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    Academic Journal

    Συνεισφορές: The article was financially supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of implementing the program of the Moscow Center for Fundamental and Applied Mathematics by Agreement no. 075-15-2022-284., Статья опубликована при финансовой поддержке Министерства науки и высшего образования Российской Федерации в рамках реализации программы Московского центра фундаментальной и прикладной математики по соглашению № 075-15-2022-284.

    Πηγή: Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series; Том 60, № 2 (2024); 95-105 ; Известия Национальной академии наук Беларуси. Серия физико-математических наук; Том 60, № 2 (2024); 95-105 ; 2524-2415 ; 1561-2430 ; 10.29235/1561-2430-2024-60-2

    Περιγραφή αρχείου: application/pdf

    Relation: https://vestifm.belnauka.by/jour/article/view/777/598; Stronge W. J. Impact Mechanics. Cambridge, Cambridge University Press, 2000. 280 p. https://doi.org/10.1017/cbo9780511626432; Boussinesq J. Du choc longitudinal d’une barre élastique prismatique fixée à un bout et heurtée à l’autre. Comptes Rendus, 1883, vol. 97, no. 2, pp. 154–157 (in French).; Saint-Venant B. Mémoire sur le choc longitudinal de deux barres élastiques de grosseurs et de matières semblables ou différentes, et sur la proportion de leur force vive qui est perdue pour la translation ultérieure; Et généralement sur le mouvement longitudinal d’un système de deux ou plusieurs prismes élastiques. Journal de Mathématiques Pures et Appliquées, 1867, vol. 12, pp. 237–376 (in French).; Saint-Venant B., Flamant M. Courbes représentatives des lois du choc longitudinal et du choc transversal d’une barre prismatique. Journal de l’École Polytechnique, 1889, vol. LIX, pp. 97–123 (in French).; Gajduk S. I. A mathematical study of certain problems concerning longitudinal impact on a finite rod. Differential Equations, 1977, vol. 13, pp. 1399–1411. https://zbmath.org/0449.73029; Gaiduk S. I. A mathematical investigation of the problem of longitudinal impact on a relaxing rod. Differential Equations, 1976, vol. 12, pp. 472–483. https://zbmath.org/0382.73043; Gaiduk S. I. Some problems related to the theory of longitudinal impact on a rod. Differential Equations, 1976, vol. 12, pp. 607–617. https://zbmath.org/0382.73044; Bityurin A. A., Manzhosov V. K. Waves induced by the longitudinal impact of a rod against a stepped rod in contact with a rigid barrier. Journal of Applied Mathematics and Mechanics, 2009, vol. 73, no. 2, pp. 162–168. https://doi.org/10.1016/j.jappmathmech.2009.04.006; Bityurin A. A. Mathematical modeling of the amplitude of transverse vibrations of homogeneous rods under longitudinal impact. Mechanics of Solids, 2021, vol. 56, no. 2, pp. 220–229. https://doi.org/10.3103/s0025654421020047; Bityurin A. A. Modeling of the maximum deflection of a stepped rod having an initial curvature upon impact against a rigid barrier. Mechanics of Solids, 2019, vol. 54, no. 7, pp. 1098–1107. https://doi.org/10.3103/s0025654419070100; Belyaev A. K., Ma C.-C., Morozov N. F., Tovstik P. E., Tovstik T. P., Shurpatov A. O. Dynamics of a rod undergoing a longitudinal impact by a body. Vestnik St. Petersburg University, Mathematics, 2017, vol. 50, pp. 310–317. https://doi.org/10.3103/S1063454117030050; Morozov N. F., Belyaev A. K., Tovstik P. E., Tovstik T. P., Shurpatov A. O. Rod Vibrations Caused by Axial Impact. Doklady Physics, 2018, vol. 63, pp. 208–218. https://doi.org/10.3103/s1063454117030050; Belyaev A. K., Tovstik P. E., Tovstik T. P. Thin rod under longitudinal dynamic compression. Mechanics of Solids, 2017, vol. 52, pp. 364–377. https://doi.org/10.3103/s0025654417040021; Stepanov R., Romenskyi D., Tsarenko S. Dynamics of Longitudinal Impact in the Variable Cross-Section Rods. IOP Conference Series: Materials Science and Engineering, 2018, vol. 317, art. ID 012029. https://doi.org/10.1088/1757-899x/317/1/012029; Etiwa R. M., Elabsy H. M., Elkaranshawy H. A. Dynamics of longitudinal impact in uniform and composite rods with effects of various support conditions. Alexandria Engineering Journal, 2023, vol. 65, pp. 1–22. https://doi.org/10.1016/j.aej.2022.09.050; Hu B., Eberhard P. Symbolic computation of longitudinal impact waves. Computer Methods in Applied Mechanics and Engineering, 2001, vol. 190, no. 37–38, pp. 4805–4815. https://doi.org/10.1016/s0045-7825(00)00348-0; Bityurin A. A. Mathematical Modeling of Longitudinal Impact of Inhomogeneous Rod Systems on a Rigid Barrier with Unilateral Constraints. Ulyanovsk, 2007. 