The problem of hydroelasticity of the plate forming at wall of the slot-hole channel with a pulsing layer of viscous incompressible liquid at the set harmonious law of a pulsation of pressure at its end face in flat statement is put and analytically solved. The set regional task represents nonlinear related system of the equations of Navier-Stokes for a layer of viscous incompressible liquid and the equation of dynamics of a plate (beam strip). Conditions of sticking of liquid act as regional conditions to impene- trable walls of the channel, a condition of the free expiration of liquid at end faces of the channel and a condition of a hinged supporting of a plate wall of the channel. The complex of dimensionless variables of a considered task is created and small parameters of a task are allocated. As small parameters we have chosen the relative thickness of a layer of liquid and relative amplitude of a deflection of a plate. Considering asymptotic decomposition in the allocated small parameters of a task we have carried out its linearization by a method of indignations. The solution of the linearized task is obtained by a method of the set forms for a mode of the established harmonic oscillations. Thus, proceeding from boundary conditions for a channel plate wall, the form of its deflection is set in the form of ranks on trigonometrical functions from longitudinal coordinate. The law of a deflection of an elastic wall of the channel and dis- tribution of hydrodynamic parameters are found in liquid. We have obtained frequency dependent func- tions of distribution of amplitudes of a deflection and dynamic pressure along the channel and frequency dependent functions of distribution of phase shift of a deflection of a wall and pressure in the channel of rather initial indignation at an end face. On the basis of calculations it is shown that resonant fluctua- tions of an elastic wall of the channel, pressure excited by insignificant pulsations at its end face, can cause essential changes of dynamic pressure and be the main reason of vibration cavitation in liquid.

About the authors

R V Ageev

Volga Region Branch of Moscow State University of Means of Communication


E L Kuznetsova

Moscow Aviation Institute (National Research University)


N I Kulikov

Moscow Aviation Institute (National Research University)


L I Mogilevich

Volga Region Branch of Moscow State University of Means of Communication


V S Popov

Saratov State Technical University of name Yu.A. Gagarin



  1. Башта Т.М. Машиностроительная гидравлика. - М.: Машино-строение, 1971. - 672 с.
  2. Идельчик И.Е. Аэродинамика промышленных аппаратов. - М.; Л.: Энергия, 1964. - 289 с.
  3. Александров В.Ю., Климовский К.К., Маслов Д.А. Движение жидкости в канале с изменением ее массы // Изв. РАН. Энергети-ка. - 2011. - № 1. - С. 88-94.
  4. Лойцянский Л.Г. Механика жидкости и газа. - М.: Дрофа, 2003. - 840 с.
  5. Слезкин Н.А. Динамика вязкой несжимаемой жидкости. - М.: Гостехиздат, 1955. - 520 с.
  6. Иванченко Н.Н., Скурдин А.А., Никитин М.Д. Кавитационные разрушения дизелей. - Л.: Машиностроение, 1970. - 152 с.
  7. Индейцев Д.А., Полипанов И.С., Соколов С.К. Расчет кавитаци-онного ресурса втулки судовых двигателей // Проблемы машино-строения и надежности машин. - 1994. - № 4. - С. 59-64.
  8. Akcabay D.T., Young Y.L. Hydroelastic response and energy har-vesting potential of flexible piezoelectric beams in viscous flow // Physics of Fluids. - 2012. - Vol. 24. - Iss. 5.
  9. Маркина Н.Л., Ревизников Д.Л., Черкасов С.Г. Исследование ка-витационных процессов в канале переменного сечения // Изв. РАН. Энергетика. - 2012. - № 1. - С. 109-118.
  10. Mogilevich L.I., Popov V.S. Investigation of the interaction between a viscous incompressible fluid layer and walls of a channel formed by coaxial vibrating discs // Fluid Dynamics. - 2011. - Vol. 46. - No. 3. - P. 375-388.
  11. Mogilevich L.I., Popov V.S., Popova A.A., Dynamics of inter¬action of elastic elements of a vibrating machine with the compressed liquid layer lying between them // Journal of Machinery Manufacture and Reliability. - 2010. - Vol. 39. - No. 4. - P. 322-331.
  12. Ageev R.V., Mogilevich L.I., Popov V.S. Vibrations of the Walls of a Slot Channel with a Viscous Fluid Formed by Three_Layer and Solid Disks // Journal of Machinery Manufacture and Reliability. - 2014. - Vol. 43. - No. 1. - P. 1-8.
  13. Amabili M. Vibrations of circular plates resting on a sloshing liquid: Solution of the fully coupled problem // Journal of Sound and Vibra-tion. - 2001. - Vol. 245. - Iss. 2. - P. 261-283.
  14. Askari E., Jeong K.-H., Amabili M. Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface // Journal of Sound and Vibration. - 2013. - Vol. 332. - Iss. 12. - P. 3064-3085.
  15. Veklich N.A. Equation of Small Transverse Vibrations of an Elastic Pipeline Filled with a Transported Fluid // Mechanics of Solids. - 2013. - Vol. 48. - No. 6. - P. 673-681.
  16. Аэрогидроупругость конструкций / А.Г. Горшков, В.И. Морозов, А.Т. Пономарев, Ф.Н. Шклярчук. - М.: Физматлит, 2000.
  17. Van Dyke, M. Perturbation methods in fluid mechanics // The Para-bolic Press, Stanford, Calif., 1975.



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Copyright (c) 2014 Ageev R.V., Kuznetsova E.L., Kulikov N.I., Mogilevich L.I., Popov V.S.

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