Most important peer-reviewed publications by A.N. Timokha
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Books:
[IMAGEMAP][IMAGEMAP] [IMAGEMAP] [IMAGEMAP]
  1. Faltinsen, O.M., Timokha A.N. (2009): Sloshing. Cambridge University Press. 608pp. (ISBN-13: 9780521881111) Chinese Version of the book issued in 2012: P.R.C.:National Defense Industry Press. 783pp. (ISBN-13: 978-7-118-08608-3)
  2. 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 966-02-3949-1)
  3. 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. [Synopsis in English] (ISBN 5-7702-1184-9)

Selected, most representative papers in peer-reviewed journals:

  1. Faltinsen, O.M., Timokha, A.N. (2019): An inviscid analysis of the Prandtl azimuthal mass-transport during swirl-type sloshing. Journal of Fluid Mechanics, 865, 884-903
  2. Raynovskyy, I.A., Timokha, A.N. (2018): Steady-state resonant sloshing in an upright cylindrical container performing a circular orbital motion. Mathematical Problems in Engineering, Article ID 5487178, 1-8
  3. Raynovskyy, I.A., Timokha, A.N. (2018): Damped steady-state resonant sloshing in a circular base container. Fluid Dynamics Research, 50, Article ID 045502 , 1-27
  4. Faltinsen, O.M., Timokha, A.N. (2017): Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 4. Oblique forcing and linear viscous damping. Journal of Fluid Mechanics, 822, 139-169
  5. Lukovsky, I.A., Timokha, A.N. (2017): Multimodal method in sloshing. Journal of Mathematical Sciences, 220, No 3, 239-253
  6. Chernova, M.O., Lukovsky, I.A., Timokha, A.N. (2017): Differential and variational formalism for an acoustically-levitating drop. Journal of Mathematical Sciences, 220, No 3, 359-375
  7. 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, 47-54
  8. 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), 71-82
  9. Faltinsen, O.M., Lukovsky, I.A., Timokha, A.N. (2016): Resonant sloshing in an upright annular tank. Journal of Fluid Mechanics, 804, 608-645
  10. Faltinsen, O.M., Timokha, A.N. (2016): Undamped eigenperiods of a sea-based gravity monotower. Applied Mathematical Modelling, 40, 8217-8243
  11. Timokha, A.N. (2016): The Bateman-Luke variational formalism in a sloshing with rotational flows. Dopovidi Nac. Akad. Ukr., 18 No 4, 30-34
  12. Faltinsen, O.M., Timokha, A.N. (2015): On damping of two-dimensional piston-mode sloshing in a rectangular moonpool under forced heave motions. Journal of Fluid Mechanics, 772, R1
  13. Faltinsen, O.M., Timokha, A.N. (2014): Analytically approximate natural sloshing modes and frequencies in two-dimensional tanks. European Journal of Mechanics B/Fluids, 47, 176-187
  14. Gavrilyuk, I., Hermann, M., Trotsenko, V., Trotsenko, Yu., Timokha, A. (2014): Eigenoscillations of a thin-walled azimuthally closed, axially open shell of revolution. Journal of Engineering Mathematics, 85, 83-97
  15. Gavrilyuk, I., Hermann, M., Trotsenko, Yu., Timokha, A. (2013): Studying the coupled eigenoscillations of an axisymmetric tower-elevated tank system by the multimodal method. Journal of Fluids and Structures, 42, 152-165
  16. Gavrilyuk, I., Hermann, M., Lukovsky, I., Solodun, O., Timokha, A. (2013): Weakly-nonlinear sloshing in a truncated circular conical tank. Fluid Dynamics Research, 45, Paper ID 055512, 1-30
  17. Faltinsen, O.M., Timokha, A.N. (2013): Multimodal analysis of weakly nonlinear sloshing in a spherical tank. Journal of Fluid Mechanics, 719, 129-164
  18. 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, 1-19
  19. Faltinsen, O.M., Timokha, A.N. (2012): Analytically approximate natural sloshing modes for a spherical tank shape. Journal of Fluid Mechanics, 703, 391-401 [Supplementary material]
  20. Faltinsen, O.M., Timokha, A.N. (2012): On sloshing modes in a circular tank. Journal of Fluid Mechanics, 695, 467-477
  21. 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, 198-220
  22. 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, 512-525
  23. Lukovsky, I.A., Timokha, A.N. (2011): Combining Narimanov--Moiseev' and Lukovsky--Miles' schemes for nonlinear liquid sloshing. Journal of Numerical and Applied Mathematics, 105, No 2, 69-82
  24. 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, 1-13
  25. Faltinsen, O.M., Firoozkoohi, R., Timokha, A.N. (2011): Analytical modeling of liquid sloshing in a two-dimensional rectangular tank with a slat screen. Journal of Engineering Mathematics, 70, 1-2, 93-109
  26. Faltinsen, O.M., Firoozkoohi, R., Timokha, A.N. (2011): Steady-state liquid sloshing in a rectangular tank with a slat-type screen in the middle: Quasilinear modal analysis and experiments. Physics of Fluids, 23, Issue 4, Art. No. 042101, 1-19
  27. Faltinsen, O.M., Timokha, A.N. (2011): Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen . Journal of Sound and Vibration, 330, 14901503
  28. Barnyak, M., Gavrilyuk, I., Hermann, M., Timokha, A. (2011): Analytical velocity potentials in cells with a rigid spherical wall. ZAMM, 91, No 1, 3845
  29. Faltinsen, O.M., Timokha, A.N. (2010): A multimodal method for liquid sloshing in a two-dimensional circular tank. Journal of Fluid Mechanics, 665, 457-479 [Supplementary material]
  30. Gavrilyuk, I., Hermann, M., Trotsenko, V., Trotsenko, Yu., Timokha, A. (2010): Axisymmetric oscillations of a cupola-shaped shell. Journal of Engineering Mathematics, 65, 165-178
  31. Gavrilyuk, I., Hermann, M., Trotsenko, Yu., Timokha, A. (2010): Eigenoscillations of three- and two-element flexible systems. International Journal of Solids and Structures, 47, 1857-1870
  32. 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, 1845-1867
