On the study of oscillatory motion of bodies in fluid
https://doi.org/10.26907/2541-7746.2025.1.54-98
Abstract
This article reviews a large body of research on the hydrodynamics of oscillatory motion of bodies, covering three different, yet closely related, classes of problems: the oscillations of solid cylindrical bodies in a still fluid, the elastic oscillations of elongated bodies in a fluid, and the propulsive motion of oscillating bodies (oscillatory propulsors). The findings available so far are summarized. Some key challenges are identified, and their potential solutions are proposed.
Keywords
oscillatory motion,
viscous incompressible fluid,
oscillatory propulsor,
Navier–Stokes equation,
asymptotic analysis,
numerical simulation,
experiment
Supporting agencies: This study was supported by the Russian Science Foundation (project no. 22-79-10033).
About the Authors
A. N. Nuriev
Kazan Federal University
Russian Federation
Russian Federation
Artem N. Nuriev, Dr. Sci. (Physics and Mathematics), Associate Professor, Leading Researcher, Laboratory of Intelligent Biomimetic and Nature-Inspired Systems
Kazan
O. N. Zaitseva
Kazan Federal University
Russian Federation
Russian Federation
Olga N. Zaitseva, Cand. Sci. (Pedagogy), Senior Researcher, Laboratory of Intelligent Biomimetic and Nature-Inspired Systems
Kazan
O. S. Zhuchkova
Kazan Federal University
Russian Federation
Russian Federation
Olga S. Zhuchkova, Cand. Sci. (Physics and Mathematics), Associate Professor, Department of Mathematical Methods in Geology, Institute of Geology and Petroleum Technologies
Kazan
References
1. Sader J.E. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys., 1998, vol. 84, no. 1, pp. 64–76. https://doi.org/10.1063/1.368002.
2. Scherer M.P., Frank G., Gummer A.W. Experimental determination of the mechanical impedance of atomic force microscopy cantilevers in fluids up to 70 kHz. J. Appl. Phys., 2000, vol. 88, no. 5, pp. 2912–2920. https://doi.org/10.1063/1.1287522.
3. Aureli M., Prince Ch., Porfiri M., Peterson S.D. Energy harvesting from base excitation of ionic polymer metal composites in fluid environments. Smart Mater. Struct., 2010, vol. 19, no. 1, art. 015003. https://doi.org/10.1088/0964-1726/19/1/015003.
4. Erturk A., Inman D.J. Piezoelectric Energy Harvesting. Chichester, John Wiley & Sons, 2011. 416 p. https://doi.org/10.1002/9781119991151.
5. Yu Y.-H., Tom N., Jenne D. Numerical analysis on hydraulic power take-off for wave energy converter and power smoothing methods. Proc. ASME 2018 37th Int. Conf. on Ocean, Offshore Mechanics and Arctic Engineering. Vol. 10: Ocean renewable energy. Art. OMAE2018-78176, V010T09A043. Madrid, ASME, 2018. https://doi.org/10.1115/OMAE2018-78176.
6. Martin P.A., Farina L. Radiation of water waves by a heaving submerged horizontal disc. J. Fluid Mech., 1997, vol. 337, pp. 365–379. https://doi.org/10.1017/S0022112097004989.
7. Bidkar R.A., Kimber M., Raman A., Bajaj A.K., Garimella S.V. Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low Keulegan–Carpenter numbers. J. Fluid Mech., 2009, vol. 634, pp. 269–289. https://doi.org/10.1017/s0022112009007228.
8. Ebrahimi N.D., Eldredge J.D., Ju Y.S. Wake vortex regimes of a pitching cantilever plate in quiescent air and their correlation with mean flow generation. J. Fluids Struct., 2019, vol. 84, pp. 408–420. https://doi.org/10.1016/j.jfluidstructs.2018.11.010.
9. Oh M.H., Seo J., Kim Y.-H., Choi M. Endwall effects on 3D flow around a piezoelectric fan. Eur. J. Mech. – B/Fluids, 2019, vol. 75, pp. 339–351. https://doi.org/10.1016/j.euromechflu.2018.10.021.
10. Kozlov V.V., Onishchenko D.A. The motion in a perfect fluid of a body containing a moving point mass. J. Appl. Math. Mech., 2003, vol. 67, no. 4, pp. 553–564. https://doi.org/10.1016/S0021-8928(03)90058-X.
11. Chernous’ko F.L. The optimal periodic motions of a two-mass system in a resistant medium. J. Appl. Math. Mech., 2008, vol. 72, no. 2, pp. 116–125. https://doi.org/10.1016/j.jappmathmech.2008.04.014.
12. Yegorov A.G., Zakharova O.S. The energy-optimal motion of a vibration-driven robot in a resistive medium. J. Appl. Math. Mech., 2010, vol. 74, no. 4, pp. 443–451. https://doi.org/10.1016/j.jappmathmech.2010.09.010.
13. Nuriev A.N., Egorov A.G., Zaitseva O.N., Kamalutdinov A.M. Asymptotic study of the aerohydrodynamics of a flapping cylindrical wing in the high-frequency approximation. Lobachevskii J. Math., 2022, vol. 43, no. 8, pp. 2250–2256. https://doi.org/10.1134/S1995080222110233.
14. Bolotnik N.N., Figurina T.Yu., Chernous’ko F.L. Optimal control of the rectilinear motion of a two-body system in a resistive medium. J. Appl. Math. Mech., 2012, vol. 76, no. 1, pp. 1–14. https://doi.org/10.1016/j.jappmathmech.2012.03.001.
15. Childress S., Spagnolie S.E., Tokieda T. A bug on a raft: Recoil locomotion in a viscous fluid. J. Fluid Mech., 2011, vol. 669, pp. 527–556. https://doi.org/10.1017/S002211201000515X.
16. Borisov A.V., Mamaev I.S., Vetchanin E.V. Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation. Regular Chaotic Dyn., 2018, vol. 23, nos. 7–8, pp. 850–874. https://doi.org/10.1134/S1560354718070043.
17. Kopman V., Porfiri M. Design, modeling, and characterization of a miniature robotic fish for research and education in biomimetics and bioinspiration. IEEE/ASME Trans. Mechatron., 2013, vol. 18, no. 2, pp. 471–483. https://doi.org/10.1109/tmech.2012.2222431.
18. Yeh P.D., Alexeev A. Free swimming of an elastic plate plunging at low Reynolds number. Phys. Fluids, 2014, vol. 26, no. 5, art. 053604. https://doi.org/10.1063/1.4876231.
