Stochastic Nonsmooth Analysis For Energy Harvesting

An international research project aimed to explore the dynamics and capabilities of vibro-impact energy harvesting devices to develop efficient design tools and methodologies to harvest vibrational energy.

Summary

This multidisciplinary project is an international collaboration between Georgia Tech, Georgia State University and University of Southampton in the area of applied mathematics, nonlinear dynamics and energy harvesting with soft electroactive polymers. The project will address gaps and opportunities in mathematical developments and in practical applications for impact-based engineering devices and systems with non-smooth dynamics, critical for understanding the harvesting of vibrational energy. The main research objective is to develop a universal suite of mathematical methodologies for the analysis and optimized performance of deterministic and stochastic non-smooth engineering systems. These approaches are pursued with a focus on practical engineering models of vibro-impacting energy harvesting systems and nonlinear dynamic dampers, within the broad area of targeted energy transfer. Integrating novel nonlinear, stochastic, and computational approaches with experimental and real-world data both for energy harvesting and for devices that mitigate vibration will pave new pathways for analysis-based design and model validation.

People

Principal Investigators

Rachel Kuske

Professor
Head of School of Mathematics
Georgia Institute of Technology
Atlanta, US

Igor Belykh

Professor
Department of Mathematics and Statistics
Georgia State University
Atlanta, US

Daniil Yurchenko

Associate Professor
Institute of Sound and Vibration Research
University of Southampton
Southampton, UK

Researchers

Christina Athanasouli

Hale Visiting Assistant Professor
School of Mathematics
Georgia Institute of Technology, Atlanta

Rahul Kumar

Visiting Assistant Professor
School of Mathematics
Georgia Institute of Technology, Atlanta

Lanjing Bao

PhD Student
Department of Mathematics and Statistics
Georgia State University, Atlanta

Henrik T Sykora

Postdoctoral Research Fellow
Institute of Sound and Vibration Research
University of Southampton, Southampton

Collaborators

Larissa Serdukova

Lecturer / Assistant Professor
School of Computing and Mathematical Sciences
University of Leicester, Leicester

Dimitri Costa

Research Fellow
School of Engineering
University of Aberdeen, Aberdeen

Participating undergratuate Students through Georgia Tech's School of Math Research Experience for Undergrads - Summer program

Sam Dulin, Kailee Lin (2020)

Ivan Gonzalez, Ruofeng Liu (Goldwater Scholar), Julia Sanger, Corrine Vicario (2021)

Emily Almgren, Samuel Kwan , Aaron Lee, Hung Nguyen, Nilay Patel (2023)

Aine Doherty, Arnav Garg, Nathan Hasegawa, Yash Permalla (2024)

(research projects available at math.gatech.edu/undergraduate-research )

Publications

Journal papers

Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method (link)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

1 March 2024

Exploring effective TET through a vibro-impact nonlinear energy sink over broad parameter regimes (link)

Rahul Kumar, Rachel Kuske, Daniil Yurchenko

3 Feb 2024

Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink (link)

Ruofeng Liu, Rachel Kuske, Daniil Yurchenko

15 May 2023

Numerical optimisation of a classical stochastic system for targeted energy transfer (link)

Oleg Gaidai, Yubin Gu, Yihan Xing, Junlei Wang, Daniil Yurchenko

28 December 2022

Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs (link)

Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

15 December 2022

Qualitative changes in bifurcation structure for soft vs hard impact models of a vibro-impact energy harvester (link)

Dimitri Costa, Rachel Kuske, Daniil Yurchenko

27 October 2022

Systematic matrix formulation for efficient computational path integration (link)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

7 September 2022

Improving the performance of a two-sided vibro-impact energy harvester with asymmetric restitution coefficients (link)

Sam Dulin, Kailee Lin, Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

1 March 2022

Post-grazing dynamics of a vibro-impacting energy generator (link)

Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

3 February 2021

Stability and bifurcation analysis of the period-T motion of a vibroimpact energy harvester (link)

Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

26 October 2019

Conference Talks

Friction and noise enhancing energy outcomes in vibro-impact pairs

Christina Athanasouli, Rahul Kumar, Rachel Kuske, Daniil Yurchenko

Investigating Dynamics in Engineering and Applied Science (IDEAS 2024), 29-31 July (Budapest, Hungary)

Stochastic characterisation of vibro-impact oscillators with frictional impacts (link to conference)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

11th European Nonlinear Dynamics Conference (ENOC 2024), 22 - 26 July, 2024 (Delft, Netherlands)

Influence of noise on energy generation in a VI-EH with dry friction (link to conference)

