Scientific Activities

Scientific workers of the Applied Mathematics Department perform scientific studies which correspond to important problems of modern science and engineering. These studies can be divided into several branches:

  • The first one refers to methods of solution of plates and shells theory problems by means of the R-functions theory. Investigations of this kind are performed by the Head of the department Prof. L. Kurpa and her followers.
  • The second one refers to problems of regular and chaotic mechanics of non-linear systems, in particular, to the nonlinear normal modes theory, problems of stability of motion, problems of vibration damping, problems of vibro-impact oscillations, etc. These investigations are performed by Prof. Yu.Mikhlin and the Non-linear Dynamics Research Group.
  • Professor  V. Burlayenko and Associate Professor L. Dzyubak work on their investigations as individuals. Their investigations refer to the fields of structural mechanics and solid mechanics.

Some of the researchers of the Department took part in international research projects. Namely, Assoc. Prof. V. Burlayenko took part in the scientific research funded by German Academic Exchange Service (DAAD) and INTAS at Martin-Luther-Universitat Halle-Wittenberg (Halle, Germany) in 2000, 2019 and 2002-2003, respectively, and by German Research Foundation at Otto-von-Guericke Magdeburg University (Magdeburg, Germany) in 2015 and by Erasmus Mundus program at University of Southampton (Southampton, England) in 2015-2016. Also, he participated in two international research projects within the FP6 and FP7 at Lublin University of Technology in 2006-2008 and 2011-2013, respectively. In 2017 V. N. Burlayenko received a 24-month fellowship for performing in cooperation with Professor T. Sadowski from Lublin University of Technology a research project “Reliability of skin-to-core interface in sandwich composites for dynamically loaded applications” at the Department of Solid Mechanics, Lublin University of Technology, Lublin, Poland. This research was supported by the National Science Centre of Poland, grant agreement No UMO-2016/21/P/ST8/00790 within the POLONEZ 2 program funded by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 665778.

Assoc. Prof. L. Dzyubak participated in an international research program at the Department of Automatics and Biomechanics at Lodz University of Technology in 2003 and the University of Southampton (Southampton, England) in 2015-2016. Earlier in 2014-2015, Assoc. Prof. Mazur O.S. stayed as an academic visitor within the Erasmus Mundus post-doc exchange program at the same University.

Assoc. Prof. N.V. Perepelkin is currently working on research at the Engineering School of Cardiff University, Cardiff, UK within the project “Cross-Disciplinary Approaches to Evaluation of the Elastic and Adhesive Properties of Micro / Nanothick Objects” funded by the Sêr Cymru ІI funding program, which is a suite of schemes part funded by the Welsh Government and the European Commission through the Horizon 2020 Marie Sklodowska-Curie Actions (MSCA) 2017-2019.

From 1999 to 2013 at the Department of the State budget grant  M0905 “Development of methods for studying non-linear problems in the dynamics of multilayered plates and gently sloping shells” was carried out, the coordinator prof. Kurpa L.V. with a total funding of 240 thousand UAH. The work was aimed at developing effective methods for solving nonlinear boundary value problems in areas of complex shape.

As part of the “Science for Peace and Security” program, established through the Agreement between NATO and the Government of Ukraine, professors Yu.V. Mikhlin and L.V. Kurpa from the Department of Applied Mathematics, in collaboration with the Department of Computer Modeling of Processes and Systems at the National Technical University “Kharkiv Polytechnic Institute”, alongside universities in Modena and Reggio Emilia, Italy, and the A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences in Ukraine, hаve been awarded a grant for the implementation of the international project SPS G6176 – “Composite Metamaterials for Aerospace Structures – CoMetA” in 2024.

Below you can see a short list of papers written in English only (the full list including papers in Ukrainian you can find here).

Defended theses in 2010 - 2024:

2024

  1. “Investigation of resonant steady-state modes and transient processes in nonlinear systems with limited power” for obtaining the scientific degree of Doctor of Philosophy in specialty 113 – Applied Mathematics, recipient assistant of the department Yana Oleksandrivna Lebedenko, scientific supervisor – professor of the department of applied mathematics, professor Yu.V. Michlin. The defense took place on February 29, 2024 in the one-time council of the National Technical University “Kharkiv Polytechnic Institute”.
  2. “Study of nonlinear vibration normal modes of coupled pendulums under the influence of magnetic forces.” for obtaining the scientific degree of Doctor of Philosophy in specialty 113 – Applied Mathematics, recipient assistant of the department Yana Oleksandrivna Lebedenko, scientific supervisor – professor of the department of applied mathematics, professor Yu.V. Michlin. The defense took place on March 29, 2024 in the one-time council of the National Technical University “Kharkiv Polytechnic Institute”.

