Most important peerreviewed publications by A.N. Timokha
Visitors can download several recent papers
FULL LIST IS AVAILABLE HERE
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Raynovskyy, I.A., Timokha A.N. (2020):
Sloshing in Upright Circular Containers:
Theory, Analytical Solutions, and Applications.
CRC Press/Taylor & Francis Group, 2020. 170 pp. (ISBN 9780367362898)

Lukovsky, I.A., Solodun, O.V., Timokha A.N. (2019):
Mathematical problems of nonlinear dynamics of conical reservoirs with liquids.
Kyiv: Naukova Dumka, 224 pp. (ISBN 9789660016910) [in Ukrainian]

Faltinsen, O.M., Timokha A.N. (2012):
Sloshing.
P.R.C.:National Defence Industry Press. 783pp. (ISBN13: 9787118086083)
Chinese Version of the book issued in 2009:

Faltinsen, O.M., Timokha A.N. (2009):
Sloshing.
Cambridge University Press. 608pp.
(ISBN13: 9780521881111)

Gavrilyuk, I.P., Lukovsky, I.A., Makarov, V.L., Timokha, A.N. (2006):
Evolutional problems of the contained fluid.
Kiev: Publishing House of the Institute of Mathematics of NASU. 233pp. (ISBN 9660239491)

Lukovsky I.A., Timokha A.N. (1995):
Variational methods in nonlinear problems of the dynamics of a limited liquid volume.
Kiev:Institute of Mathematics of NASU. 400pp.
[in Russian, Synopsis in English] (ISBN 5770211849)
Selected, most representative papers in peerreviewed journals:

Miliaiev, A., Timokha, A. (2023):
Viscous damping of steadystate resonant sloshing in a clean rectangular tank.
Journal of Fluid Mechanics, 965, R1, 111

Lukovsky, I.A., Timokha, A.N. (2022):
A note on the variational formalism for sloshing with rotational flows in a rigid tank with unprescribed motion.
Ukrainian Mathematical Journal, 73, No 10, 15801589

Faltinsen, O.M., Timokha, A.N. (2021):
Coupling between resonant sloshing and lateral motions of a twodimensional rectangular tank.
Journal of Fluid Mechanics, 916, A60, 141

Faltinsen, O.M., Lagodzinskyi, O., Timokha, A.N. (2020):
Resonant threedimensional nonlinear sloshing in a square base basin. Part 5. Threedimensional nonparametric tank forcing.
Journal of Fluid Mechanics, 894, A10, 142

Faltinsen, O.M., Timokha, A.N. (2019):
An inviscid analysis of the Prandtl azimuthal masstransport during swirltype sloshing.
Journal of Fluid Mechanics, 865, 884903

Raynovskyy, I.A., Timokha, A.N. (2018):
Steadystate resonant sloshing in an upright cylindrical container performing a circular orbital motion.
Mathematical Problems in Engineering, Article ID 5487178, 18

Raynovskyy, I.A., Timokha, A.N. (2018):
Damped steadystate resonant sloshing in a circular base container.
Fluid Dynamics Research, 50, Article ID 045502 , 127

Faltinsen, O.M., Timokha, A.N. (2017):
Resonant threedimensional nonlinear sloshing in a squarebase basin. Part 4. Oblique forcing and linear viscous damping.
Journal of Fluid Mechanics, 822, 139169

Lukovsky, I.A., Timokha, A.N. (2017):
Multimodal method in sloshing.
Journal of Mathematical Sciences, 220, No 3,
239253

Chernova, M.O., Lukovsky, I.A., Timokha, A.N. (2017):
Differential and variational formalism for an acousticallylevitating drop.
Journal of Mathematical Sciences, 220, No 3,
359375

Timokha, A.N. (2016):
Analytically approximate natural sloshing modes and frequencies for an upright circular container with poles.
Journal of Engineering Mathematics, 101, Issue 1, 4754

Raynovskyy, I.A., Timokha, A.N. (2016):
Resonant liquid sloshing in an upright circular tank performing a periodic motion.
Journal of Numerical and Applied Mathematics, No 2 (122), 7182

Faltinsen, O.M., Lukovsky, I.A., Timokha, A.N. (2016):
Resonant sloshing in an upright annular tank.
Journal of Fluid Mechanics, 804, 608645