19. Yeh P.D., Demirer E., Alexeev A. Turning strategies for plunging elastic plate propulsor. Phys. Rev. Fluids, 2019, vol. 4, art. 064101. https://doi.org/10.1103/PhysRevFluids.4.064101.
20. Shintake J., Cacucciolo V., Shea H., Floreano D. Soft biomimetic fish robot made of dielectric elastomer actuators. Soft Rob., 2018, vol. 5, no. 4, pp. 466–474. https://doi.org/10.1089/soro.2017.0062.
21. Feng J., Cho S.K. Two-dimensionally steering microswimmer propelled by oscillating bubbles. Proc. 2014 IEEE 27th Int. Conf. on Micro Electro Mechanical Systems (MEMS). San Francisco, CA, 2014, pp. 188–191. https://doi.org/10.1109/MEMSYS.2014.6765606.
22. Dijkink R.J., van der Dennen J.P., Ohl C.D., Prosperetti A. The ‘acoustic scallop’: A bubblepowered actuator. J. Micromech. Microeng., 2006, vol. 16, no 8, pp. 1653–1659. https://doi.org/10.1088/0960-1317/16/8/029.
23. Chen C., Zhang S.P., Mao Z., Nama N., Gu Y., Huang P.-H., Jing Y., Guo X., Costanzo F., Huang T.J. Three-dimensional numerical simulation and experimental investigation of boundarydriven streaming in surface acoustic wave microfluidics. Lab Chip, 2018, vol. 18, no. 23, pp. 3645–3654. https://doi.org/10.1039/C8LC00589C.
24. Zhu H., Zhang P., Zhong Z., Xia J., Rich J., Mai J., Su X., Tian Z., Bachman H., Rufo J., Gu Y., Kang P., Chakrabarty K., Witelski T.P., Huang T.J. Acoustohydrodynamic tweezers via spatial arrangement of streaming vortices. Sci. Adv., 2021, vol. 7, no. 2, art. eabc7885. https://doi.org/10.1126/sciadv.abc7885.
25. Gubaidullin D.A., Zaripov R.G., Osipov P.P., Tkachenko L.A., Shaidullin L.R. Wave dynamics of gas suspensions and individual particles during resonance oscillations. High Temp., 2021, vol. 59, nos. 2–6, pp. 384–404. https://doi.org/10.1134/S0018151X21030056.
26. Zhu L., Lim H.-C. Hydrodynamic characteristics of a separated heave plate mounted at a vertical circular cylinder. Ocean Eng., 2017, vol. 131, pp. 213–223. https://doi.org/10.1016/j.oceaneng.2017.01.007.
27. McNamara K.P., Love J.S., Tait M.J. Nonlinear modeling of series-type pendulum tuned mass damper-tuned liquid damper. J. Vib. Acoust., 2022, vol. 144, no. 4, art. 041006. https://doi.org/10.1115/1.4053636.
28. McNamara K.P., Tait M.J. Modeling the response of structure–tuned liquid damper systems under large amplitude excitation using smoothed particle hydrodynamics. J. Vib. Acoust., 2022, vol. 144, no. 1, art. 011008. https://doi.org/10.1115/1.4051266.
29. Buzhinskii V.A. Fluid oscillations in cylindrical tanks with longitudinal damping partitions. Fluid Dyn., 2020, vol. 55, no. 1, pp. 7–19. https://doi.org/10.1134/S001546281906003X.
30. Buzhinskii V.A., Petryakhin D.A., Solomonov E.V. Oscillations of plates with stiffeners in fluid. Fluid Dyn., 2022, vol. 57, no. 1, pp. 37–44. https://doi.org/10.1134/S0015462822010025.
31. Egorov A.G., Kamalutdinov A.M., Nuriev A.N., Paimushin V.N. Theoretical-experimental method for determining the parameters of damping based on the study of damped flexural vibrations of test specimens 2. Aerodynamic component of damping. Mech. Compos. Mater., 2014, vol. 50, no. 3, pp. 267–278. https://doi.org/10.1007/s11029-014-9413-3.
32. Egorov A.G., Kamalutdinov A.M., Nuriev A.N., Paimushin V.N. Experimental determination of damping of plate vibrations in a viscous fluid. Dokl. Phys., 2017, vol. 62, no. 5, pp. 257–261. https://doi.org/10.1134/S1028335817050068.
33. Paimushin V.N., Firsov V.A., Shishkin V.M. Identification of the dynamic elasticity characteristics and damping properties of the OT-4 titanium alloy based on study of damping flexural vibrations of the test specimens. J. Mach. Manuf. Reliab., 2019, vol. 48, no. 2, pp. 119–129. https://doi.org/10.3103/S1052618819020110.
34. Payam A.F., Trewby W., Vo¨ıtchovsky K. Simultaneous viscosity and density measurement of small volumes of liquids using a vibrating microcantilever. Analyst, 2017, vol. 142, no. 9, pp. 1492–1498. https://doi.org/10.1039/C6AN02674E.
35. Stokes G.G. On the effect of the internal friction of fluids on the motion of pendulums. Trans. Cambridge Philos. Soc., 1851, vol. 9, pt. 2, pp. 8–106.
36. Schlichting H. Berechnung ebener periodischer Grenzschichtstr¨omungen. Phys. Zeit, 1932, Bd. 33, S. 327–335. (In German)
37. Schlichting H. Teoriya pogranichnogo sloya [Boundary-Layer Theory]. Loizjanski L.G. (Ed.). Moscow, Nauka, 1974. 712 p. (In Russian)
38. Holtsmark J., Johnsen I., Sikkeland T., Skavlem S. Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am., 1954, vol. 26, no. 1, pp. 26–39. https://doi.org/10.1121/1.1907285.
39. Egorov A.G., Nuriev A.N. Steady streaming generated by low-amplitude oscillations of a cylinder. Lobachevskii J. Math., 2021, vol. 42, no. 9, pp. 2102–2108. https://doi.org/10.1134/S1995080221090067.
40. Wang C.-Y. On high-frequency oscillatory viscous flows. J. Fluid Mech., 1968, vol. 32, no. 1, pp. 55–68. https://doi.org/10.1017/S0022112068000583.
41. Stuart J. Double boundary layers in oscillatory viscous flow. J. Fluid Mech., 1966, vol. 24, no. 4, pp. 673–687. https://doi.org/10.1017/S0022112066000910.