2019

  1. “Nonlinear oscillations and stability of layered plates of complex shape” for obtaining the scientific degree of Candidate of Physical and Mathematical Sciences. 01.02.04 – Mechanics of deformable solids, researcher Tkachenko Viktoriya Valeryivna, supervisor: Doctor of Science, Prof. Kurpa L.V. The defense took place in 2019 at the Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstrygach, Lviv.

2016

  1. “Methods for solving problems of bending and oscillations of hollow shells based on the theory of R-functions and spline approximation”, awarded by A.O. Osetrova, scientific supervisor: Doctor of Science, Prof. Kurpa L.V. The defense took place on March 17, 2016 at the Institute of Mechanical Engineering Problems named after A.M. Pidgorny National Academy of Sciences of Ukraine.

2015

  1. “Normal Forms of Oscillations in a Non-Linear System Containing a Pendulum Oscillation Damper” awarded by A. Klymenko, supervisor: Doctor of Technical Sciences, Prof. Michlin Yu.V. The defense took place on 04/23/2015. at the Institute of Mechanical Engineering Problems named after A.M. Pidgorny National Academy of Sciences of Ukraine.

2013

  1. “Nonlinear normal forms of forced oscillations and their application in the dynamics of single-disk rotors”, recipient M.V. Perepelkin, supervisor: Doctor of Science in Technology, prof. Michlin Yu.V. Defense took place on 30.05.2013. at the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
  2. “Investigation of forced geometrically nonlinear oscillations of multilayer hollow shells and plates using the method of R-functions” winner M.A. Budnikov, supervisor: Doctor of Science, Prof. L.V. Kurpa. The defense was held on August 29, 2013 in Donetsk the national university
  3. “The stress-deformed state of flexible orthotropic plates and positive shells of complex plan form” winner K.I. Lyubitska, scientific supervisor: Doctor of Science, Prof. Kurpa L.V. Defense took place on 19.12.2013. at the Institute of Mechanical Engineering Problems named after A.M. Pidgorny National Academy of Sciences of Ukraine

Published scientific books in 2009 - 2016:

Курпа Л. В., О. С. Мазур, Т. В. Шматко. Застосування теорії R-функцій до вирішення нелінійних завдань динаміки багатошарових пластин / Л. В. Курпа, О. С. Мазур, Т. В. Шматко. – Харьков: ООО «В деле», 2016. – 492 с.

Аврамов К.В., Михлин Ю. В. Нелінійна динаміка пружних систем. Том 2: Застосування, 2015. — 699 с.

К.В. Аврамов, Ю.В. Михлин. Нелінійна динаміка пружних систем. Том 1: Моделі, методи, явища, 2010 . – 704 с.

Курпа Л.В. Метод R-функцій для вирішення лінійних завдань вигину та коливань пластин та пологих оболонок. – Харків: НТУ “ХПІ”, 2009. – 408 с.

Published scientific papers in 2010 - 2016:

2016:

  1. Awrejcewicz J., Kurpa L., Mazur O. Dynamical instability of laminated plates with external cutout. Journal of Non-linear Mechanics 81 (2016) 103-114.
  2. Burlayenko V.N., Altenbach H., Sadowski T., Dimitrova S.D. Computational simulations of thermal shock cracking by the virtual crack closure technique in a functionally graded plate. Computational Materials Science 116 (2016) 11–21.
  3. Burlayenko V.N. Modelling thermal shock in functionally graded plates with finite element method. Advances in Materials Science and Engineering Volume 2016 Issue: Brittle or Quasi-Brittle Fracture of Engineering Materials (2016), Article ID 7514638, 12 pages.
  4. Mikhlin Yu. V., Cartmell M. P. and Warminski J. Special Issue on Nonlinear Dynamics In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science Vol. 230, No. 1 (2016) p. 3-4.

