An Object-oriented Application for Analyzing Nonlinear Dynamic Systems with Hysteretic Behavior
Keywords:
engineering software, object-oriented application, interface, verification, nonlinear dynamics, Dahl and LuGre friction models, rubber-metal shock absorbers
Abstract
The article presents the structure, interface and functionality of an object-oriented educational application for modeling and analysis of 1D nonlinear dynamic systems with hysteresis: oscillators with Dahl, Lu Gre friction elements, and with a rubber-metal shock absorber. Using the application, it is possible to study free and forced oscillations of nonlinear systems under kinematic disturbances. The nonlinear differential equations are solved by the Runge-Kutta and Adams-Bashfort methods. The modular structure of the object-oriented application makes it easy to expand the collections of nonlinear models and numerical methods for solving nonlinear differential equations.
References
1. Zhou C. e. a. Hysteresis Dynamic Model of Metal Rubber Based on Higher-order Nonlinear Friction (HNF) // Mechanical Systems and Signal Proc. 2023. V. 189. P. 110117. https://doi.org/10.1016/j.ymssp.2023.110117.
2. Dahl P.R. Solid Friction Damping of Mechanical Vibrations // AIAA J. 1976. V. 14(12). Pp. 1675—1682. https://arc.aiaa.org/doi/10.2514/3.61511.
3. Piatkowski T. Dahl and LuGre Dynamic Friction Models — the Analysis of Selected Properties // Mechanism and Machine Theory. 2014. V. 73. Pp. 91—100. https://doi.org/10.1016/j.mechmachtheory.2013.10.009.
4. Olsson H. Control Systems with Friction. Department of Automatic Control [Электрон. ресурс] https://lucris.lub.lu.se/ws/portalfiles/portal/4768278/8840259.pdf (дата обращения 08.02.2024.)
5. Leus M., Gutowski P. Analysis of Longitudinal Tangential Contact Vibration Effect on Friction Force Using Coulomb and Dahl Models // J. Theoretical and Appl. Mechanics. 2008. V. 46. Pp. 171—184.
6. Johanastrom K., Canudas-de-Wit C. Revisiting the LuGre Friction Model // IEEE Control Systems. 2008. V. 28. Pp. 101—114. https://doi.org/10.1109/MCS.2008.929425.
7. De Wit C.C., Olsson H., Åström K.J., Lischinsky P.A New Model for Control of Systems with Friction // IEEE Trans. Automatic Control. 1995. V. 40. Pp. 419—425. https://doi.org/10.1109/9.376053.
8. Zhen Zhoua e. a. Modeling and Simulation of Point Contact Multibody System Dynamics Based on the 2D LuGre Friction Model // Mechanism and Machine Theory. 2021. V. 158. Pp. 104—244. https://doi.org/10.1016/j.mechmachtheory.2021.104244.
9. Shalmaee M.M., Pourzeynali S. A Modal Displacement-based Design Method for Irregular Building Frames Equipped with Elastomeric Bearings // Structures. 2022. V. 41. Pp. 542—552. https://doi.org/10.1016/j.istruct.2022.05.021.
10. Радин В.П., Позняк Е.В., Чирков В.П., Новикова О.В. Динамические характеристики и настройка виброизоляторов с билинейным гистерезисом // Известия высших учебных заведений. Серия «Машиностроение». 2022. № 12. С. 14—23. https://doi.org/10.18698/0536–1044–2022–12–14–23.
11. Радин В.П., Позняк Е.В., Новикова О.В., Чирков В.П. Разработка и исследование модели здания на резинометаллических сейсмоопорах // Вестник МЭИ. 2022. № 2. С. 105—112. https://doi.org/10.24160/1993–6982–2022–2–105–112.
12. Alberdi Celaya E., Anza Aguirrezabala J.J. Object Oriented Programming for Partial Differential Equations // Proc. Computer Sci. 2015. V. 51. Pp. 1013—1022.
13. Innerberger M., Praetorius D. MooAFEM: an Object Oriented Matlab Code for Higher-order Adaptive FEM for (Nonlinear) Elliptic PDEs // Appl. Math. and Computation. 2023. V. 442. P. 127731. https://doi.org/10.48550/arXiv.2203.01845.