42. Riley N. Oscillatory viscous flows. Review and extension. IMA J. Appl. Math., 1967, vol. 3, no. 4, pp. 419–434. https://doi.org/10.1093/imamat/3.4.419.
43. Riley N. The steady streaming induced by a vibrating cylinder. J. Fluid Mech., 1975, vol. 68, no. 4, pp. 801–812. https://doi.org/10.1017/S0022112075001243.
44. Haddon E.W., Riley N. The steady streaming induced between oscillating circular cylinders. Q. J. Mech. Appl. Math., 1979, vol. 32, no. 3, pp. 265–282. https://doi.org/10.1093/qjmam/32.3.265.
45. Nuriev A.N. Viscous flow around an oscillating cylinder: Numerical experiment, bifurcation and asymptotic analysis. Extended Abstract of Cand. Sci. (Physics and Mathematics) Diss. Kazan, 2013. 174 p. (In Russian)
46. Nuriev A.N., Egorov A.G. Asymptotic investigation of hydrodynamic forces acting on an oscillating cylinder at finite streaming reynolds numbers. Lobachevskii J. Math., 2019, vol. 40, no 6, pp. 794–801. https://doi.org/10.1134/S1995080219060180.
47. Tuck E.O. Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. J. Eng. Math., 1969, vol. 3, no. 1, pp. 29–44. https://doi.org/10.1007/BF01540828.
48. Brumley D.R., Willcox M., Sader J.E. Oscillation of cylinders of rectangular cross section immersed in fluid. Phys. Fluids, 2010, vol. 22, no. 5, art. 052001. https://doi.org/10.1063/1.3397926.
49. Ahsan S.N., Aureli M. Finite amplitude oscillations of flanged laminas in viscous flows: Vortex–structure interactions for hydrodynamic damping control. J. Fluids Struct., 2015, vol. 59, pp. 297–315. https://doi.org/10.1016/j.jfluidstructs.2015.09.010.
50. Aureli M., Porfiri M. Low frequency and large amplitude oscillations of cantilevers in viscous fluids. Appl. Phys. Lett., 2010, vol. 96, no. 16, art. 164102. https://doi.org/10.1063/1.3405720.
51. Aureli M., Porfiri M., Basaran M.E. Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids. J. Sound Vib., 2012, vol. 331, no. 7, pp. 1624–1654. https://doi.org/10.1016/j.jsv.2011.12.007.
52. Phan C.N., Aureli M., Porfiri M. Finite amplitude vibrations of cantilevers of rectangular cross sections in viscous fluids. J. Fluids Struct., 2013, vol. 40, pp. 52–69. https://doi.org/10.1016/j.jfluidstructs.2013.03.013.
53. Nuriev A.N., Zaitseva O.N., Kamalutdinov A.M., Bogdanovich E.E., Baimuratova A.R. Asymptotic study of flows induced by oscillations of cylindrical bodies. Fluid Dyn., 2024, vol. 59, no. 2, pp. 314–330. https://doi.org/10.1134/S0015462824602110.
54. Kim S.K., Troesch A.W. Streaming flows generated by high-frequency small-amplitude oscillations of arbitrarily shaped cylinders. Phys. Fluids A, 1989, vol. 1, no. 6, pp. 975–985. https://doi.org/10.1063/1.857409.
55. Ray M. Vibration of an infinite elliptic cylinder in a viscous liquid. Z. Angew. Math. Mech., 1936, Bd. 16, H. 2, S. 99–108. https://doi.org/10.1002/zamm.19360160204.
56. Kanwal R.P Vibrations of an elliptic cylinder and a flat plate in a viscous fluid. Z. Angew. Math. Mech., 1955, Bd. 35, H. 1–2, S. 17–22. https://doi.org/10.1002/zamm.19550350104.
57. Davidson B.J., Riley N. Jets induced by oscillatory motion. J. Fluid Mech., 1972, vol. 53, no. 2, pp. 287–303. https://doi.org/ 10.1017/S0022112072000163.
58. Nuriev A.N., Egorov A.G., Kamalutdinov A.M. Hydrodynamic forces acting on the elliptic cylinder performing high-frequency low-amplitude multi-harmonic oscillations in a viscous fluid. J. Fluid Mech., 2021, vol. 913, art. A40. https://doi.org/10.1017/jfm.2020.1180.
59. Tamada K., Miyagi T. Secondary flow around an oscillating cylinder. J. Phys. Soc. Jpn., 1974, vol. 37, no. 1, pp. 249–253. https://doi.org/10.1143/JPSJ.37.249.
60. Nama N., Huang P.-H., Huang T.J., Costanzo F. Investigation of micromixing by acoustically oscillated sharp-edges. Biomicrofluidics, 2016, vol. 10, no. 2, art. 024124. https://doi.org/10.1063/1.4946875.
61. Lei J., Cheng F., Li K. Numerical simulation of boundary-driven acoustic streaming in microfluidic channels with circular cross-sections. Micromachines, 2020, vol. 11, no. 3, art. 240. https://doi.org/10.3390/mi11030240.
62. Keulegan G.H., Carpenter L.H. Forces on cylinders and plates in an oscillating fluid. J. Res. Natl. Bur. Stand., 1958, vol. 60, no. 5, art. 2857, pp. 423–440. https://doi.org/10.6028/jres.060.043.
63. Bearman P.W., Graham J.M.R., Singh S. Forces on cylinders in harmonically oscillating flow. In: Shaw T.L. (Ed.) Mechanics of Wave-Induced Forces on Cylinders. Water Resources Engineering Ser. Pitman Publ., 1979, pp. 437–449.
64. Singh S. Forces on bodies in oscillatory flow. PhD Thesis. London, Imp. Coll., Univ. of London, 1979. 367 p.
65. Bearman P.W., Downie M.J., Graham J.M.R., Obasaju E.D. Forces on cylinders in viscous oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech., 1985, vol. 154, pp. 337–356. https://doi.org/10.1017/S0022112085001562.
66. Bearman P.W. An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech., 1971, vol. 46, no. 1, pp. 177–198. https://doi.org/10.1017/S0022112071000478.
67. Bearman P.W., Obasaju E.D. An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders. J. Fluid Mech., 1982, vol. 119, pp. 297–321. https://doi.org/10.1017/S0022112082001360.
68. Morison J.R., Johnson J.W., Schaaf S.A. The force exerted by surface waves on piles. J. Pet. Technol., 1950, vol. 2, no. 05, art. SPE-950149-G, pp. 149–154. https://doi.org/10.2118/950149-g.