2015:

  1. Awrejcewicz J., Kurpa L., Shmatko T. Investigating geometrically vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory. Composite Structures 125 (2015) 575-585.
  2. Burlayenko V.N., Altenbach H., Sadowski T. An evaluation of displacement-based finite element models used for free vibration analysis of homogeneous and composite plates. Journal of Sound and Vibration 358 (2015) 152-175.
  3. Mikhlin Yu., Plaksij K. Dynamics of nonlinear dissipative systems in the vicinity of resonance Journal of Sound and Vibration 334 (2015) 319-337.
  4. Plaksiy K.Y., Mikhlin Yu.V. Resonance behavior of the limited power-supply system coupled with the nonlinear absorber Mathematics in Engineering, Science and Aerospace Vol. 6, No. 3 (2015) 475-495.

2014:

  1. L.V.Kurpa, T.V. Shmatko. Nonlinear vibrations of laminated shells with layers of variable thickness./ Shell Structures: Theory and Applications, 2014 Taylor & Francis Group, London,UK.- V.3,p.305-308
  2. L.V. Kurpa,O.S.Mazur & V.V.Tkachenko. Parametric Vibrations and Dynamic Instability of thin laminated plates with complex form. ./ Shell Structures: Theory and Applications, 2014 Taylor & Francis Group, London,UK.- V.3,p.309-312
  3. L.V. Kurpa, Parametric Vibrations of Multilayer Plates of Complex Shape/ L.V. Kurpa, O.S.Mazur & V.V.Tkachenko.//Journal of Mathematical Sciences,Vol.174,No 2, February ,2014,- P. 101-114.
  4. Burlayenko V.N., Sadowski T. Nonlinear dynamic analysis of harmonically excited debonded sandwich plates using finite element modelling. Composite Structures, Volume 108, February 2014, Pages 354–366.
  5. Burlayenko V.N., Sadowski T. Transient dynamic response of debonded sandwich plates predicted with finite element analysis. Meccanica, Volume 49, Issue 11 (2014), Page 2617-263.
  6. Burlayenko V.N., Sadowski T. Simulations of post-impact skin/core debond growth in sandwich plates under impulsive loading. Journal of Applied Nonlinear Dynamics 3(4) (2014) 369–379.
  7. A.A. Klimenko, Y.V. Mikhlin. Analytical-numerical approach to analyze forced and parametric vibrations of some pendulum systems. Вісник Харківського національного університету ім. В.М. Каразіна. Серія Математичне моделювання. Інформаційні технології. Автоматизовані системи керування». 2014.

2013:

  1. Yu.V.Mikhlin, K.V. Avramov. Review of Applications of Nonlinear Normal Modes for Vibrating Mechanical Systems. Applied Mechanics Review, 65(2), 2013 (20 pages).
  2. Nikolay Perepelkin, Yuri Mikhlin. Nonlinear normal modes of forced vibrations in systems with internal resonance. Проблемы нелинейной динамики и физики кон¬денсированных сред. Москва, ИХФ РАН, 2013, 158-166.
  3. Dynamical stability and parametrical vibrations of the laminated plates with complex shape Lidiya Kurpa, Olga Mazur, Victoria Tkachenko.  Latin American Journal of Solids and Structures 10(2013) 175 –188.
  4. N.V. Perepelkin, Yu.V. Mikhlin, C. Pierre. Non-linear normal forced vibration modes in systems with internal resonance. International Journal of Non-Linear Mechanics, Volume 57, December 2013, 102–115.
  5. Jan Awrejcewicz. Large amplitude free vibration of orthotropic shallow shells of complex form with variable thickness. Jan Awrejcewicz, Lidiya Kurpa, Tatiana Shmatko // Latin American Joirnal of Solid and Structures, 10(2013). – p.147-160.

2012:

  1. Mikhlin Yu.V. Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems / Yu.V. Mikhlin, N.V. Perepelkin, A A Klimenko,  E. Harutyunyan // Journal of Physics [електронний ресурс]. – 2012. – Volume. 382 (012052) conference 1. – Режим доступу:  http://iopscience.iop.org/1742-6596/382/1/012052/pdf/1742-6596_382_1_012052.pdf.
  2. A.A. Klimenko, Y.V. Mikhlin, J. Awrejcewicz. Nonlinear normal modes in pendulum systems.  Nonlinear Dynamics, Vol. 70, Issue 1, 2012, 797-813.
  3. Burlayenko V.N., Sadowski T. A Numerical Study of the Dynamic Response of Sandwich Plates Initially Damaged by Low Velocity Impact. Computational Materials Science 52(1) (2012): 212-216
  4. Burlayenko V.N., Sadowski T. Finite Element Nonlinear Dynamic Analysis of Sandwich Plates with Partially Detached Facesheet and Core. Finite Elements in Analysis & Design 62 (2012)  49-64.

