DMS-EPSRC Stochastic Nonsmooth Analysis For Energy Harvesting
Lead Research Organisation:
Heriot-Watt University
Department Name: Sch of Engineering and Physical Science
Abstract
Please, see the attachment with the entire proposal.
Publications
Costa D
(2022)
Qualitative changes in bifurcation structure for soft vs hard impact models of a vibro-impact energy harvester.
in Chaos (Woodbury, N.Y.)
Dulin S
(2022)
Improving the performance of a two-sided vibro-impact energy harvester with asymmetric restitution coefficients
in International Journal of Mechanical Sciences
Gaidai O
(2023)
Numerical optimisation of a classical stochastic system for targeted energy transfer
in Theoretical and Applied Mechanics Letters
Kumar R
(2024)
Exploring effective TET through a vibro-impact nonlinear energy sink over broad parameter regimes
in Journal of Sound and Vibration
Liu R
(2023)
Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink
in Mechanical Systems and Signal Processing
Sykora H
(2022)
Systematic matrix formulation for efficient computational path integration
in Computers & Structures
| Description | The project has already generated significant new knowledge in the area of non-smooth dynamical systems, namely: 1. We have presented a systematic study of prevalence of "standard" bifurcations, such as period doubling bifurcation, vs. bifurcations related to non-smooth character of the model, e.g. grazing bifurcations. It has been shown for the first time that classical period doubling bifurcations, predicted analytically may in fact not be observed physically due to interplay and appearance of grazing bifurcation, typical for non-smooth vibroimpact (VI) systems and non-smooth energy harvesting (EH). This result has never been reported before and explains the confusion raised earlier in a number of publications regarding the inability to observe classical theoretically developed bifurcations. 2. We have developed and calibrated soft impact and hard impact models for the VI-EH, and compared the models with each other and with data collected for dielectric polymers used in the VI-EH device. Bifurcation study of these models, to be used in larger stochastic studies conducted by the UK and worldwide researchers as a benchmark. 3. We conducted dynamical and stochastic analyses of the influence of variable parameters in the VI-EH system, both in terms of design parameters and in terms of input parameters from the external forcing. We have also developed new methods for analysis of stochastic systems, namely: 4. We conducted a modernisation of Stochastic Path Integration(PI) method, developing a new Step Matrix Multiplication methodology that can be used for nonlinear and non-smooth multi-degree-of-freedom systems. We provided a thorough error and efficiency analysis through numerical experiments on a one, two, three and four-dimensional problem. By comparing the results obtained through the SMM-PI method with analytical solutions and with previous formulations of the path integration method, we demonstrate the superior ability of this formulation to provide accurate results. The developed new approach proved to be robust, consistent and accurate, and thus can be used by others in estimating dynamic characteristics of stochastic systems, such as moments of various orders as well as the new approach can help in better understanding of rare events. 5. We develop a new approach for the dynamical and stochastic analyses of general models of Target Energy Transfer (TET), utilising impact pairs as Nonlinear Energy Sink (NES) for the underlying mechanism for TET. Our map approach is not limited to certain parameter regimes, in contrast to previous studies using continuous approximations, or other types of models based on continuous models of dynamic dampers. By adapting the map-based approach, developed for the VI-EH system, to the full VI-NES system, we provide the flexibility to consider different types of periodic solutions that include any possible combination of impact sequences in the full two DoF model of VI-NES. |
| Exploitation Route | The developed results can be used by engineers, applied mathematicians, people using numerical methods and other researches, including PhDs and PostDocs, working with dynamical and stochastic systems as well as non-smooth systems. The developed numerical method can be of special interest to companies working with uncertainties to estimate structural failure of a civil or mechanical system, like a bridge or gearbox, under stochastic loading. |
| Sectors | Construction,Energy |
| URL | https://sites.google.com/view/vienergyharvest |
| Description | Georgia Institute of Technology |
| Organisation | Georgia Institute of Technology |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | This proposal targets a largely unexplored area in nonlinear science, advancing systematic mathematical analyses and modeling of non-smooth dynamics and bifurcations in impacting systems in the presence of variability, uncertainty and stochasticity. The main research objective of this proposal is to develop the first universal suite of mathematical methodologies for the analysis and performance optimization of stochastic non-smooth engineering systems. This goal is pursued with a focus on practical engineering models of vibroimpacting energy harvesting (VI-EH) and nonlinear dynamic dampers, within the broad area of targeted energy transfer (TET). Integrating these novel nonlinear, stochastic, and computational approaches within the broader context of applied analysis of non-smooth dynamics systems will define general semi-analytical methodologies for larger classes of impacting systems. Integration with experimental and real world data for VI-EH and TET devices will also pioneer new paths for analysis-based design and model validation. Our contribution to the project is: 1. Modernization of Stochastic Path Integration methods that can be used for VI systems for larger degrees of freedom. At this stage we have developed a new approach to tackle the multidimensional problems of stochastic synamics, which allow to scale up the proposed methodology to higher order nonlinear systems. This is rather combursome and computationally demanding work, which takes a lot of efforts and the hired DPRA has been specifically focused on compliting this work. A research paper what will report this adbvancement has been prepared and it is going through proof-reading stage before to be submitted to a peer-review journal. 2. We have contibuted to the extension of the dynamical and stochastic analyses to general models of Target Energy Transfer (TET), utilizing impact pairs as the underlying mechanism for TET, in contrast to previous models based on continuous models of dynamic dampers. 3. We have started the process of building the dielectric membranes for the VI-EH device, collecting data on physical properties to build in to the models, and then building a prototype of the Vi-EH device for on-going testing for synergistic feedback with the models. Unfortunately due to COVID and Braxit, not all the required equioment has arrived on time, some of it was delayed for 3 months. Nevertheless, we currently have all the required equioment to go ahead and build and test the DE membranes. This will help us to calibrate the numerical models we have developed. 4. For the broader dissemination of the project results we have pressented our work at various online coferences and we are going to present our work during summer 2022. Moreover, the dedicated website has been created ( https://vienergyharvest.site.hw.ac.uk ) and it is regularly updated with the project progress, publications and presentations, and project mentioning by media. |
| Collaborator Contribution | Georgia Institute of Technology (GT) has been the led university from the USA side. During this year the GT parners led regular project meetings. They have also contributed in: 1. Development and calibration of soft impact and hard impact models for the VI-EH, for comparison with each other and with data collected for dielectric polymers used in the VI-EH device. Bifurcation study of these models, to be used in larger stochastic studies. 2. Dynamical and stochastic analyses of the influence of variable parameters in the VI- EH system, both in terms of design parameters and in terms of input parameters from the external forcing. P3. Systematic study of prevalence of "standard" bifurcations, such as period doubling bifurcation, vs. bifurcations related to non-smooth character of the model, e.g. grazing bifurcations. |
| Impact | We have published an article in peer review open access jounral (see the outputs in the table of publications) Minisymposia and presentations at the 2021 SIAM Applied Dynamical Systems Conference 1. A two-part minisymposium "MS11 Non-Smooth Dynamics: Discontinuity-Induced Bifurcations, Stability, and Control " - organized 2. "Multiple Routes to Grazing in Vibro-Impact Energy Harvesters," Larissa Serdukova, presenter, collaboration with R. Kuske and D. Yurchenko. |
| Start Year | 2021 |