69. Lighthill J. Fundamentals concerning wave loading on offshore structures. J. Fluid Mech., 1986, vol. 173, pp. 667–681. https://doi.org/10.1017/S0022112086001313.
70. Chaplin J.R. History forces and the unsteady wake of a cylinder. J. Fluid Mech., 1999, vol. 393, pp. 99–121. https://doi.org/10.1017/S0022112099005480.
71. Tatsuno M. Circulatory streaming around an oscillating circular cylinder at low Reynolds numbers. J. Phys. Soc. Jpn., 1973, vol. 35, no. 3, pp. 915–920. https://doi.org/10.1143/JPSJ.35.915.
72. Tatsuno M. Circulatory streaming in the vicinity of an oscillating square cylinder. J. Phys. Soc. Jpn., 1974, vol. 36, no. 4, pp. 1185–1191. https://doi.org/10.1143/JPSJ.36.1185.
73. Tatsuno M. Circulatory streaming in the vicinity of an oscillating triangular cylinder. J. Phys. Soc. Jpn., 1975, vol. 38, no. 1, pp. 257–264. https://doi.org/10.1143/JPSJ.38.257.
74. Tatsuno M., Bearman P.W. A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech., 1990, vol. 211, pp. 157–182. https://doi.org/10.1017/S0022112090001537. 75. Honji H. Streaked flow around an oscillating circular cylinder. J. Fluid Mech., 1981, vol. 107, pp. 509–520. https://doi.org/10.1017/S0022112081001894.
75. Sarpkaya T. Force on a circular cylinder in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech., 1986, vol. 165, pp. 61–71. https://doi.org/10.1017/S0022112086002999.
76. Sarpkaya T. Experiments on the stability of sinusoidal flow over a circular cylinder. J. Fluid Mech., 2002, vol. 457, pp. 157–180. https://doi.org/10.1017/S002211200200784X.
77. Sarpkaya T. Structures of separation on a circular cylinder in periodic flow. J. Fluid Mech., 2006, vol. 567, pp. 281–297. https://doi.org/10.1017/s0022112006002278.
78. Hall P. On the stability of unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech., 1984, vol. 146, pp. 347–367. https://doi.org/10.1017/S0022112084001907.
79. Nuriev A.N., Egorov A.G., Zaitseva O.N. Numerical analysis of secondary flows around an oscillating cylinder. J. Appl. Mech. Tech. Phys., 2018, vol. 59, no. 3, pp. 451–459. https://doi.org/10.1134/S0021894418030082.
80. Justesen P. A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech., 1991, vol. 222, pp. 157–196. https://doi.org/10.1017/S0022112091001040.
81. D¨utsch H., Durst F., Becker S., Lienhart H. Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers. J. Fluid Mech., 1998, vol. 360, pp. 249–271. https://doi.org/10.1017/S002211209800860X.
82. Iliadis G., Anagnostopoulos P. Viscous oscillatory flow around a circular cylinder at low Keulegan–Carpenter numbers and frequency parameters. Int. J. Numer. Methods Fluids, 1998, vol. 26, no. 4, pp. 403–442. https://doi.org/10.1002/(SICI)1097-0363(19980228)26:4<403::AID-FLD640>3.0.CO;2-V.
83. Uzuno˘glu B., Tan M., Price W.G. Low-Reynolds-number flow around an oscillating circular cylinder using a cell viscousboundary element method. Int. J. Numer. Methods Eng., 2001, vol. 50, no. 10, pp. 2317–2338. https://doi.org/10.1002/nme.122.
84. Anagnostopoulos P., Minearb R. Blockage effect of oscillatory flow past a fixed cylinder. Appl. Ocean Res., 2004, vol. 26, nos. 3–4, pp. 147–153. https://doi.org/10.1016/j.apor.2004.11.001.
85. Nehari D., Armeni V., Balli F. Three-dimensional analysis of the unidirectional oscillatory flow around a circular cylinder at low Keulegan–Carpenter and 𝛽 numbers. J. Fluid Mech., 2004, vol. 520, pp. 157–186. https://doi.org/10.1017/S002211200400134X.
86. Elston J.R., Blackburn H.M., Sheridan J. The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech., 2006, vol. 550, pp. 359–389. https://doi.org/10.1017/S0022112005008372.
87. An H. Numerical modelling of flow characteristics and hydrodynamic forces on a cylinder subject to oscillatory flow. PhD Thesis. Perth, Univ. of West. Aust., 2009.
88. An H., Cheng L., Zhao M. Steady streaming around a circular cylinder in an oscillatory flow. Ocean Eng., 2009, vol. 36, no. 14, pp. 1089–1097. https://doi.org/10.1016/j.oceaneng.2009.06.010.
89. Rashid F., Vartdal M., Grue J. Oscillating cylinder in viscous fluid: Calculation of flow patterns and forces. J. Eng. Math., 2011, vol. 70, no. 1, pp. 281–295. https://doi.org/10.1007/s10665-010-9395-7.
90. Suthon P., Dalton C. Streakline visualization of the structures in the near wake of a circular cylinder in sinusoidally oscillating flow. J. Fluids Struct., 2011, vol. 27, no. 7, pp. 885–902. https://doi.org/10.1016/j.jfluidstructs.2011.03.003.
91. Suthon P., Dalton C. Observations on the Honji instability. J. Fluids Struct., 2012, vol. 32, pp. 27–36. https://doi.org/10.1016/j.jfluidstructs.2011.12.008.
92. Malakhova T.V. Unsteady hydrodynamics and heat transfer of oscillating bodies. Extended Abstract of Cand. Sci. (Physics and Mathematics) Diss. Moscow, 2012. 150 p. (In Russian)
93. Ren C., Lu L., Cheng L., Chen T. Hydrodynamic damping of an oscillating cylinder at small Keulegan–Carpenter numbers. J. Fluid Mech., 2021, vol. 913, art. A36. https://doi.org/10.1017/jfm.2020.1159.
94. Egorov A.G., Kamalutdinov A.M., Nuriev A.N. Evaluation of aerodynamic forces acting on oscillating cantilever beams based on the study of the damped flexural vibration of aluminium test samples. J. Sound Vib., 2018, vol. 421, pp. 334–347. https://doi.org/10.1016/j.jsv.2018.02.006.