253 p. (in Russian).; Korzyuk V. I., Rudzko J. V., Kolyachko V. V. Solutions of problems with discontinuous conditions for the wave equation. Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika = Journal of the Belarusian State University. Mathematics and Informatics, 2023. vol. 3, pp. 6–18 (in Russian).; Korzyuk V. I., Rudzko J. V. Classical Solution of One Problem of a Perfectly Inelastic Impact on a Long Elastic SemiInfinite Bar with a Linear Elastic Element at the End. Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika = Journal of the Belarusian State University. Mathematics and Informatics, 2022, vol. 2, pp. 34–46 (in Russian). https://doi.org/10.33581/2520-6508-2022-2-34-46; Korzyuk V. I., Rudzko J. V. The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar. Vestsі Natsyyanalʼnai akademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2021, vol. 57, no. 4, pp. 417–427 (in Russian). https://doi.org/10.29235/1561-2430-2021-57-4-417-427; Korzyuk V. I., Rudzko J. V. The classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition. Vestsі Natsyyanalʼnai akademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2021, vol. 57, no. 1, pp. 23–32 (in Russian). https://doi.org/10.29235/1561-2430-2021-57-1-23-32; Korzyuk V. I. Equations of Mathematical Physics. Moscow, URSS Publ., 2021. 480 p. (in Russian).; Yurchuk N. I., Novikov E. N. Necessary conditions for existence of classical solutions to the equation of semi-bounded string vibration. Vestsі Natsyyanalʼnai akademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2016, no. 4, pp. 116–120 (in Russian).; Korzyuk V. I., Rudzko J. V. Classical Solution of the Third Mixed Problem for the Telegraph Equation with a Nonlinear Potential. Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya XXXIV: Materialy mezhdunarodnoi Voronezhskoi vesennei matematicheskoi shkoly, posvyashchennoi 115-letiyu so dnya rozhdeniya akademika L. S. Pontryagina, 3–8 maya 2023 g. [Modern methods of the theory of boundary value problems. Pontryagin readings XXXIV: Materials of the international Voronezh spring mathematical school dedicated to the 115th anniversary from the birth of academician L. S. Pontryagin, May 3–8, 2023]. Voronezh, 2023, pp. 442–444.; Korzyuk V. I., Kozlovskaya I. S. Classical Solutions of Problems for Hyperbolic Equations. Part 2. Minsk, Belarusian State University, 2017. 52 p. (in Russian).; Korzyuk V. I., Kovnatskaya O. A. Solutions of problems for the wave equation with conditions on the characteristics. Vestsі Natsyyanalʼnai akademіі navuk Belarusі. Seryya fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2021, vol. 57, no. 2, pp. 148–155 (in Russian). https://doi.org/10.29235/1561-2430-2021-57-2-148-155; Korzyuk V. I., Stolyarchuk I. I. Classical Solution of the First Mixed Problem for Second-Order Hyperbolic Equation in Curvilinear Half-Strip with Variable Coefficients. Differential Equations, 2017, vol. 53, no. 1, pp. 74–85. https://doi.org/10.1134/S0012266117010074; Korzyuk V. I., Rudzko J. V. Classical Solution of the Second Mixed Problem for the Telegraph Equation with a Nonlinear Potential. Differential Equations, 2023, vol. 59, no. 9, pp. 1216–1234. https://doi.org/10.1134/S0012266123090070; Rabotnov Yu. N. Mechanics of Deformable Solid. Moscow, Nauka Publ., 1979. 744 p. (in Russian).; Goldsmith W. Impact: The Theory and Physical Behavior of Colliding Solid. London, Arnold, 1960. 379 p.; Moiseev E. I., Kholomeeva A. A. Optimal boundary control by displacement at one end of a string under a given elastic force at the other end. Proceedings of the Steklov Institute of Mathematics, 2012, vol. 276, pp. 153–160. https://doi.org/10.1134/s0081543812020125; Il’in V. A., Moiseev E. I. Optimization of the boundary control of string vibrations by an elastic force on an arbitrary sufficiently large time interval. Differential Equations, 2006, vol. 42, no. 12, pp. 1775–1786. https://doi.org/10.1134/S0012266106120123; Il’in V. A., Moiseev E. I. Optimization of the boundary control by shift or elastic force at one end of string in a sufficiently long arbitrary time. Automation and Remote Control, 2008, vol. 69, no. 3, pp. 354–362. https://doi.org/10.1134/s0005117908030028; https://vestifm.belnauka.by/jour/article/view/777

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