---
Для цитирования: Позняк Е.В., Медведева И.Н., Иванова Ю.Ю., Новикова О.В., Цой В.Э., Стенина Т.Е. Объектно-ориентированное приложение для анализа нелинейных динамических систем с гистерезисным поведением // Вестник МЭИ. 2024. № 6. С. 147—153. DOI: 10.24160/1993-6982-2024-6-147-153
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Статья опубликована по материалам доклада E.V. Poznyak, I.N. Medvedeva, J.J. Ivanova, V.E. Tsoy, O.V. Novikova, T.E. Stenina. On the Experience of Developing an Engineering OOP Application by a Student Group // Proc. 7th Intern. Conf. Information Technologies in Engineering Education (Inforino). Moscow, 2024. Pp. 1—4. DOI: 10.1109/Inforino60363.2024.10552029
---
Работа выполнена в рамках проекта «Разработка программных модулей для моделирования динамического поведения элементов конструкций с гистерезисом» при поддержке гранта НИУ «МЭИ» на реализацию программы научных исследований «Приоритет 2030: Технологии будущего» в 2022—2024 гг.»
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. Zhou C. e. a. Hysteresis Dynamic Model of Metal Rubber Based on Higher-order Nonlinear Friction (HNF). Mechanical Systems and Signal Proc. 2023;189:110117. https://doi.org/10.1016/j.ymssp.2023.110117.
2. Dahl P.R. Solid Friction Damping of Mechanical Vibrations. AIAA J. 1976;14(12):1675—1682. https://arc.aiaa.org/doi/10.2514/3.61511.
3. Piatkowski T. Dahl and LuGre Dynamic Friction Models — the Analysis of Selected Properties. Mechanism and Machine Theory. 2014;73:91—100. https://doi.org/10.1016/j.mechmachtheory.2013.10.009.
4. Olsson H. Control Systems with Friction. Department of Automatic Control [Elektron. Resurs] https://lucris.lub.lu.se/ws/portalfiles/portal/4768278/8840259.pdf (Data Obrashcheniya 08.02.2024.)
5. Leus M., Gutowski P. Analysis of Longitudinal Tangential Contact Vibration Effect on Friction Force Using Coulomb and Dahl Models. J. Theoretical and Appl. Mechanics. 2008;46:171—184.
6. Johanastrom K., Canudas-de-Wit C. Revisiting the LuGre Friction Model. IEEE Control Systems. 2008;28:101—114. https://doi.org/10.1109/MCS.2008.929425.
7. De Wit C.C., Olsson H., Åström K.J., Lischinsky P.A New Model for Control of Systems with Friction. IEEE Trans. Automatic Control. 1995;40:419—425. https://doi.org/10.1109/9.376053.
8. Zhen Zhoua e. a. Modeling and Simulation of Point Contact Multibody System Dynamics Based on the 2D LuGre Friction Model. Mechanism and Machine Theory. 2021;158:104—244. https://doi.org/10.1016/j.mechmachtheory.2021.104244.
9. Shalmaee M.M., Pourzeynali S. A Modal Displacement-based Design Method for Irregular Building Frames Equipped with Elastomeric Bearings. Structures. 2022;41:542—552. https://doi.org/10.1016/j.istruct.2022.05.021.
10. Radin V.P., Poznyak E.V., Chirkov V.P., Novikova O.V. Dinamicheskie Kharakteristiki i Nastroyka Vibroizolyatorov s Bilineynym Gisterezisom. Izvestiya Vysshikh Uchebnykh Zavedeniy. Seriya «Mashinostroenie». 2022;12:14—23. https://doi.org/10.18698/0536–1044–2022–12–14–23. (in Russian).
11. Radin V.P., Poznyak E.V., Novikova O.V., Chirkov V.P. Razrabotka i Issledovanie Modeli Zdaniya na Rezinometallicheskikh Seysmooporakh. Vestnik MEI. 2022;2:105—112. https://doi.org/10.24160/1993–6982–2022–2–105–112. (in Russian).
12. Alberdi Celaya E., Anza Aguirrezabala J.J. Object Oriented Programming for Partial Differential Equations. Proc. Computer Sci. 2015;51:1013—1022.
13. Innerberger M., Praetorius D. MooAFEM: an Object Oriented Matlab Code for Higher-order Adaptive FEM for (Nonlinear) Elliptic PDEs. Appl. Math. and Computation. 2023;442:127731. https://doi.org/10.48550/arXiv.2203.01845
---
For citation: Poznyak E.V., Medvedeva I.N., Ivanova Yu.Yu., Novikova O.V., Tsoy V.E., Stenina T.E. An Object-oriented Application for Analyzing Nonlinear Dynamic Systems with Hysteretic Behavior. Bulletin of MPEI. 2024;6:147—153. (in Russian). DOI: 10.24160/1993-6982-2024-6-147-153
---
The article is based on the materials of the report E.V. Poznyak, I.N. Medvedeva, J.J. Ivanova, V.E. Tsoy, O.V. Novikova, T.E. Stenina. On the Experience of Developing an Engineering OOP Application by a Student Group. Proc. 7th Intern. Conf. Information Technologies in Engineering Education (Inforino). Moscow, 2024: 1—4. DOI: 10.1109/Inforino60363.2024.10552029
---
The work is executed within the Framework of the Project «Development of Software Modules for Modeling the Dynamic Behavior of Structural Elements with Hysteresis» with the Support of a Grant from the National Research University «MPEI» for the Implementation of the Research Program «Priority 2030: Technologies of the Future» in 2022—2024»
---
Conflict of interests: the authors declare no conflict of interest
2. Dahl P.R. Solid Friction Damping of Mechanical Vibrations // AIAA J. 1976. V. 14(12). Pp. 1675—1682. https://arc.aiaa.org/doi/10.2514/3.61511.
