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  S. Iglin and associate professors L. Dzyubak and V. Burlayenko work on their investigations as individuals. Their investigations refer to a field of structural mechanics and solid mechanics.

Professor S. Iglin is a member of the editorial board of the journal “Exponenta Pro“. He took part in conferences Matlab-2002, 2004. At the conference Matlab-2004 (Moscow, May 2004) Iglin was a head of the section “Matlab in Education and the Internet”.

Some of the researchers of the Department took part in international research projects. Namely, Assoc. Prof. V. Burlayenko took part in the scientific researches funded by German Academic Exchange Service (DAAD) and INTAS at Martin-Luther-Universitat Halle-Wittenberg (Halle, Germany) in 2000 and 2002-2003, by German Research Foundation at Otto-von-Guericke Magdeburg University (Magdeburg, Germany) in 2015 and by Erasmus Mundus programme 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. V. N. Burlayenko has just now received a 24-month fellowship for performing in cooperation with Professor T. Sadowski from Lublin University of Technology a research projectReliability of skin-to-core interface in sandwich composites for dynamically loaded applicationsat the Department of Solid Mechanics, Lublin University of Technology, Lublin, Poland. This research is supported by National Science Centre of Poland, grant agreement No UMO-2016/21/P/ST8/00790 within the POLONEZ 2 programme funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665778.

Assoc. Prof. L. Dzyubak participated in international research program at the Department of Automatics and Biomechanics at Lodz University of Technology in 2003 and 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 programme at the same University.

Assoc. Prof. N.V. Perepelkin is currently working for 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 programme, 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 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.

During 2010-2016 postgraduate students of the Department successfully defended 5 PhD theses. Since 2009 the staff of the Department published 1 monograph, 3 scientific books and more than 50 papers in scientific journals as well as took part in more than 30 international conferences and published there more than 70 papers in proceedings of the scientific conferences.

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

Defended theses in 2010 - 2016:


  1. «Методи розв’язання задач згину та коливань пологих оболонок на основі теорії R-функцій і сплайн-апроксимації», здобувач Осетрова А.О., науковий керівник: д.т.н., проф. Курпа Л.В. Захист відбувся 17.03.2016 р. в Інституті проблем машинобудування ім. А.М. Підгорного НАН України.


  1. “ Нормальные формы колебаний в нелинейной системе, содержащей маятниковый гаситель колебаний ” здобувач Клименко А., науковий керівник: д.т.н., проф. Міхлін Ю.В. Захист відбувся 23.04.2015р. в Інституті проблем машинобудування ім. А.М. Підгорного НАН України.


  1. «Нелінійні нормальні форми вимушених коливань і їх застосування в динаміці одно дискових роторів», здобувач Перепелкін М.В., науковий керівник: д.т.н., проф. Міхлін Ю.В. Захист відбувся 30.05.2013р. в Інституті прикладної математики і механіки НАН України;
  2. “Дослідження вимушених геометрично нелінійних коливань багатошарових пологих оболонок та пластин за допомогою метода R-функцій» здобувач Будніков М.А., науковий керівник: д.т.н., проф. Курпа Л.В. Захист відбувся 29.08.2013р. в Донецькому національному університеті;
  3. «Напружено-деформований стан гнучких ортотропних пластин і положистих оболонок складної форми плану» здобувач Любицька К.І., науковий керівник: д.т.н., проф. Курпа Л.В. Захист відбувся 19.12.2013р. в Інституті проблем машинобудування ім. А.М. Підгорного НАН України.

Published scientific books in 2009 - 2016:

Курпа Л. В., О. С. Мазур, Т. В. Шматко. Применение теории R-функций к решению нелинейных задач динамики многослойных пластин: / Л. В. Курпа, О. С. Мазур, Т. В. Шматко. – Харьков: ООО «В деле», 2016. – 492 с. – На рус. яз.

Аврамов К.В., Михлин Ю. В. Нелинейная динамика упругих систем. Том 2: Приложения.   — М. : R&C Dynamics; Ижевск : Ин-т компьютер. исслед., 2015. — 699 с.