95. Facci A.L., Porfiri M. Nonlinear hydrodynamic damping of sharp-edged cantilevers in viscous fluids undergoing multi-harmonic base excitation. J. Appl. Phys., 2012, vol. 112, no. 12, art. 124908. https://doi.org/10.1063/1.4769307.
96. Graham J.M.R. The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech., 1980, vol. 97, no. 2, pp. 331–346. https://doi.org/10.1017/s0022112080002595.
97. Tafuni A., Sahin I. Non-linear hydrodynamics of thin laminae undergoing large harmonic oscillations in a viscous fluid. J. Fluids Struct., 2015, vol. 52, pp. 101–117. https://doi.org/10.1016/j.jfluidstructs.2014.10.004.
98. De Rosis A., L´evˆeque E. Harmonic oscillations of a thin lamina in a quiescent viscous fluid: A numerical investigation within the framework of the lattice Boltzmann method. Comput. Struct., 2015, vol. 157, pp. 209–217. https://doi.org/10.1016/j.compstruc.2015.05.034.
99. Nuriev A.N., Kamalutdinov A.M., Egorov A.G. A numerical investigation of fluid flows induced by the oscillations of thin plates and evaluation of the associated hydrodynamic forces. J. Fluid Mech., 2019, vol. 874, pp. 1057–1095. https://doi.org/10.1017/jfm.2019.477.
100. Shrestha B., Ahsan S., Aureli M. Experimental study of oscillating plates in viscous fluids: Qualitative and quantitative analysis of the flow physics and hydrodynamic forces. Phys. Fluids, 2018, vol. 30, no. 1, art. 013102. https://doi.org/10.1063/1.5001330.
101. Kamalutdinov A.M. Theoretical and experimental study of aerodynamic properties in an oscillating plate. Extended Abstract of Cand. Sci. (Physics and Mathematics) Diss. Kazan, 2017. 142 p. (In Russian)
102. Nuriev A.N., Kamalutdinov A.M. Identification of characteristics of the force aerodynamic action on oscillating cantilevered beams. Fluid Dyn., 2022, vol. 57, no. 5, pp. 608–624. https://doi.org/10.1134/S001546282205010X.
103. Facci A.L., Porfiri M. Analysis of three-dimensional effects in oscillating cantilevers immersed in viscous fluids. J. Fluids Struct., 2013, vol. 38, pp. 205–222. https://doi.org/10.1016/j.jfluidstructs.2012.11.006.
104. Agarwal A., Nolan K., Stafford J., Jeffers N. Visualization of three-dimensional structures shed by an oscillating beam. J. Fluids Struct., 2017, vol. 70, pp. 450–463. https://doi.org/10.1016/j.jfluidstructs.2017.02.013.
105. Peterson S.D., Porfiri M., Rovardi A. A particle image velocimetry study of vibrating ionic polymer metal composites in aqueous environments. IEEE/ASME Trans. Mechatron., 2009, vol. 14, no. 4, pp. 474–483. https://doi.org/10.1109/TMECH.2009.2020979.
106. Nuriev A, Kamalutdinov A., Zaitseva O. Hydrodynamics around long vibrating beams. J. Fluids Struct., 2021, vol. 101, art. 103203. https://doi.org/10.1016/j.jfluidstructs.2020.103203.
107. Prandtl L. Uber die Entstehung von Wirbeln in der idealen Fl¨ussigkeit, mit Anwendung auf die ¨ Tragfl¨ugeltheorie und andere Aufgaben. In: v. K´arm´an Th., Levi-Civita T. (Hrsg.) Vortr¨age aus dem Gebiet der Hydro- und Aerodynamik (Innsbruck 1922). Berlin, Heidelberg, Springer, 1924, S. 18–33. https://doi.org/10.1007/978-3-662-00280-3_2. (In German)
108. Birnbaum W. Der Schlagfl¨ugelpropeller und die Kleinen Schwingungen elastisch befestigter Tragfl¨ugel. Z. Flugtech. Motorluftschiffahrt, 1924, Bd. 15, S. 128–134. (In German)
109. Theodorsen T. General theory of aerodynamic instability and the mechanism of flutter. NACA Technical Report No. NACA R-496. Washington, DC, Natl. Advis. Comm. Aeronaut., 1935, pp. 291–311.
110. Garrick I. E. Propulsion of a flapping and oscillating airfoil. NACA Technical Report No. NACATR-567. Washington, DC, Natl. Advis. Comm. Aeronaut., 1936, pp. 1–10.
111. Wagner H. Uber die Entstehung des dynamischen Auftriebes von Tragfl¨ugeln. ¨ Z. Angew. Math. Mech., 1925, Bd. 15, H. 1, S. 17–35. https://doi.org/10.1002/zamm.19250050103. (In German)
112. Glauert H. The force and moment on an oscillating aerofoil. In: Gilles A., Hopf L., v. K´arm´an Th. (Hrsg.) Vortr¨age aus dem Gebiete der Aerodynamik und verwandter Gebiete (Aachen 1929). Berlin, Heidelberg, Springer, 1930, S. 88–95. https://doi.org/10.1007/978-3-662-33791-2_16. (In German)
113. K¨ussner H.G. Zusammenfassender Bericht ¨uber den instation¨aren Auftrieb von Fl¨ugeln. Luftfahrtforschung, 1936, Bd. 13, H. 12, S. 410–424. (In German)
114. K¨ussner H.G., Schwartz I.R. The oscillating wing with aerodynamically balanced elevator. NACA Technical Report No. NACA-TM-991. Washington, DC, Natl. Advis. Comm. Aeronaut., 1941, pp. 1–32.
115. Keldysh M.V., Lavrentiev M.A. On the theory of the oscillating wing. Tekh. Zametki TsaGI, 1935, no. 4, pp. 48–52. (In Russian)
116. Sedov L.I. Ploskie zadachi gidrodinamiki i aerodinamiki [Two-Dimensional Problems in Hydrodynamics and Aerodynamics]. Moscow, Leningrad, 1950. 443 p. (In Russian)
117. Nekrasov A.I. Teoriya kryla v nestatsionarnom potoke [Theory of Wings in Nonstationary Flow]. Moscow, Leningrad, Izd. Akad. Nauk SSSR, 1947. 258 p. (In Russian)
118. Durand W.F. (Ed.) Aerodynamic Theory: A General Review of Progress under a Grant of the Guggenheim Fund for the Promotion of Aeronautics. Vol. II: von K´arm´an Th., Burgers J.M. General aerodynamic theory: Perfect fluids. Berlin, Heidelberg, Springer, 1935. xvi, 368 p. https://doi.org/10.1007/978-3-642-91485-0.