Faltinsen, O.M., Timokha, A.N. (2016):
Undamped eigenperiods of a seabased gravity monotower.
Applied Mathematical Modelling, 40, 82178243

Timokha, A.N. (2016):
The BatemanLuke variational formalism in a sloshing with rotational flows.
Dopovidi Nac. Akad. Ukr., 18 No 4,
3034

Faltinsen, O.M., Timokha, A.N. (2015):
On damping of twodimensional pistonmode sloshing in a rectangular moonpool under forced heave motions.
Journal of Fluid Mechanics, 772, R1

Faltinsen, O.M., Timokha, A.N. (2014):
Analytically approximate natural sloshing modes and frequencies in twodimensional tanks.
European Journal of Mechanics B/Fluids, 47, 176187

Gavrilyuk, I., Hermann, M., Trotsenko, V., Trotsenko, Yu., Timokha, A. (2014):
Eigenoscillations of a thinwalled azimuthally closed, axially open shell of revolution.
Journal of Engineering Mathematics, 85, 8397

Gavrilyuk, I., Hermann, M., Trotsenko, Yu., Timokha, A. (2013):
Studying the coupled eigenoscillations of an axisymmetric towerelevated tank system by the multimodal method.
Journal of Fluids and Structures, 42, 152165

Gavrilyuk, I., Hermann, M., Lukovsky, I., Solodun, O., Timokha, A. (2013):
Weaklynonlinear sloshing in a truncated circular conical tank.
Fluid Dynamics Research, 45, Paper ID 055512,
130

Faltinsen, O.M., Timokha, A.N. (2013):
Multimodal analysis of weakly nonlinear sloshing in a spherical tank.
Journal of Fluid Mechanics, 719, 129164

Chernova, M.O., Lukovsky, I.A., Timokha, A.N. (2012):
Generalizing the multimodal method for the levitating drop dynamics
.
ISRN Mathematical Physics, 2012, Article ID 869070, 119

Faltinsen, O.M., Timokha, A.N. (2012):
Analytically approximate natural sloshing modes
for a spherical tank shape.
Journal of Fluid Mechanics, 703, 391401
[Supplementary material]

Faltinsen, O.M., Timokha, A.N. (2012):
On sloshing modes in a circular tank.
Journal of Fluid Mechanics, 695, 467477

Gavrilyuk, I., Hermann, M., Lukovsky, I., Solodun, O., Timokha, A. (2012):
Multimodal method for linear liquid sloshing in a rigid tapered conical tank.
Engineering Computations, 29, No 2,
198220

Lukovsky, I.A., Ovchynnykov, D.V., Timokha, A.N. (2012):
Asymptotic nonlinear multimodal method for liquid sloshing in an upright circular cylindrical tank.
Part 1: Modal equations.
Nonlinear Oscillations, 14, No 4,
512525

Lukovsky, I.A., Timokha, A.N. (2011):
Combining NarimanovMoiseev' and LukovskyMiles' schemes for nonlinear liquid sloshing.
Journal of Numerical and Applied Mathematics, 105, No 2,
6982

Faltinsen, O.M., Firoozkoohi, R., Timokha, A.N. (2011):
Effect of central slotted screen with a high solidity ratio on the secondary resonance phenomenon for liquid
sloshing in a rectangular tank.
Physics of Fluids, 23, Issue 6, Art. No. 062106, 113

Faltinsen, O.M., Firoozkoohi, R., Timokha, A.N. (2011):
Analytical modeling of liquid sloshing in a twodimensional rectangular tank with a slat screen.
Journal of Engineering Mathematics, 70, 12, 93109

Faltinsen, O.M., Firoozkoohi, R., Timokha, A.N. (2011):
Steadystate liquid sloshing in a rectangular tank with a slattype screen in the middle: Quasilinear modal analysis and experiments.
Physics of Fluids, 23, Issue 4, Art. No. 042101, 119

Faltinsen, O.M., Timokha, A.N. (2011):
Natural sloshing frequencies and modes in a rectangular tank with a slattype screen
.
Journal of Sound and Vibration, 330, 14901503

Barnyak, M., Gavrilyuk, I., Hermann, M., Timokha, A. (2011):
Analytical velocity potentials in cells with a rigid spherical wall.
ZAMM, 91, No 1, 3845

Faltinsen, O.M., Timokha, A.N. (2010):
A multimodal method for liquid sloshing
in a twodimensional circular tank.
Journal of Fluid Mechanics, 665, 457479
[Supplementary material]

