Serge Gavrilov - Leading Researcher - Laboratory for Mathematical Modelling of Wave Phenomena

Master thesis: “Mathematical model of Kelvin's medium” (superviser is Prof. P.A. Zhilin, Head of Department of Theoretical Mechanics, Faculty of Physics and Mechanics, SPbPU), 1996.

PhD thesis: “Non-stationary processes in elastic waveguides subjected to a moving load overcoming the critical velocity” (supervisers are Prof. D.A. Indeitsev and Prof. P.A. Zhilin, IPME), 1999.

Habilitation thesis: “Non-stationary dynamics of elastic bodies with moving inclusions and boundaries”, IPME, 2013.

List of principal publications:

1. S.N. Gavrilov, I.O. Poroshin, E.V. Shishkina, Yu.A. Mochalova. Formal asymptotics for oscillation of a discrete mass-spring-damper system of time-varying properties, embedded into a one-dimensional medium described by the telegraph equation with variable coefficients. Nonlinear Dyn, 2024. DOI: 10.1007/s11071-024-10154-4.
2. S.N. Gavrilov, E.V. Shishkina. Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect. Continuum Mechanics and Thermodynamics, 36(3), 699–724 (2024). DOI: 10.1007/s00161-024-01289-1
3. E.V. Shishkina, S.N. Gavrilov. Localized Modes in a 1D Harmonic Crystal with a Mass-Spring Inclusion. In book: Editors: Altenbach, H., Eremeyev, V. Advances in Linear and Nonlinear Continuum and Structural Mechanics, Advanced Structured Materials 198, p. 461-479 (2023). DOI: 10.1007/978-3-031-43210-1_25
4. S.N. Gavrilov, E.V. Shishkina, Yu.A. Mochalova.An example of the anti-localization of non-stationary quasi-waves in a 1D semi-infinite harmonic chain. Proc.Int. Conf. DAYS on DIFFRACTION 2023, pp. 67–72. DOI: 10.1109/DD58728.2023.10325733.
5. E.V. Shishkina, S.N. Gavrilov, Yu.A. Mochalova. The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem. Journal of Sound and Vibration, 553, 117673 (2023). DOI: 10.1016/j.jsv.2023.117673
6. E.V. Shishkina, S.N. Gavrilov. Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect. Continuum Mechanics and Thermodynamics 35, 431–456 (2023). DOI: 10.1007/s00161-023-01188-x
7. S.N. Gavrilov. Discrete and continuum fundamental solutions describing heat conduction in a 1D harmonic crystal: discrete-to-continuum limit and slow-and-fast motions decoupling. International Journal of Heat and Mass Transfer 194C (2022), 123019. DOI: 10.1016/j.ijheatmasstransfer.2022.123019
8. S.N. Gavrilov, E.V. Shishkina, I.O. Poroshin. Non-stationary oscillation of a string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a sub-critical speed. Journal of Sound and Vibration 522 (2022), 116673. DOI: 10.1016/j.jsv.2021.116673
9. S.N. Gavrilov, A.M. Krivtsov. Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source. Continuum Mechanics and Thermodynamics 34 (2022), p. 297-319. DOI: 10.1007/s00161-021-01059-3
10. A.A. Sokolov, W.H.Müller, A.V.Porubov, S.N.Gavrilov. Heat conduction in 1D harmonic crystal: Discrete and continuum approaches. International Journal of Heat and Mass Transfer, 176, 121442 (2021) DOI: 10.1016/j.ijheatmasstransfer.2021.121442
11. E.V. Shishkina, S.N. Gavrilov, Yu.A. Mochalova. Passage through a resonance for a mechanical system, having time-varying parameters and possessing a single trapped mode. The principal term of the resonant solution. Journal of Sound of Vibration, 484, p. 115422 (2020) DOI: 10.1016/j.jsv.2020.115422
12. 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
13. 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, 97(4), pp. 2201-2218 (2019). DOI: 10.1007/s11071-019-05117-z.
14. 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, 32, pp. 41–61 (2020) DOI: 10.1007/s00161-019-00782-2.
15. 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.
16. 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 (2019). DOI: 10.1007/s11071-018-04735-3.
17. 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, 440 (2019) 174–185. DOI: 10.1016/j.jsv.2018.10.016.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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.
23. 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. DOI: 10.1007/s11071-016-3080-y.
24. 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.
25. E.V. Shishkina, S.N. Gavrilov. A strain-softening bar with rehardening revisited. Mathematics and Mechanics of Solids (2016) 21(2):137-151. DOI: 10.1177/1081286515572247.
26. S.N. Gavrilov, E.V. Shishkina. A strain-softening bar revisited. ZAMM (2015) 95(12): 1521–1529. DOI: 10.1002/zamm.201400155
27. S.N. Gavrilov, E.V. Shishkina. New phase nucleation due to the collision of two nonstationary waves. Doklady Physics (2014) 59(12): 577–581. DOI: 10.1134/S1028335814120027.
28. 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. DOI: 10.1016/j.jsv.2012.05.022
29. 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. DOI: 10.1007/s00161-010-0139-8.
30. 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. DOI: 10.1007/s11071-008-9331-9.
31. S. N. Gavrilov. Dynamics of a free phase boundary in an infinite bar with variable cross-sectional area. ZAMM (2007) 87(2):117-127. DOI: 10.1002/zamm.200610306.
32. S. N. Gavrilov. Proper dynamics of phase interface in an infinite elastic bar with variable cross section. Doklady Physics (2007) 52(3):161-164. DOI: 10.1134/S1028335807030081.
33. 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. DOI: 10.1016/j.jappmathmech.2006.09.009.
34. 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. DOI: 10.1007/s10659-004-5902-2.
35. 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. DOI: 10.1016/S0021-8928(02)90013-4.
36. S. Gavrilov. Nonlinear investigation of the possibility to exceed the critical speed by a load on a string. Acta Mechanica (2002) 154:47-60. DOI: 10.1007/BF01170698.
37. S. Gavrilov. Transition through the critical velocity for a moving load in an elastic waveguide. Technical Physics (2000) 45(4):515-518. DOI: 10.1134/1.1259668.
38. 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. DOI: 10.1006/jsvi.1998.2051.