Serge N. Gavrilov

Date of birth: May 27, 1973.

Address: Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Bolshoy pr. V.O., 61, 199178, St. Petersburg, Russia.

E-mail: serge AT pdmi.ras.ru, serge.gavrilov AT gmail.com

Keywords to the fields of interest: rational mechanics, non-stationary wave propagation, elastodynamics, trapped modes, lattice dynamics, ballistic thermal conductivity, asymptotics, configurational forces, dynamics of phase transitions, constitutive theory.

Affiliation:

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, SPbSTU), 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.

ORCID profile.

Google Scholar profile.

SCOPUS profile.

Publons profile.

Teaching: Non-stationary elastic waves (slides in Russian)

List of principal publications

Drafts of some papers are available at ResearchGate or arXiv.

  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. 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.

  13. 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

  14. 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.

  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.

Last updated: 2024-09-28