Christina Athanasouli, Rachel Kuske, Daniil Yurchenko

11th European Nonlinear Dynamics Conference (ENOC 2024), 22 - 26 July, 2024 (Delft, Netherlands)

Computer-assisted global dynamics of a vibro-impact pair via reduced smooth maps (link to conference)

Lanjing Bao, Igor Belykh, Rachel Kuske, Daniil Yurchenko

11th European Nonlinear Dynamics Conference (ENOC 2024), 22 - 26 July, 2024 (Delft, Netherlands)

Understanding Energy Transfer Through VINES Under Random External Excitation (link to conference)

Rahul Kumar, Rachel Kuske, Daniil Yurchenko

11th European Nonlinear Dynamics Conference (ENOC 2024), 22 - 26 July, 2024 (Delft, Netherlands)

Computer-assisted global analysis of non-smooth impact dynamics inspired by energy harvesting

Lanjing Bao, Rachel Kuske, Daniil Yurchenko, Igor Belykh

Workshop on Multiple Scales: Theory and Applications, 8 - 12 July, 2024 (Leiden, Netherlands)

Keynote: Computer-assisted analysis for the global dynamics of a vibro-impact pair via reduced smooth maps

Rachel Kuske

Euromech Colloquium 641: Non-smooth Dynamical Systems, 11 - 13 December, 2024 (Dublin, Ireland)

Keynote: Complex behaviour of a 2D vibroimpact energy harvesting system

Daniil Yurchenko

Euromech Colloquium 641: Non-smooth Dynamical Systems, 11 - 13 December, 2024 (Dublin, Ireland)

Influence of Noisy Excitation on Dynamics and Energy Transfer Through VINES

Rahul Kumar, Daniil Yurchenko, Rachel Kuske

Euromech Colloquium 641: Non-smooth Dynamical Systems, 11 - 13 December, 2024 (Dublin, Ireland)

Influence of stiffness variations in the chaos control of a vibro-impact energy harvester

Dimitri Costa, Daniil Yurchenko, Rachel Kuske, Ekaterina Pavlovskaia

Euromech Colloquium 641: Non-smooth Dynamical Systems, 11 - 13 December, 2024 (Dublin, Ireland)

Desirable energy generation in a VI-EH with dry friction

Christina Athanasouli, Daniil Yurchenko, Rachel Kuske

Euromech Colloquium 641: Non-smooth Dynamical Systems, 11 - 13 December, 2024 (Dublin, Ireland)

Analysis of two types of non-smooth dynamics in an energy harvester

Christina Athanasouli, Daniil Yurchenko, Rachel Kuske

AWM Research Symposium, 30 September - 02 October, 2023 (Atlanta, USA)

Computer-assisted analysis of the global dynamics of a vibro-impact pair

Lanjing Bao, Daniil Yurchenko, Rachel Kuske, Igor Belykh

AWM Research Symposium, 30 September - 02 October, 2023 (Atlanta, USA)

Efficient path integral formulation for the response statistics of stochastic vibro-impact systems (abstract)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

Third International Nonlinear Dynamics Conference (NODYCON 2023), 18-22 June, 2023 (Rome, Italy)

Performance Enhancement of Vibro-Impact Targeted Energy Transfer Within a Random Environment

Rahul Kumar, Daniil Yurchenko, Rachel Kuske

ASCE Engineering Mechanics Institute Conference 2023 (ASCE EMI 2023), 6-9 June, 2023 (Atlanta, USA)

Response statistics of vibro-impact system via the Step Matrix Multiplication based on Path Integration method

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

ASCE Engineering Mechanics Institute Conference 2023 (ASCE EMI 2023), 14-18 May, 2023 (Atlanta, USA)

Parametric Study of Targeted Energy Transfer Through Vibro-Impact System Using Map Based Approach (abstract)

Rahul Kumar, Daniil Yurchenko, Rachel Kuske

SIAM Conference on Applications of Dynamical Systems (SIAM DS23), 14-18 May, 2023 (Portland, USA)

Reduction to Smooth Maps for the Global Dynamics of a Vibro-Impact Pair Model (abstract)

Lanjing Bao, Rachel Kuske, Daniil Yurchenko, Igor Belykh

SIAM Conference on Applications of Dynamical Systems (SIAM DS23), 14-18 May, 2023 (Portland, USA)

Bifurcations of Periodic Solutions in a Vibro-Impact System with Dry Friction (abstract)