К.В. Аврамов, Ю.В. Михлин.  Нелинейная динамика упругих систем. Том 1: модели, методы, явления.— М.:  Регулярная и хаотическая динамика; Ижевск: Ин-т компьют. исслед., 2010 . – 704 с.

Курпа Л.В. Метод R-функций для решения линейных задач изгиба и колебаний пластин и пологих оболочек. – Харків: НТУ “ХПІ”, 2009. – 408 с.

Published scientific papers in 2010 - 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.


  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.


  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. Вестник Харьковского национального университета им. В.Н. Каразина. Серия «Математическое моделирование. Информационные технологии. Автоматизированные системы управления». 2014.


  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.


  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:
  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.


  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.


  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:


  1. The 5th International Conference on Nonlinear Dynamics September 27-30, 2016, Kharkov, Ukraine
  2. 5-а Міжнародна спеціалізована науково-практична конференція «Ресурсо- та енергоощадні технології виробництва і пакування харчової продукції – основні засади її конкурентоздатності», 14 вересня 2016 р. – Київ, Украина
  3. 24-а Міжнародна науково-практична конференція. “Інформаційні технології : наука, техніка, технологія, освіта, здоров’я” (MicroCAD–2016), 18-20 травня 2016 р. , Україна
  4. 5-а Міжнародна конференція ” Тараповські читання -2016″, 1-15 березня 2016 р., Харків, Украина
  5. The 6th Intrelational Conference on Nonlinear Vibrations, Localization and Energy Transfer. University of Liege, July, 4-8, 2016.


  1. 23-а Міжнародна науково-практична конференція. “Інформаційні технології: наука, техніка, технологія, освіта, здоров’я” MicroCAD – 2015, 20-22 травня 2015р., Харків, Україна
  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. Міжнародна наукова конференція «Сучасні проблеми математичного моделювання та обчислювальних методів». 19 – 22 лютого 2015 року.
  5. XXII International Conference Dynamical System Modelling And Stability Investigation. 2015. Kiev, Ukraine
  6. V Міжнародну науково-технічну конференцію: «Актуальні проблеми прикладної механіки та міцності конструкцій». Запорізький нац. ун-т, 2015, Запоріжжя, Україна


  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 міжнародна наукова конференція “Математичні проблеми механіки неоднорідних структур”, 15-19 вересня 2014 р., Львів, Украина
  4. 22-а Международная научно-практическая конференция. “Информационные технологии: наука, техника, технология, образование, здоровье” MicroCAD-2014, НТУ “ХПИ”, 21-23 мая, 2014, Харьков, Украина


  1. Сучасні проблеми механіки та математики. Інститут прикладних проблем механіки і математики ім. Я.С.Підстригача НАН України, 2013, Львів, Украина
  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- Международная конференция Nonlinear Dynamics ND-KhPI2013, 19-22 июня 2013г., Севастополь, Украина
  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. Международная Научная Школа-Конференция «Тараповские Чтения» 29 сентября – 4 октября 2013 г., Харьков, Украина


  1. 21-а Міжнародна науково-практична конференція. “Інформаційні технології: наука, техніка, технологія, освіта, здоров’я” MicroCAD – 2012, травень 2012 р. Харків, Україна
  2. Моделирование, управление и устойчивость (MCS-2012): Международная конференция, Севастополь, 10-14 сентября 2012 г., Украина
  3. XXV Международная научная конференция: Математические методы в технике и технологиях – ММТТ-25, Волгогр. гос. техн. ун-т, 2012
  4. 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
  5. The International Workshop “Dynamics of Functionally Graded Materials and Systems with Hysteresis”, 19 March, 2012, Lublin, Poland.
  6. The 8th European Solid Mechanics Conference ESMC 2012, 9 – 13 July 2012, Graz, Austria
  7. The 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria
  8. The International Workshop “Nonlinear Dynamic Phenomena in Mechanical, Aerospace, and Civil