 |
| Description | Nanoscale application of nonlinear techniques |
| Organisation | University of Glasgow |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | This internal collaboration with the James Watt Nanofabrication Centre is a combined investigation into the nonlinear dynamics of nanoscale structures. My contribution to this collaboration is to develop the modelling side of the investigation and to create predictions of nonlinear behaviour that can be investigated experimentally. |
| Collaborator Contribution | My collaborators are to construct and test the nanoscale structures to test the accuracy of the nonlinear reduced-order models. |
| Impact | This collaboration is still in its infancy, but a conference presentation application has been submitted and it is hoped that at least one journal paper will be published. |
| Start Year | 2018 |
| Description | International Modal Analysis Conference (IMAC) presentation 2017 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Around 50-60 conference attendees at IMAC watched my presentation "Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems". This invited some interesting discussion once the floor was opened for questions, as well as leading to some researchers initiating discussions at other points in the conference. |
| Year(s) Of Engagement Activity | 2017 |
| URL | https://link.springer.com/chapter/10.1007/978-3-319-54404-5_4#aboutcontent |
| Description | International Modal Analysis Conference (IMAC) presentation 2018 |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Around 40-50 conference attendees at IMAC watched my presentation "Investigating Modal Contributions using a Galerkin Model". This led to some interesting questions from the audience, as well as further discussions into the project at later points. |
| Year(s) Of Engagement Activity | 2018 |
| URL | http://sem.org/imac |
| Description | Speak Out for Engineering - IMechE Competition |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | On 16th March 2018, I am presenting a talk entitled "Nonlinear Dynamics: Modelling challenges for 21st century systems" at the IMechE competition, Speak Out for Engineering. This is a regional heat of an international competition which will give me the opportunity to present the progress I have made in my PhD to a wider engineering audience. There is a section dedicated entirely to questions from the audience and judges, which will hopefully create some interesting discussion into how the outcomes of my work can be applied in a wider setting. |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://www.imeche.org/get-involved/young-members-network/speak-out-for-engineering |