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, asymptotics, configurational forces, phase transitions, constitutive theory, ballistic heat propagation.
Professor, Department of Theoretical Mechanics, Peter the Great St. Petersburg Polytechnic University (SPbPU), St. Petersburg, Russia.
Master thesis: “Mathematical model of Kelvin's medium” (science adviser 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” (science advisers 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.
Google Scholar profile.
Teaching: Non-stationary elastic waves (slides in Russian)
List of principal publications
Drafts of some papers are available at ResearchGate or arXiv.
S.N. Gavrilov. Heat conduction in 1D harmonic crystal: discrete-to-continuum limit and slow-and-fast motions decoupling. arXiv:2006.08197 (PREPRINT)
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. DOI: 10.1016/j.jsv.2020.115422 (NEW!)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
S.N. Gavrilov, E.V. Shishkina. A strain-softening bar revisited. ZAMM (2015) 95(12): 1521–1529. DOI: 10.1002/zamm.201400155
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.
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
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.
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
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.
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
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
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
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
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
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
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: 2020-09-29