3. Piatkowski T. Dahl and LuGre Dynamic Friction Models — the Analysis of Selected Properties // Mechanism and Machine Theory. 2014. V. 73. Pp. 91—100. https://doi.org/10.1016/j.mechmachtheory.2013.10.009.
4. Olsson H. Control Systems with Friction. Department of Automatic Control [Электрон. ресурс] https://lucris.lub.lu.se/ws/portalfiles/portal/4768278/8840259.pdf (дата обращения 08.02.2024.)
5. Leus M., Gutowski P. Analysis of Longitudinal Tangential Contact Vibration Effect on Friction Force Using Coulomb and Dahl Models // J. Theoretical and Appl. Mechanics. 2008. V. 46. Pp. 171—184.
6. Johanastrom K., Canudas-de-Wit C. Revisiting the LuGre Friction Model // IEEE Control Systems. 2008. V. 28. Pp. 101—114. https://doi.org/10.1109/MCS.2008.929425.
7. De Wit C.C., Olsson H., Åström K.J., Lischinsky P.A New Model for Control of Systems with Friction // IEEE Trans. Automatic Control. 1995. V. 40. Pp. 419—425. https://doi.org/10.1109/9.376053.
8. Zhen Zhoua e. a. Modeling and Simulation of Point Contact Multibody System Dynamics Based on the 2D LuGre Friction Model // Mechanism and Machine Theory. 2021. V. 158. Pp. 104—244. https://doi.org/10.1016/j.mechmachtheory.2021.104244.
9. Shalmaee M.M., Pourzeynali S. A Modal Displacement-based Design Method for Irregular Building Frames Equipped with Elastomeric Bearings // Structures. 2022. V. 41. Pp. 542—552. https://doi.org/10.1016/j.istruct.2022.05.021.
10. Радин В.П., Позняк Е.В., Чирков В.П., Новикова О.В. Динамические характеристики и настройка виброизоляторов с билинейным гистерезисом // Известия высших учебных заведений. Серия «Машиностроение». 2022. № 12. С. 14—23. https://doi.org/10.18698/0536–1044–2022–12–14–23.
11. Радин В.П., Позняк Е.В., Новикова О.В., Чирков В.П. Разработка и исследование модели здания на резинометаллических сейсмоопорах // Вестник МЭИ. 2022. № 2. С. 105—112. https://doi.org/10.24160/1993–6982–2022–2–105–112.
12. Alberdi Celaya E., Anza Aguirrezabala J.J. Object Oriented Programming for Partial Differential Equations // Proc. Computer Sci. 2015. V. 51. Pp. 1013—1022.
13. Innerberger M., Praetorius D. MooAFEM: an Object Oriented Matlab Code for Higher-order Adaptive FEM for (Nonlinear) Elliptic PDEs // Appl. Math. and Computation. 2023. V. 442. P. 127731. https://doi.org/10.48550/arXiv.2203.01845.
---
Для цитирования: Позняк Е.В., Медведева И.Н., Иванова Ю.Ю., Новикова О.В., Цой В.Э., Стенина Т.Е. Объектно-ориентированное приложение для анализа нелинейных динамических систем с гистерезисным поведением // Вестник МЭИ. 2024. № 6. С. 147—153. DOI: 10.24160/1993-6982-2024-6-147-153
---
Статья опубликована по материалам доклада E.V. Poznyak, I.N. Medvedeva, J.J. Ivanova, V.E. Tsoy, O.V. Novikova, T.E. Stenina. On the Experience of Developing an Engineering OOP Application by a Student Group // Proc. 7th Intern. Conf. Information Technologies in Engineering Education (Inforino). Moscow, 2024. Pp. 1—4. DOI: 10.1109/Inforino60363.2024.10552029
---
Работа выполнена в рамках проекта «Разработка программных модулей для моделирования динамического поведения элементов конструкций с гистерезисом» при поддержке гранта НИУ «МЭИ» на реализацию программы научных исследований «Приоритет 2030: Технологии будущего» в 2022—2024 гг.»