2011:

  1. Jan Awrejcewicz, Lidiya Kurpa, and Andrey Osetrov. Investigation of the stress-strain state of the laminated shallow shells by R-functions method combined with spline-approximation // ZAMM Z. Angew. Math. Mech., 1 – 10 (2011) / DOI 10.1002/zamm.201000164
  2. Mikhlin Yu.V. Non-linear normal modes and their applications in mechanical systems / Yu.V. Mikhlin, N.V. Perepelkin // Proc. of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. – 2011. – 225 (10) – p.2369-2384.
  3. J. Awrejcewicz and L.P. Dzyubak, Modelling, chaotic behavior and control of dissipation properties of hysteretic systems, In: Models and Applications of Chaos Theory in Modern Sciences,  Z. Elhadj, (Ed.), Science Publishers, British Isles, ISBN 978-1-57808-722-8; May 2011, pp. 1–23.
  4. J. Awrejcewicz and L.P. Dzyubak, Numerical analysis of a rotor dynamics in the magneto-hydrodynamic field, In: Numerical Simulations / Book 2, Jan Awrejcewicz, (Ed.), In Tech, ISBN 979-953-307-249-3, July 2011, pp. 1-22.
  5. Burlayenko V.N., Sadowski T. Dynamic Behavior of Sandwich Plates Containing Single/Multiple Debonding, Computational Materials Science 50 (2011) 1263–1268.
  6. Burlayenko V.N., Sadowski T. Dynamic Analysis of Debonded Sandwich Plates with Flexible Core – Numerical Aspects and Simulation. Advanced Structured Materials, Volume 15, Shell-like Structures, H. Altenbach and V.A. Eremeyev (eds.) Springer-Verlag 2011. Part V, p. 415-440.
  7. Burlayenko V.N., Sadowski T. A Numerical Study of the Dynamic Response of Sandwich Plates Initially Damaged by Low Velocity Impact. Computational Materials Science 52(1) (2012): 212-216.

2010:

  1. J. Awrejcewicz and L.P. Dzyubak, 2-dof nonlinear dynamics of a rotor suspended in the magneto-hydrodynamic field in the case of soft and rigid magnetic materials // Int. J. of Non-Linear Mechanics. – 2010. – 45 – Р. 919–930.
  2. Burlayenko V.N., Sadowski T. Free vibration of sandwich plates with impact-induced damage. Wiley’s Webserver Wiley-InterScience in the PAMM, Volume 9, Issue 1, March 2010, p. 179-180.
  3. Burlayenko V.N., Sadowski T. Effective Elastic Properties of Foam-Filled Honeycomb Cores of Sandwich Panels, Composite Structures. (2010), doi: 10.1016/j.compstruct.2010.04.015.
  4. Awrejcewicz J., Kurpa L., Mazur O. On the parametric vibrations and meshless discretization of orthotropic plates with complex shape// The International Journal of Nonlinear Science & Numerical Simulation 2010, 11(5). – C.371–386.
  5. Lidiya Kurpa, Tatiana Shmatko, Galina Timchenko. Free vibration analysis of laminated shallow shells with complex shape using the R-functions method // Composite Structures 93, 2010. – P. 225–233.
  6. Special Issue “Models, Methods and Applications of Dynamics and Control in Engineering Systems” (Eds. J.-M. Balthazar, B.Goncalves, S.Lenci, Y.V.Mikhlin). Mathematical Problems in Engineering, v. 2010, Article ID487684.
  7. Yu.V.Mikhlin. Nonlinear normal vibration modes and their applications. In: Advanced Problems in Mechanics of Heterogeneous Media and Thin-Walled Structures (Eds. V.I.Bolshakov, D,Weichert). Dniepropetrovsk, ENEM, 2010, 263-297.