119. Golubev V.V. Lektsii po teorii kryla [Lectures on Wing Theory]. Moscow, Leningrad, Izd. Tekh.- Teor. Lit., 1949. 480 p. (In Russian)
120. Golubev V.V. Issledovaniya po teorii mashushchego kryla [Studies on the Theory of a Flapping Wing]. Moscow, Leningrad, Gos. Izd. Tekh.-Teor. Lit., 1957. (In Russian)
121. Rozhdestvensky K.V. Metod srashchivaemykh asimptoticheskikh razlozhenii v gidrodinamike kryla [Method of Matched Asymptotic Expansions in Wing Hydrodynamics]. Leningrad, Sudostroenie, 1979. 208 p. (In Russian)
122. Rozhdestvensky K.V., Ryzhov V.A. Matematicheskie modeli v teorii mashushchego kryla [Mathematical Models in the Theory of the Flapping Wing]. Leningrad, Leningr. Korablestroit. Inst., 1985. 177 p. (In Russian)
123. Gorelov D.N. Metody resheniya ploskikh kraevykh zadach teorii kyla [Methods for Solving TwoDimensional Boundary Value Problems of the Wing Theory]. Novosibirsk, Izd. Sib. Otd. Ross. Akad. Nauk, 2000. 214 p. (In Russian)
124. Zbikowski R. On aerodynamic modelling of an insect–like flapping wing in hover for micro air ˙ vehicles. Philos. Trans. R. Soc., A, 2002, vol. 360, no. 1791, pp. 273–290. http://doi.org/10.1098/rsta.2001.0930.
125. Azuma A., Okamoto M. Theoretical study on two-dimensional aerodynamic characteristics of unsteady wings. J. Theor. Biol., 2005, vol. 234, no. 1, pp. 67–78. https://doi.org/10.1016/j.jtbi.2004.11.016.
126. Mateescu D., Abdo M. Theoretical solutions for unsteady flows past oscillating flexible airfoils using velocity singularities. J. Aircr., 2003, vol. 40, no. 1, pp. 153–163. https://doi.org/10.2514/2.3070.
127. Glegg S.A.L., Devenport W.J. Unsteady loading on an airfoil of arbitrary thickness. J. Sound Vib., 2009, vol. 319, nos. 3–5, pp. 1252–1270. https://doi.org/10.1016/j.jsv.2008.06.053.
128. Dynnikova G.Ya., Dynnikov Ya.A., Guvernyuk S.V., Malakhova T.V. Stability of a reverse Karman vortex street. Phys. Fluids, 2021, vol. 33, no. 2, art. 024102. https://doi.org/10.1063/5.0035575.
129. Ryzhov V.A. Hydrodynamics of propulsive and energy-saving devices with oscillating wing elements. Extended Abstract of Cand. Sci. (Engineering) Diss. St. Petersburg, 1997. (In Russian)
130. Peters D.A., Hsieh M.A., Torrero A. A state-space airloads theory for flexible airfoils. J. Am. Helicopter Soc., 2007, vol. 52, no. 4, pp. 329–342. https://doi.org/10.4050/JAHS.52.329.
131. Peters D.A. Two-dimensional incompressible unsteady airfoil theory — an overview. J. Fluids Struct., 2008, vol. 24, no. 3, pp. 295–312. https://doi.org/10.1016/j.jfluidstructs.2007.09.001.
132. Siekmann J. Theoretical studies of sea animal locomotion, Part 1. Ing.-Arch., 1962, vol. 31, no. 3, pp. 214–228. https://doi.org/10.1007/BF00534511.
133. Wu T.Y.-T. Swimming of a waving plate. J. Fluid Mech., 1961, vol. 10, no. 3, pp. 321–344. https://doi.org/10.1017/S0022112061000949.
134. Schwarz L. Berechnung der Druckverteilung einer harmonisch sich verformenden Tragfl¨ache in ebener Str¨omung. Luftfahrtforschung, 1940, Bd. 17, S. 379–386. (In German)
135. Kelly H.R., Rentz A.W., Siekmann J. Experimental studies on the motion of a flexible hydrofoil. J. Fluid Mech., 1964, vol. 19, no. 1, pp. 30–48. https://doi.org/10.1017/S0022112064000520.
136. Uldrick J.P., Siekmann J. On the swimming of a flexible plate of arbitrary finite thickness. J. Fluid Mech., 1964, vol. 20, no. 1, pp. 1–33. https://doi.org/10.1017/S0022112064000994.
137. Reece J.W., Uldrick J.P., Siekmann J. Some recent developments in sea animal locomotion hydrodynamics. In: Developments in Theoretical and Applied Mechanics: Proc. 2nd Southeast. Conf. on Theoretical and Applied Mechanics. Atlanta, Georgia, March 5–6, 1964. Oxford, London, New York, NY, Pergamon Press, 1965, pp. 337–349.
138. Uldrick J.P. On the propulsion efficiency of swimming flexible hydrofoils of finite thickness. J. Fluid Mech., 1968, vol. 32, no. 1, pp. 29–53. https://doi.org/10.1017/S0022112068000571.
139. Korennaya L.I. Mechanism of frictional resistance in the undulating body. In: Gidrodinamicheskie voprosy bioniki [Hydrodynamic Problems of Bionics]. Kyiv, Naukova Dumka, 1983, pp. 71–81. (In Russian)
140. Korennaya L.I. Viscous drag components in the undulating body. Bionika, 1987, vol. 21, pp. 53—58. (In Russian)
141. Lighthill M.J. Note on the swimming of slender fish. J. Fluid Mech., 1960, vol. 9, no. 2, pp. 305–317. https://doi.org/10.1017/S0022112060001110.
142. Lighthill M.J. Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech., 1969, vol. 1, no. 1, pp. 413–446. https://doi.org/10.1146/annurev.fl.01.010169.002213.
143. Lighthill M.J. Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech., 1970, vol. 44, no. 2, pp. 265–301. https://doi.org/10.1017/S0022112070001830.
144. Lighthill M.J. Large-amplitude elongated-body theory of fish locomotion. Proc. R. Soc. London, Ser. B, 1971, vol. 179, no. 1055, pp. 125–138. https://doi.org/10.1098/rspb.1971.0085.
145. Wu T.Y.-T. Hydromechanics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J. Fluid Mech., 1971, vol. 46, no. 2, pp. 337–355. https://doi.org/10.1017/S0022112071000570.