Gavrilyuk, I., Hermann, M., Trotsenko, V., Trotsenko, Yu., Timokha, A. (2010):
Axisymmetric oscillations of a cupolashaped shell.
Journal of Engineering Mathematics, 65, 165178

Gavrilyuk, I., Hermann, M., Trotsenko, Yu., Timokha, A. (2010):
Eigenoscillations of three and twoelement flexible systems.
International Journal of Solids and Structures, 47, 18571870

Hermann, M., Timokha, A. (2008):
Modal modelling of the nonlinear resonant fluid sloshing in a rectangular tank II: Secondary resonance.
Mathematical Models and Methods in Applied Sciences, 18, N 11, 18451867

Gavrilyuk, I., Hermann, M., Lukovsky, I., Solodun, O., Timokha, A. (2008):
Natural sloshing frequencies in rigid truncated conical tanks.
Engineering Computations, 25, Issue 6, 518540

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2007):
Twodimensional resonant pistonlike sloshing in a moonpool.
Journal of Fluid Mechanics, 575, 359397
[Supplementary material]

Gavrilyuk, I., Lukovsky, I., Trotsenko, Yu., Timokha, A. (2007):
Sloshing in a vertical circular cylindrical tank with an annular baffle. Part 2. Nonliear resonant waves.
Journal of Engineering Mathematics, 57, 5778

Gavrilyuk, I., Hermann, M., Timokha, A., Trotsenko, V. (2006):
Modelling of the eigenfield of a prestressed hypereleastic membrane encapsulating a liquid.
Computational Methods in Applied Mathematics, 6, N 4, 367385

Gavrilyuk, I., Lukovsky, I., Trotsenko, Yu., Timokha, A. (2006):
Sloshing in a vertical circular cylindrical tank with an annular baffle. Part 1. Linear fundamental solutions.
Journal of Engineering Mathematics, 54, 7188

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2006):
Resonant threedimensional nonlinear sloshing in a squarebase basin. Part 3. Base ratio perturbations.
Journal of Fluid Mechanics, 551, 93116

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2006):
Transient and steadystate amplitudes of resonant threedimensional sloshing in a square base tank with a finite fluid depth.
Physics of Fluids, 18, Art. No. 012103, 114
[Movie to Figure 1]

Timokha, A.N. (2005):
Planimetry of vibrocapillary equilibria at small wave numbers.
International Journal of Fluid Mechanics Research, 32, Issue 4, 454487

Gavrilyuk, I.P., Lukovsky, I.A., Timokha, A.N. (2005):
Linear and nonlinear sloshing in a circular conical tank.
Fluid Dynamics Research, 37, 399429

Hermann, M., Timokha, A. (2005):
Modal modelling of the nonlinear resonant sloshing in a rectangular tank I: A singledominant model.
Mathematical Models and Methods in Applied Sciences, 15, N 9, 14311458

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2005):
Classification of threedimensional nonlinear sloshing in a squarebase tank with finite depth.
Journal of Fluids and Structures, 20, Issue 1, 81103

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2005):
Resonant threedimensional nonlinear sloshing in a square base basin. Part 2. Effect of higher modes.
Journal of Fluid Mechanics, 523, 199218

Beyer, K., Guenther, M., Timokha, A.N. (2004):
Variational and finite element analysis of vibroequilibria.
Computational Methods in Applied Mathematics, 4, N 3, 290323

Gavrilyuk, I., Lukovsky, I., Timokha, A. (2004):
Twodimensional variational vibroequilibria and Faraday's drops.
ZAMP, 55, 10151033

Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2003):
Resonant threedimensional nonlinear sloshing in a square base basin.
Journal of Fluid Mechanics, 487, 142

Faltinsen, O.M., Timokha, A.N. (2002):
Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth.
Journal of Fluid Mechanics, 470, 319357

Lukovsky, I.A., Timokha, A.N. (2002):
Modal modeling of nonlinear sloshing in tanks with nonvertical walls. Nonconformal mapping technique.
International Journal of Fluid Mechanics Research, 29, Issue 2, 216242

Gavrilyuk, I., Lukovsky, I.A., Timokha, A.N. (2001):
Sloshing in a circular conical tank.
Hybrid Methods in Engineering, 3, Issue 4, 322378

