Сергей Гаврилов

Научные интересы

Рациональная механика, нестационарные волны, подвижные нагрузки, локализация волн, асимптотика, конфигурационные силы, фазовые превращения, реология, баллистическое распространение тепла.

Место работы

• Институт проблем машиноведения РАН, лаб. математического моделирования волновых процессов, ведущий научный сотрудник.
• Санкт-Петербургский политехнический университет Петра Великого, кафедра "Теоретическая механика", профессор

Образование

• д.ф.-м.н., 2013, ИПМаш РАН, "Нестационарная динамика упругих тел с подвижными включениями и границами".
• к.ф.-м.н., 1999, ИПМаш РАН, "Нестационарные процессы в упругих волноводах при преодолении критической скорости подвижной нагрузкой", научные руководители Д.А. Индейцев, П.А. Жилин.
• магистр т.н., 1996, каф. "Механика и процессы управления" СПбГПУ, "Математическая модель среды Кельвина", научный руководитель П.А. Жилин.

Преподавание

• Курс "Нестационарные упругие волны" для студентов кафедры "Теоретическая Механика".
• слайды (1ый семестр) [1]
• слайды (2ой семестр) [2]

Основные публикации

1. E.V. Shishkina, S.N. Gavrilov, Yu.A. Mochalova. Passage through resonance for a system with time-varying parameters possessing a single trapped mode. ArXiv:1907.00067.
2. S.N. Gavrilov, A.M. Krivtsov. Thermal equilibration in a one-dimensional damped harmonic crystal. Phys. Rev. E, 100, 022117, 2019. DOI: 10.1103/PhysRevE.100.022117.
3. M. Ferretti, S.N. Gavrilov, V.A. Eremeyev, A. Luongo. Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass. Nonlinear Dynamics, 2019. DOI: 10.1007/s11071-019-05117-z.
4. S.N. Gavrilov, A.M. Krivtsov. Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source. Continuum Mechanics and Thermodynamics. DOI: 10.1007/s00161-019-00782-2.
5. S.N. Gavrilov, E.V. Shishkina, Yu.A. Mochalova. An infinite-length system possessing a unique trapped mode versus a single degree of freedom system: a comparative study in the case of time-varying parameters. In book: Editors: Altenbach H. et al. Dynamical Processes in Generalized Continua and Structures, Advanced Structured Materials 103,pp.231-251, Springer, 2019. DOI: 10.1007/978-3-030-11665-1_13.
6. S.N. Gavrilov, E.V. Shishkina, Yu.A. Mochalova. Non-stationary localized oscillations of an infinite string, with time-varying tension, lying on the Winkler foundation with a point elastic inhomogeneity. Nonlinear Dynamics. 95(4), pp. 2995–3004, DOI: 10.1007/s11071-018-04735-3
7. E.V. Shishkina, S.N. Gavrilov, Yu.A. Mochalova. Non-stationary localized oscillations of an infinite Bernoulli-Euler beam lying on the Winkler foundation with a point elastic inhomogeneity of time-varying stiffness. Journal of Sound and Vibration 440C (2019) pp. 174-185. DOI: 10.1016/j.jsv.2018.10.016
8. S.N. Gavrilov, A.M. Krivtsov, D.V. Tsvetkov. Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply. Continuum Mechanics and Termodynamics (2019), 31(1), pp. 255-272. DOI: 10.1007/s00161-018-0681-3.
9. S.N. Gavrilov, Yu.A. Mochalova, E.V. Shishkina. Evolution of a trapped mode of oscillation in a string on the Winkler foundation with point inhomogeneity. Proc.Int. Conf. DAYS on DIFFRACTION 2017, pp. 128–133. DOI: 10.1109/DD.2017.8168010.
10. E.V. Shishkina, S.N. Gavrilov. Stiff phase nucleation in a phase-transforming bar due to the collision of non-stationary waves. Arch. Appl. Mech. (2017) 87(6): pp. 1019-1036. DOI: 10.1007/s00419-017-1228-y.
11. D.A. Indeitsev, S.N. Gavrilov, Yu.A. Mochalova, E.V. Shishkina. Evolution of a trapped mode of oscillation in a continuous system with a concentrated inclusion of variable mass. Doklady Physics (2016) 61(12): pp. 620–624. DOI: 10.1134/S1028335816120065.
12. S.N. Gavrilov, Yu.A. Mochalova, E.V. Shishkina. Trapped modes of oscillation and localized buckling of a tectonic plate as a possible reason of an earthquake. Proc. Int. Conf. DAYS on DIFFRACTION 2016, pp. 161–165. DOI: 10.1109/DD.2016.7756834.
13. S.N. Gavrilov, V. A. Eremeyev, G. Piccardo, A. Luongo. A revisitation of the paradox of discontinuous trajectory for a mass particle moving on a taut string. Nonlinear Dynamics (2016) 86(4): 2245-2260
14. S.N. Gavrilov, E.V. Shishkina. Scale-invariant initial value problems with applications to the dynamical theory of stress-induced phase transformations. Proc.Int. Conf. DAYS on DIFFRACTION 2015, pp. 96–101. DOI: 10.1109/DD.2015.7354840.
15. E.V. Shishkina, S.N. Gavrilov. A strain-softening bar with rehardening revisited. Mathematics and Mechanics of Solids (2016) 21(2):137-151 .
16. S.N. Gavrilov, E.V. Shishkina. A strain-softening bar revisited. ZAMM (2015) 95(12): 1521–1529.
17. S.N. Gavrilov, E.V. Shishkina. New phase nucleation due to the collision of two nonstationary waves. Doklady Physics (2014) 59(12): 577–581.
18. S.N. Gavrilov, G.C. Herman. Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading. Journal of Sound and Vibration, (2012), 331(20): 4464-4480.
19. S.N. Gavrilov, E.V. Shishkina. On stretching of a bar capable of undergoing phase transitions. Continuum Mechanics and Thermodynamics (2010), 22(4), 299-316.
20. E.V. Shishkina, I.I. Blekhman, M.P. Cartmell, S.N. Gavrilov. Application of the method of direct separation of motions to the parametric stabilization of an elastic wire. Nonlinear Dynamics (2008) 54: 313-331.
21. S. N. Gavrilov. Dynamics of a free phase boundary in an infinite bar with variable cross-sectional area. ZAMM (2007) 87(2):117-127.
22. S. N. Gavrilov. Proper dynamics of phase interface in an infinite elastic bar with variable cross section. Doklady Physics (2007) 52(3):161-164.
23. S.N. Gavrilov. The effective mass of a point mass moving along a string on a Winkler foundation. PMM J. Appl. Math. Mechs (2006) 70: 582-589.
24. S.N. Gavrilov, G.C. Herman. Oscillation of a punch moving on the free surface of an elastic half space. Journal of Elasticity (2004) 75: 247-265.
25. S.N. Gavrilov, D.A. Indeitsev. On the evolution of localized mode of oscillation in system "string on an elastic foundation - moving inertial inclusion". PMM J. Appl. Math. Mechs (2002) 66(5):825-833.
26. S. Gavrilov. Nonlinear investigation of the possibility to exceed the critical speed by a load on a string. Acta Mechanica (2002) 154:47-60.
27. S. Gavrilov. Transition through the critical velocity for a moving load in an elastic waveguide. Technical Physics (2000) 45(4):515-518.
28. S. Gavrilov. Non-stationary problems in dynamics of a string on an elastic foundation subjected to a moving load. Journal of Sound and Vibration (1999) 222(3):345-361.