---
Конфликт интересов: авторы заявляют об отсутствии конфликта интересов
#
1. Zhou C. e. a. Hysteresis Dynamic Model of Metal Rubber Based on Higher-order Nonlinear Friction (HNF). Mechanical Systems and Signal Proc. 2023;189:110117. https://doi.org/10.1016/j.ymssp.2023.110117.
2. Dahl P.R. Solid Friction Damping of Mechanical Vibrations. AIAA J. 1976;14(12):1675—1682. https://arc.aiaa.org/doi/10.2514/3.61511.
3. Piatkowski T. Dahl and LuGre Dynamic Friction Models — the Analysis of Selected Properties. Mechanism and Machine Theory. 2014;73:91—100. https://doi.org/10.1016/j.mechmachtheory.2013.10.009.
4. Olsson H. Control Systems with Friction. Department of Automatic Control [Elektron. Resurs] https://lucris.lub.lu.se/ws/portalfiles/portal/4768278/8840259.pdf (Data Obrashcheniya 08.02.2024.)
5. Leus M., Gutowski P. Analysis of Longitudinal Tangential Contact Vibration Effect on Friction Force Using Coulomb and Dahl Models. J. Theoretical and Appl. Mechanics. 2008;46:171—184.
6. Johanastrom K., Canudas-de-Wit C. Revisiting the LuGre Friction Model. IEEE Control Systems. 2008;28:101—114. https://doi.org/10.1109/MCS.2008.929425.
7. De Wit C.C., Olsson H., Åström K.J., Lischinsky P.A New Model for Control of Systems with Friction. IEEE Trans. Automatic Control. 1995;40:419—425. https://doi.org/10.1109/9.376053.
8. Zhen Zhoua e. a. Modeling and Simulation of Point Contact Multibody System Dynamics Based on the 2D LuGre Friction Model. Mechanism and Machine Theory. 2021;158:104—244. https://doi.org/10.1016/j.mechmachtheory.2021.104244.
9. Shalmaee M.M., Pourzeynali S. A Modal Displacement-based Design Method for Irregular Building Frames Equipped with Elastomeric Bearings. Structures. 2022;41:542—552. https://doi.org/10.1016/j.istruct.2022.05.021.
10. Radin V.P., Poznyak E.V., Chirkov V.P., Novikova O.V. Dinamicheskie Kharakteristiki i Nastroyka Vibroizolyatorov s Bilineynym Gisterezisom. Izvestiya Vysshikh Uchebnykh Zavedeniy. Seriya «Mashinostroenie». 2022;12:14—23. https://doi.org/10.18698/0536–1044–2022–12–14–23. (in Russian).
11. Radin V.P., Poznyak E.V., Novikova O.V., Chirkov V.P. Razrabotka i Issledovanie Modeli Zdaniya na Rezinometallicheskikh Seysmooporakh. Vestnik MEI. 2022;2:105—112. https://doi.org/10.24160/1993–6982–2022–2–105–112. (in Russian).
12. Alberdi Celaya E., Anza Aguirrezabala J.J. Object Oriented Programming for Partial Differential Equations. Proc. Computer Sci. 2015;51:1013—1022.
13. Innerberger M., Praetorius D. MooAFEM: an Object Oriented Matlab Code for Higher-order Adaptive FEM for (Nonlinear) Elliptic PDEs. Appl. Math. and Computation. 2023;442:127731. https://doi.org/10.48550/arXiv.2203.01845
---
For citation: Poznyak E.V., Medvedeva I.N., Ivanova Yu.Yu., Novikova O.V., Tsoy V.E., Stenina T.E. An Object-oriented Application for Analyzing Nonlinear Dynamic Systems with Hysteretic Behavior. Bulletin of MPEI. 2024;6:147—153. (in Russian). DOI: 10.24160/1993-6982-2024-6-147-153
---
The article is based on the materials of the report E.V. Poznyak, I.N. Medvedeva, J.J. Ivanova, V.E. Tsoy, O.V. Novikova, T.E. Stenina. On the Experience of Developing an Engineering OOP Application by a Student Group. Proc. 7th Intern. Conf. Information Technologies in Engineering Education (Inforino). Moscow, 2024: 1—4. DOI: 10.1109/Inforino60363.2024.10552029
---
The work is executed within the Framework of the Project «Development of Software Modules for Modeling the Dynamic Behavior of Structural Elements with Hysteresis» with the Support of a Grant from the National Research University «MPEI» for the Implementation of the Research Program «Priority 2030: Technologies of the Future» in 2022—2024»
---
Conflict of interests: the authors declare no conflict of interest
Published
2024-09-04
Section
Mathematical and Software Support of Computer Systems, Complexes and Computer Networks (Technical Sciences) (2.3.5)