Christina Athanasouli, Daniil Yurchenko, Rachel Kuske

SIAM Conference on Applications of Dynamical Systems (SIAM DS23), 14-18 May, 2023 (Portland, USA)

Efficient Path Integration for the Computation of Response Probability Density Functions of Oscillators with Impacts (abstract)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

SIAM Conference on Applications of Dynamical Systems (SIAM DS23), 14-18 May, 2023 (Portland, USA)

Nonlinear and stochastic dynamics in a forced vibro-impact energy harvester (book of abstracts)

Rachel Kuske, Daniil Yurchenko, Larissa Serdukova

10th European Nonlinear Dynamics Conference (ENOC 2020+2), 17-22 July, 2022 (Lyon, France)

Dynamical analysis of TET in a non-smooth vibro-impact system (book of abstracts)

Ruofeng Liu, Dimitri Costa, Daniil Yurchenko, Rachel Kuske

10th European Nonlinear Dynamics Conference (ENOC 2020+2), 17-22 July, 2022 (Lyon, France)

An efficient method to obtain the response PDF of nonlinear stochastic dynamical systems (book of abstracts)

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

10th European Nonlinear Dynamics Conference (ENOC 2020+2), 17-22 July, 2022 (Lyon, France)

Dynamic non-smooth fold bifurcations influenced by oscillations and noise (book of abstracts)
Rachel Kuske, Chris Budd, Cody Griffith

10th European Nonlinear Dynamics Conference (ENOC 2020+2), 17-22 July, 2022 (Lyon, France)

Stability of rotatory solitary states in Kuramoto networks with inertia (Workshop program)

Igor Belykh (invited speaker)

Chimera states: From Theory and Experiments to Technology, 16-20 May, 2022 (Dresden, Germany)

Comparisons of hard and soft impact on a vibro-impact energy harvester: a semi-analytical approach

Dimitri Danulussi Alves Costa, Daniil Yurchenko, Rachel Kuske

The 10th international Conference on Wave Mechanics and Vibrations (WMVC 2022), 4-6 July, 2022 (Lisbon, Portugal)

Probability density functions of stochastic vibro-impact systems via the path-integration method

Henrik T Sykora, Rachel Kuske, Daniil Yurchenko

The 10th international Conference on Wave Mechanics and Vibrations (WMVC 2022), July 4-6, 2022 (Lisbon, Portugal)

Dynamic non-smooth bifurcations influenced by noise and oscillations (talk)

Rachel Kuske (invited speaker)

ICMC Summer Meeting on Differential Equations, 31 January - 2 February, 2022 (virtual)

Multiple Routes to Grazing in Vibro-Impact Energy Harvesters (abstract)

Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

SIAM Conference on Applications of Dynamical Systems (SIAM DS21), May 23-27, 2021 (virtual)

Stability and bifurcation analysis of the period-T motion of a vibro-impacting energy generator (abstract)

Larissa Serdukova, Rachel Kuske, Daniil Yurchenko

SIAM Conference on Applications of Dynamical Systems (SIAM DS19), May 19-23, 2019 (Snowbird, UT, USA)

Thematic sessions / Special issues

Session at the AWM Research Symposium (30.09-02.10 2023):
Women in Dynamical Systems and Applications
Organisers: Christina Athanasouli, Rachel Kuske

Two part minisymposium at SIAM DS23:
Non-Smooth Dynamical Systems With Impacts: Analysis and Applications
Organisers: Rahul Kumar, Christina Athanasouli, Henrik T Sykora, Darlington David

Two part minisymposium at SIAM DS21:
Non-Smooth Dynamics: Discontinuity-Induced Bifurcations, Stability and Control
Organisers: Rachel Kuske, Igor Belykh

Focus issue and review paper in Chaos (2023):
Beyond the Bristol book: Advances and perspectives in non-smooth dynamics and applications (focus issue, review paper)
Igor Belykh, Rachel Kuske, Maurizio Porfiri, David J. W. Simpson

Other publications

Dynamic tipping and cyclic folds, in a one-dimensional non-smooth dynamical system linked to climate models (link)
Chris Budd, Rachel Kuske
January 2024

Dynamic tipping in the non-smooth Stommel-box model, with fast oscillatory forcing (link)
Chris Budd, Cody Griffith, Rachel Kuske
April 2022

Find us

University of Southampton

Southampton, SO17 1BJ, UK

Georgia Institute of Technology

Atlanta, GA 30332, USA

Georgia State University

Atlanta, GA 30302-3965, USA

Funding

NSF: CMMI/DMS 2009270 (USA)

EPSRC: EP/V034391/1 (UK)

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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