The list of conferences attended in 2010 - 2016:

2016

  1. The 5th International Conference on Nonlinear Dynamics September 27-30, 2016, Kharkov, Ukraine
  2. 5th International Specialized Scientific and Practical Conference “Resource- and Energy-Saving Technologies of Production and Packaging of Food Products – Basic Principles of Its Competitiveness”, September 14, 2016 – Kyiv, Ukraine
  3. 24th International Scientific and Practical Conference. “Information technologies: science, engineering, technology, education, health” (MicroCAD–2016), May 18-20, 2016, Ukraine
  4. 5th International Conference “Tarapov Readings -2016”, March 1-15, 2016, Kharkiv, Ukraine
  5. The 6th International Conference on Nonlinear Vibrations, Localization, and Energy Transfer. University of Liege, July, 4-8, 2016.

2015

  1. 23rd International Scientific and Practical Conference. “Information technologies: science, engineering, technology, education, health” MicroCAD – 2015, May 20-22, 2015, Kharkiv, Ukraine
  2. Euromech Colloquium 577, Micromechanics of metal-ceramic composites, 2-5 March, 2015, IMWF-University of Stuttgart, Germany
  3. The 13th International Conference Dynamical Systems Theory and Applications DSTA-2015, December 7-10, 2015., Lodz, Poland
  4. International scientific conference “Modern problems of mathematical modeling and computational methods”. February 19-22, 2015.
  5. XXII International Conference Dynamical System Modelling And Stability Investigation. 2015. Kiev, Ukraine
  6. V International scientific and technical conference: “Actual problems of applied mechanics and strength of structures.” Zaporozhye National University, 2015, Zaporizhzhia, Ukraine

2014

  1. Shell Structures: Theory and Applications, 2014 Taylor & Francis Group, London, UK
  2. The 8th European Nonlinear Dynamics Conference ENOC-2014, July 6-11 2014, Vienna, Austria
  3. IX International Scientific Conference “Mathematical Problems of the Mechanics of Inhomogeneous Structures”, September 15-19, 2014, Lviv, Ukraine
  4. 22nd International Scientific and Practical Conference. “Information technologies: science, technology, technology, education, health” MicroCAD-2014, NTU “KhPI”, May 21-23, 2014, Kharkiv, Ukraine

2013

  1. Modern problems of mechanics and mathematics. Institute of applied problems of Mechanics and Mathematics named after Ya.S. Pidstrygacha of the National Academy of Sciences of Ukraine, 2013, Lviv, Ukraine
  2. Dynamical Systems Modeling and Stability Investigation: XVI International Conference: Modeling and Stability Kiev, Ukraine, 29-31 may, 2013
  3. Conference “Nonlinear Dynamics in Engineering: Modelling, Analysis and Applications”, 21-23 August 2013. CADR, School of Engineering, University of Aberdeen, UK
  4. IV- International Conference of Nonlinear Dynamics ND-KhPI2013, June 19-22, 2013, Sevastopol, Ukraine
  5. Th 10th International Conference “Shell Structures, Theory and Applications” (10th SSTA 2013), October 16 – 18, 2013, Gdańsk (Poland).
  6. The 12th Conference on Dynamical Systems – Theory and Applications, DSTA-2013, December 2-5 Łódź, Poland
  7. International Scientific School-Conference “Tarapov Readings” September 29 – October 4, 2013, Kharkiv, Ukraine

2012

  1. 21st International Scientific and Practical Conference. “Information technologies: science, technology, technology, lighting, health” MicroCAD – 2012, May 2012 Kharkiv, Ukraine
  2. Modeling, Control and Sustainability (MCS-2012): International Conference, Sevastopol, September 10-14, 2012, Ukraine
  3. The 4th Int. Conference on Localization, Transfer of Energy and Nonlinear Normal Modes in Mechanics and Physics. Booklet of Abstracts. Haifa, Israel, July 1-5, 2012
  4. The International Workshop “Dynamics of Functionally Graded Materials and Systems with Hysteresis”, 19 March, 2012, Lublin, Poland.
  5. The 8th European Solid Mechanics Conference ESMC 2012, 9 – 13 July 2012, Graz, Austria
  6. The 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria
  7. The International Workshop “Nonlinear Dynamic Phenomena in Mechanical, Aerospace, and Civil