146. Wu T.Y.-T. Hydromechanics of swimming propulsion. Part 2. Some optimum shape problems. J. Fluid Mech., 1971, vol. 46, no. 3, pp. 521–544. https://doi.org/10.1017/S0022112071000685.
147. Wu T.Y.-T. Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins. J. Fluid Mech., 1971, vol. 46, no. 3, pp. 545–568. https://doi.org/10.1017/S0022112071000697.
148. Newman J.N., Wu T.Y. A generalized slender-body theory for fish-like forms. J. Fluid Mech., 1973, vol. 57, no. 4, pp. 673–693. https://doi.org/10.1017/S0022112073001953.
149. Newman J.N., Wu T.Y. Hydromechanical aspects of fish swimming. In: Wu T.Y.-T., Brokaw C.J., Brennen C. (Eds.) Swimming and Flying in Nature. Boston, MA, Springer, 1975, pp. 615–634. https://doi.org/10.1007/978-1-4757-1326-8_10.
150. Chopra M.G. Hydromechanics of lunate-tail swimming propulsion. J. Fluid Mech., 1974, vol. 64, no. 2, pp. 375–392. https://doi.org/10.1017/S002211207400245X.
151. Chopra M.G. Large amplitude lunate-tail theory of fish locomotion. J. Fluid Mech., 1976, vol. 74, no. 1, pp. 161–182. https://doi.org/10.1017/S0022112076001742.
152. Chopra M.G., Kambe T. Hydromechanics of lunate-tail swimming propulsion. Part 2. J. Fluid Mech., 1977, vol. 79, no. 1, pp. 49–69. https://doi.org/10.1017/S0022112077000032.
153. Lavrentiev M.A., Lavrentiev M.M. On a principle for creating a tractive force of motion. Prikl. Mekh. Tekh. Fiz., 1962, vol. 4, pp. 3–9. (In Russian)
154. Logvinovich G.V. Gidrodinamika techenii so svobodnymi granitsami [Hydrodynamics of FreeBoundary Flows]. Kyiv, Naukova Dumka, 1969. 208 p. (In Russian)
155. Longvinovich G.V. Hydrodynamics of a thin flexible body (hydrodynamic characteristics of fish). Bionika, 1970, vol. 4, pp. 5–11. (In Russian)
156. Longvinovich G.V. Hydrodynamics of fish swimming. Bionika, 1973, vol. 7, pp. 3–8. (In Russian)
157. Romanenko E.V. Teoriya plavaniya ryb i del’finov [Theory of Fish and Dolphin Swimming]. Moscow, Nauka, 1986. 148 p. (In Russian)
158. Romanenko E.V. Gidrodinamika ryb i del’finov [Hydrodynamics of Fish and Dolphins]. Moscow, KMK, 2001. 411 p. (In Russian)
159. Candelier F., Boyer F., Leroyer A. Three-dimensional extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion. J. Fluid Mech., 2011, vol. 674, pp. 196–226. https://doi.org/10.1017/S002211201000649X.
160. Candelier F., Porez M., Boyer F. Note on the swimming of an elongated body in a non-uniform flow. J. Fluid Mech., 2013, vol. 716, pp. 616–637. https://doi.org/10.1017/jfm.2012.560.
161. Eloy C., Souilliez C., Schouveiler L. Flutter of a rectangular plate. J. Fluids Struct., 2007, vol. 23, no. 6, pp. 904–919. https://doi.org/10.1016/j.jfluidstructs.2007.02.002.
162. Yu Zh., Eloy Ch. Extension of Lighthill’s slender-body theory to moderate aspect ratios. J. Fluids Struct., 2018, vol. 76, pp. 84–94. https://doi.org/10.1016/j.jfluidstructs.2017.09.010.
163. Michelin S., Doar´e O. Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech., 2013, vol. 714, pp. 489–504. https://doi.org/10.1017/jfm.2012.494.
164. Gorelov D.N. Propulsive characteristics of a flapping wing with with an elastically restrained aileron. Bionika, 1991, vol. 24, pp. 18–24. (In Russian)
165. Gruntfest R.A., Derezina N.P. Vibration of an elastic fin in a fluid flow. Bionika, 1981, vol. 15, pp. 29–39. (In Russian)
166. Gruntfest R.A., Derezina N.P. Vibration of a fin of an arbitrary planform in a fluid flow. Bionika, 1984, vol. 18, pp. 45–52. (In Russian)
167. Shklyarchuk F.N. Aerouprugost’ samoleta. Ucheb. posobie [Aircraft Aeroelasticity. A Study Guide]. Moscow, MAI, 1985. 77 p. (In Russian)
168. Grishanina T.V., Shklyarchuk F.N. Unsteady oscillation of a deformable airfoil section in incompressible flow. Russ. Aeronaut., 2009, vol. 52, no. 2, pp. 129–137. https://doi.org/10.3103/S1068799809020019.
169. Kurapov A.A., Rozhdestvensky K.V., Ryzhov V.A. Hydrodynamics of an elastic wing. Optimal characteristics. Tr. V Vsesoyuz. shk. “Gidrodinamika vysokikh skorostei” [Proc. V All-Union School “Hydrodynamics of High Speeds”]. Cheboksary, 1994, pp. 32–41. (In Russian)
170. Rozhdestvensky K.V., Ryzhov V.A. Aerohydrodynamics of flapping-wing propulsors. Prog. Aerosp. Sci., 2003, vol. 39, no. 8, pp. 585–633. https://doi.org/10.1016/S0376-0421(03)00077-0.
171. Katz J., Weihs D. Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J. Fluid Mech., 1978, vol. 88, no. 3, pp. 485–497. https://doi.org/10.1017/S0022112078002220.
172. Kartuzov E.I. Optimization of propulsive systems with wing elements. Extended Abstract of Dr. Sci. (Physics and Mathematics) Diss. St. Petersburg, 2000. 313 p. (In Russian)
173. Sumbatyan M.A., Tarasov A.E. A mathematical model for the propulsive thrust of the thin elastic wing harmonically oscillating in a flow of non-viscous incompressible fluid. Mech. Res. Commun., 2015, vol. 68, pp. 83–88. https://doi.org/10.1016/j.mechrescom.2015.02.005.