  33. Gavrilyuk, I., Hermann, M., Lukovsky, I., Solodun, O., Timokha, A. (2008): Natural sloshing frequencies in rigid truncated conical tanks. Engineering Computations, 25, Issue 6, 518-540
  34. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2007): Two-dimensional resonant piston-like sloshing in a moonpool. Journal of Fluid Mechanics, 575, 359-397 [Supplementary material]
  35. 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, 57-78
  36. 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, 367-385
  37. 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, 71-88
  38. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2006): Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 3. Base ratio perturbations. Journal of Fluid Mechanics, 551, 93-116
  39. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2006): Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth. Physics of Fluids, 18, Art. No. 012103, 1-14 [Movie to Figure 1]
  40. Timokha, A.N. (2005): Planimetry of vibrocapillary equilibria at small wave numbers. International Journal of Fluid Mechanics Research, 32, Issue 4, 454-487
  41. Gavrilyuk, I.P., Lukovsky, I.A., Timokha, A.N. (2005): Linear and nonlinear sloshing in a circular conical tank. Fluid Dynamics Research, 37, 399-429
  42. Hermann, M., Timokha, A. (2005): Modal modelling of the nonlinear resonant sloshing in a rectangular tank I: A single-dominant model. Mathematical Models and Methods in Applied Sciences, 15, N 9, 1431-1458
  43. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2005): Classification of three-dimensional nonlinear sloshing in a square-base tank with finite depth. Journal of Fluids and Structures, 20, Issue 1, 81-103
  44. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2005): Resonant three-dimensional nonlinear sloshing in a square base basin. Part 2. Effect of higher modes. Journal of Fluid Mechanics, 523, 199-218
  45. Beyer, K., Guenther, M., Timokha, A.N. (2004): Variational and finite element analysis of vibroequilibria. Computational Methods in Applied Mathematics, 4, N 3, 290-323
  46. Gavrilyuk, I., Lukovsky, I., Timokha, A. (2004): Two-dimensional variational vibroequilibria and Faraday's drops. ZAMP, 55, 1015-1033
  47. Faltinsen, O.M., Rognebakke, O.F., Timokha, A.N. (2003): Resonant three-dimensional nonlinear sloshing in a square base basin. Journal of Fluid Mechanics, 487, 1-42
  48. 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, 319-357
  49. Lukovsky, I.A., Timokha, A.N. (2002): Modal modeling of nonlinear sloshing in tanks with non-vertical walls. Non-conformal mapping technique. International Journal of Fluid Mechanics Research, 29, Issue 2, 216-242
  50. Gavrilyuk, I., Lukovsky, I.A., Timokha, A.N. (2001): Sloshing in a circular conical tank. Hybrid Methods in Engineering, 3, Issue 4, 322-378
  51. Lukovsky, I.A., Timokha, A.N. (2001): Sound effect on dynamics and stability of fluid sloshing in zero-gravity. International Journal of Fluid Mechanics Research, 28, Issues 1-2, 19-41
  52. Faltinsen, O.M., Timokha, A.N. (2001): Adaptive multimodal approach to nonlinear sloshing in a rectangular tank. Journal of Fluid Mechanics, 432, 167-200
  53. 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, 261-271
  54. 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, 477-485
  55. 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, 201-234
  56. 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, 463-483
  57. Lukovsky, I.A., Timokha, A.N. (2000): Steady-state nonlinear sloshing in a rectangular tank: passage to shallow water. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki., Issue 11, 48-51
  58. Lukovsky, I.A., Timokha, A.N. (1999): Sound effect on dynamics and stability of fluid sloshing in zero-gravity. Acoustic Bulletin, 2, Issue 3, 69-83
  59. 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, 1688-1695
  60. Lukovskii, I.A., Timokha, A.N. (1996): One version of the linearized theory of nonstationary boundary-value problems with free boundary. Ukrainian Mathematical Journal, 48, Issue 6, 890-904
  61. Lukovskij, I.A., Timokha, A.N. (1995): Nonlinear dynamics of a gas-liquid system under high frequency acoustic vibration. Fluid Mechanics Research, 21(1992), Issue 6, 124-130
  62. 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, 38-40
  63. Lukovskii, I.A., Timokha, A.N. (1993): Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields. Ukrainian Mathematical Journal, 45, Issue 12, 1849-1860
  64. Timokha, A.N. (1993): Influence of sound on the normal modes of oscillation of a liquid-gas interface in a bounded volume. Acoustical Physics. 39, Issue 2, March 1993, 187-189
  65. 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
  66. Lukowsky, I.A., Timoha, A.N. (1992): Waves on the liquid-gas free surface in the presence of the acoustic field in gas. International Series of Numerical Mathematics, 106, 187-194
  67. Lukovskii, I.A., Timokha, A.N. (1991): Acoustic modification of the free surface of a bounded liquid volume. Soviet Physical Acoustics 37(1), 72-74
  68. Lukovskii, I.A., Timokha, A.N. (1991): Stabilization of liquid-gas interface in the presence of interaction with acoustic fields in the gas. Fluid Dynamics, 26, Issue 3, 382-388
  69. 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, 1106-1110
  70. 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, 322-328
  71. Lukovskii, I.A., Timokha, A.N. (1990): Self-adjointness of a certain integro-differential operator. Ukrainian Mathematical Journal, 42, Issue 3, 375-376