DMS-EPSRC Stochastic Nonsmooth Analysis For Energy Harvesting

Lead Research Organisation: University of Southampton
Department Name: Sch of Engineering

Abstract

Please, see the attachment with the entire proposal.
 
Description 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.

Major Activities:
Here is a list of the major subprojects, with the notation P#. used in the rest of the report and achieved by all the teams involved in the project.

P1. 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. We will also include dry friction in the VI-EH model, exploring the influence of sticking in the bifurcation structure, and its influence on state transitions which cause changes in energy output.
P2. 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.
P4. Development of a new approach for identifying basins of attraction and characterizing global bifurcations for impacting systems. To be combined with stochastic analysis for identification of basins of attraction for different states.
P5. Modernization of Stochastic Path Integration methods that can be used for VI systems for larger degrees of freedom.
P6. Extension of the dynamical and stochastic analyses to general models of Target Energy Transfer (TET), utilizing impact pairs as the underlying mechanism for TET, generally referred to as VI-NES (Vibro Impact Nonlinear Energy Sink). 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.
P7. Complementary experimental work (ongoing) at ISVR involves building the membranes for the VI-EH device, collecting data on physical properties to build into the models, and then building a prototype of the Vi-EH device for ongoing testing for synergistic feedback with the models.
Exploitation Route Outcomes of the project can be both academic and non-academic. Scientists working in the area of nonlinear and stochastic systems can use the generated results to predict the dynamics of the intricated non-smooth systems and explain the stability of different types of motion, and how the instability occurs in vibroimpact systems. Non-academics can use the result to build a prototype of the vibroimpact energy harvester, which can be used in the vibrating environment where high amplitude pulses or high amplitude period response can be observed as the input excitation to the system. Apart from other well-known energy harvesters, which utilise piezoelectric transduction and can be broken under high amplitude excitation, the proposed device benefits from low-frequency high amplitude excitations.
Sectors Aerospace

Defence and Marine

Energy

Transport
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
 
Title Path Integration Method Tool 
Description The software solves numerically the Chapman-Kolmogorov integral equation and has three separate parts: interpolation of the probability density function, approximation of the transitional probability density function of the process and evaluation of the integral of the Chapman-Kolmogorov equation. The developed tool is placed in GitHub and the theory behind the software is published in this paper: https://doi.org/10.1016/j.compstruc.2022.106896. 
Type Of Technology Webtool/Application 
Year Produced 2023 
Open Source License? Yes  
Impact The created novel methodology allows numerical treatment of the Chapman-Kolmogorov equation, which is used in the path integration method, which is used for computing the response probability density function (pdf) of stochastic dynamical systems. Thus, the diverse variety of scientists from different fields of science, including engineering, physics, mathematics, finance, etc. who work with stochastic differential equations will be able to swiftly evalute a response pdf and find essential statistical characteristics of their specific system. 
URL https://github.com/HTSykora/PathIntegrationMethod.jl