Lukovsky, I.A., Timokha, A.N. (2001):
Sound effect on dynamics and stability of fluid sloshing in zerogravity.
International Journal of Fluid Mechanics Research, 28, Issues 12, 1941

Faltinsen, O.M., Timokha, A.N. (2001):
Adaptive multimodal approach to nonlinear sloshing in a rectangular tank.
Journal of Fluid Mechanics, 432, 167200

Beyer, K., Guenther, M., Gawrilyuk, I., Lukovsky, I., Timokha, A.N. (2001):
Compressible potential flows with free boundaries. Part I: Vibrocapillary equilibria.
ZAMM, 81, Issue 4, 261271

Lukovsky, I.A., Timokha, A.N. (2001):
Asymptotic and variational methods in nonlinear problems on interaction of surface waves with acoustic field.
J. Applied Mathematics and Mechanics. 65, Issue 3, 477485

Faltinsen, O.M., Rognebakke, O.F., Lukovsky, I.A., Timokha, A.N. (2000):
Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth.
Journal of Fluid Mechanics, 407, 201234

Gavrilyuk, I., Lukovsky, I.A., Timokha, A.N. (2000):
A multimodal approach to nonlinear sloshing in a circular cylindrical tank.
Hybrid Methods in Engineering, 2, Issue 4, 463483

Lukovsky, I.A., Timokha, A.N. (2000):
Steadystate nonlinear sloshing in a rectangular tank: passage to shallow water.
Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki., Issue 11, 4851

Lukovsky, I.A., Timokha, A.N. (1999):
Sound effect on dynamics and stability of fluid sloshing in zerogravity.
Acoustic Bulletin, 2, Issue 3, 6983

Lukovs'kyi, I.O., Mikhayluk, A.V., Tymokha, O.M. (1996):
On one variational criterion of stability of pseudoequilibrium forms.
Ukrainian Mathematical Journal, 48, Issue 11, 16881695

Lukovskii, I.A., Timokha, A.N. (1996):
One version of the linearized theory of nonstationary boundaryvalue problems with free boundary.
Ukrainian Mathematical Journal, 48, Issue 6, 890904

Lukovskij, I.A., Timokha, A.N. (1995):
Nonlinear dynamics of a gasliquid system under high frequency acoustic vibration.
Fluid Mechanics Research, 21(1992), Issue 6, 124130

Mikhayluk, A.V., Timokha, A.N. (1995):
Variational formulations for a spectral problem with parameter on the interface of two mediums.
Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki., Issue 10, 3840

Lukovskii, I.A., Timokha, A.N. (1993):
Variational formulations of nonlinear boundaryvalue problems with a free boundary in the theory of interaction of surface waves with acoustic fields.
Ukrainian Mathematical Journal, 45, Issue 12, 18491860

Timokha, A.N. (1993):
Influence of sound on the normal modes of oscillation of a liquidgas interface in a bounded volume.
Acoustical Physics. 39, Issue 2, March 1993, 187189

Limarchenko, O.S., Lukovskii, I.A., Timokha, A.N. (1992):
Nonlinear models in applied dynamics problems of bodies with a free surface liquid.
International Applied Mechanics, 28, Issue 11, 757  763

Lukowsky, I.A., Timoha, A.N. (1992):
Waves on the liquidgas free surface in the presence of the acoustic field in gas.
International Series of Numerical Mathematics, 106, 187194

Lukovskii, I.A., Timokha, A.N. (1991):
Acoustic modification of the free surface of a bounded liquid volume.
Soviet Physical Acoustics 37(1), 7274

Lukovskii, I.A., Timokha, A.N. (1991):
Stabilization of liquidgas interface in the presence of interaction with acoustic fields in the gas.
Fluid Dynamics, 26, Issue 3, 382388

Lukovskii, I.A., Timokha, A.N. (1991):
The Bateman variational principle for a class of problems on the dynamics and stability of surface waves.
Ukrainian Mathematical Journal, 43, Issue 9, 11061110

Lukovskii, I.A., Timokha, A.N. (1991):
A class of boundary value problems in the theory of surface waves.
Ukrainian Mathematical Journal, 43, Isssue 3, 322328

Lukovskii, I.A., Timokha, A.N. (1990):
Selfadjointness of a certain integrodifferential operator.
Ukrainian Mathematical Journal, 42, Issue 3, 375376