174. Tarasov A.E. Aero-hydrodynamic analysis of elastic propulsive elements using the method of integral equations. Extended Abstract of Cand. Sci. (Physics and Mathematics) Diss. Rostov-onDon, 2015. 139 p. (In Russian)
175. Berci M., Toropov V., Hewson R., Gaskell P. Aeroelastic analysis and gust response of a flexible airfoil. Proc. 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. Orlando, FL, 2010, art. AIAA 2010-3119. https://doi.org/10.2514/6.2010-3119.
176. K¨ussner H.G. Allgemeine Tragfl¨achentheorie. Luftfahrtforschung, 1940, Bd. 17, S. 370–378. (In German)
177. Khrabrov A.N. Mathematical modeling of the influence of vortex shedding on the unsteady aerodynamic characteristics of an airfoil during its arbitrary motion. Uch. Zap. TsaGI, 2002, vol. 33, nos. 3–4, pp. 3–17. (In Russian)
178. Liu H., Ellington C.P., Kawachi K., van den Berg C., Willmott A.P. A computational fluid dynamic study of hawkmoth hovering. J. Exp. Biol., 1998, vol. 201, no. 4, pp. 461–477. https://doi.org/10.1242/jeb.201.4.461.
179. Isogai K., Shinmoto Y., Watanabe Y. Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. AIAA J., 1999, vol. 37, no. 10, pp. 1145–1151. https://doi.org/10.2514/2.589.
180. Pedro G., Suleman A., Djilali N. A numerical study of the propulsive efficiency of a flapping hydrofoil. Int. J. Numer. Methods Fluids, 2003, vol. 42, no. 5, pp. 493–526. https://doi.org/10.1002/fld.525.
181. Lewin G.C., Haj-Hariri H. Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech., 2003, vol. 492, pp. 339–362. https://doi.org/0.1017/S0022112003005743.
182. Alben S., Shelley M. Coherent locomotion as an attracting state for a free flapping body. Proc. Natl. Acad. Sci. U.S.A., 2005, vol. 102, no. 32, pp. 11163–11166. https://doi.org/10.1073/pnas.0505064102.
183. Zhang J., Liu N.-S., Lu X.-Y. Locomotion of a passively flapping flat plate. J. Fluid Mech., 2010, vol. 659, pp. 43–68. https://doi.org/10.1017/S0022112010002387.
184. Spagnolie S.E., Moret L., Shelley M.J., Zhang J. Surprising behaviors in flapping locomotion with passive pitching. Phys. Fluids, 2010, vol. 22, art. 041903. https://doi.org/10.1063/1.3383215.
185. Maertens A.P., Triantafyllou M.S., Yue D.K.P. Efficiency of fish propulsion. Bioinspiration Biomimetics, 2015, vol. 10, no. 4, art. 046013. https://doi.org/10.1088/1748-3190/10/4/046013.
186. Lua K.B., Dash S.M., Lim T.T., Yeo K.S. On the thrust performance of a flapping twodimensional elliptic airfoil in a forward flight. J. Fluids Struct., 2016, vol. 66, pp. 91–109. https://doi.org/10.1016/j.jfluidstructs.2016.07.012.
187. Koval’ K.A., Sukhorukov A.L., Chernyshev I.A. Results of verification of the numerical method of calculating the hydrodynamic and hydroacoustic characteristics of a fin propeller. Fundam. Prikl. Gidrofiz., 2016, vol. 9, no. 4, pp. 60–72. (In Russian)
188. Dynnikov Ya.A. On the calculation of a flapping flexible airfoil in the flow of viscous incompressible fluid. Izv. Vyssh. Uchebn. Zaved., Mashinostr., 2016, no. 4, pp. 22–30. https://doi.org/10.18698/0536-1044-2016-4-22-30. (In Russian)
189. Taha H.E. Geometric nonlinear control of the lift dynamics of a pitching-plunging wing. Proc. AIAA Scitech 2020 Forum. Orlando, FL, AIAA, 2020. https://doi.org/10.2514/6.2020-0824.
190. Alben S. Collective locomotion of two-dimensional lattices of flapping plates. Part 1. Numerical method, single-plate case and lattice input power. J. Fluid Mech., 2021, vol. 915, art. A20. https://doi.org/10.1017/jfm.2021.6.
191. Alben S. Collective locomotion of two-dimensional lattices of flapping plates. Part 2. Lattice flows and propulsive efficiency. J. Fluid Mech., 2021, vol. 915, art. A21. https://doi.org/10.1017/jfm.2021.43.
192. Borazjani I., Sotiropoulos F. On the role of form and kinematics on the hydrodynamics of selfpropelled body/caudal fin swimming. J. Exp. Biol., 2010, vol. 213, no. 1, pp. 89–107. https://doi.org/10.1242/jeb.030932. 194. Yeh P.D., Alexeev A. Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids, 2016, vol. 124, pp. 220–225. https://doi.org/10.1016/j.compfluid.2015.07.009.
193. Maertens A.P., Gao A., Triantafyllou M.S. Optimal undulatory swimming for a single fishlike body and for a pair of interacting swimmers. J. Fluid Mech., 2017, vol. 813, pp. 301–345. https://doi.org/10.1017/jfm.2016.845.
194. Zhang D., Huang W.-X. Hydrodynamics of a swimming batoid fish at Reynolds numbers up to 148 000. J. Fluid Mech., 2023, vol. 963, art. A16. https://doi.org/10.1017/jfm.2023.325.
195. Wu X., Zhang X., Tian X., Li X., Lu W. A review on fluid dynamics of flapping foils. Ocean Eng., 2020, vol. 195, art. 106712. https://doi.org/10.1016/j.oceaneng.2019.106712.
196. Riley N., Watson E.J. Eccentric oscillations of a circular cylinder in a viscous fluid. Mathematika, 1993, vol. 40, no. 2, pp. 187–202. https://doi.org/10.1112/S0025579300006975.
197. Nuriev A.N., Egorov A.G. Asymptotic theory of a flapping wing of a circular cross-section. J. Fluid Mech., 2022, vol. 941, art. A23. https://doi.org/10.1017/jfm.2022.287.
198. Egorov A.G., Nuriev A.N. Cruising speed of a cylindrical wing performing small translationalrotational oscillations. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, no. 2–3, pp. 170–180. https://doi.org/10.26907/2541-7746.2022.2-3.170-180. (In Russian)
Review
For citations:
Nuriev A.N., Zaitseva O.N., Zhuchkova O.S. On the study of oscillatory motion of bodies in fluid. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2025;167(1):54-98. (In Russ.) https://doi.org/10.26907/2541-7746.2025.1.54-98
Views:
163
Email this article 