On the frequency spectrum of free vibrations of membranes and plates in contact with fluid

Authors

  • Denis N. Ivanov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Institute of Problems of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;
  • Natalya V. Naumova St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Institute of Problems of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;
  • Valentin S. Sabaneev St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Institute of Problems of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;
  • Petr E. Tovstik St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Institute of Problems of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;
  • Tatiana P. Tovstik St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; Institute of Problems of Mekhanical Engineering RAS, Bolshoy pr. V.O., 61, St. Petersburg, 199178, Russian Federation;

DOI:

https://doi.org/10.21638/11701/spbu01.2016.110

Abstract

A container of rectangular parallelepiped form filled by ideal incompressible fluid is studied. The container is closed by an elastic cover which is modeled by a membrane or by a plate of constant thickness. The rest container sides are undeformable. The frequency spectrum of small free vibrations of the cover is built. The motion of fluid is assumed potential and the attached mass of fluid is taken into account. The main peculiarity of problem is that the fluid volume under cover is not changed. As a result the mode of cover deflection satisfies to a restriction equation which follows from the condition that the fluid volume under cover is constant. Refs 11. Figs 5.

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References

Литература

1. Ильгамов М.А. Колебания упругих оболочек, содержащих жидкость и газ. М.: Наука, 1969. 182 с.

2. Вольмир А.С. Оболочки в потоке жидкости и газа. Задачи гидроупругости. М.: Наука, 1979. 320 с.

3. Перцев А.К., Платонов Э.Г. Динамика оболочек и пластин. Л.: Судостроение, 1987. 316 с.

4. Попов А.Л., Чернышев Г.Н. Механика звукоизлучения пластин и оболочек. М.: Наука, 1994. 208 с.

5. Rayleigh J. On waves propagation along the plane surface of an elastic solid // Proc. London Math. Soc. N 17. 1885. P. 4-11.

6. Lamb H. On the vibrations of an elastic plate in contact with water // Proc. Roy. Soc. A 98. 1921. P. 205-216.

7. Ткачева Л.А. Плоская задача о колебаниях плавающей упругой пластины под действием периодической внешней нагрузки // Прикл. мех. и техн. физ. 2004. Т. 45, №3. C. 136-145.

8. Lakis A.A., Neagu S. Free surface effects on the dynamics of cylindrical shell partially filled with liquid // J. Sound and Vibration. Vol. 207, N 2. 1997. P. 175-205.

9. Kerboua Y., Lakis A.A., Thomas M., Marcouil ler L. Vibration analysis of rectangular plates coupled with fluid // Appl. Math. Model. Vol. 32. 2008. P. 2570-2586.

10. Kaczor A., Sygulsky R. Analysis of free vibrations of a plate and fluid in container // Civil and Envir. Eng. Rep. N 1. 2005. P. 75-83.

11. Курант Р., Гильберт Д. Методы математической физики. Т. 1. М.; Л.: ГТТИ, 1951. 425 с.

References

1. Il’gamov M.A., Vibrations of elastic shells, containing fluid and gas (Nauka, Moscow, 1969) [in Russian].

2. Vol’mir A. S., Shells in stream of fluid and gas. Problems of hydroelasticity (Nauka, Moscow, 1979) [in Russian].

3. Pertsev A.K., Platonov E. G., Dynamics of shells and plates (Sudostroenie, Leningrad, 1987) [in Russian].

4. Popov A. L., Chernyshev G.N., Mechanics of plates and shells sound radiation (Nauka, Moscow, 1994) [in Russian].

5. Rayleigh J., “On waves propagation along the plane surface of an elastic solid”, Proc. London Math. Soc. (17), 4–11 (1885).

6. Lamb H., “On the vibrations of an elastic plate in contact with water”, Proc. Roy. Soc. A 98, 205–216 (1921).

7. Tkacheva L.A., “Plane vibration problem of a floating elastic plate under periodic external excitation”, Prikl. Mekh. and Tekhn. Phys. 45(3), 136–145 (2004) [in Russian].

8. Lakis A.A., Neagu S., “Free surface effects on the dynamics of cylindrical shell partially filled with liquid”, J. Sound and Vibration 207(2), 175–205 (1997).

9. Kerboua Y., Lakis A.A., Thomas M., Marcouiller L., “Vibration analysis of rectangular plates coupled with fluid”, Appl. Math. Model. 32, 2570–2586 (2008).

10. Kaczor A., Sygulsky R., “Analysis of free vibrations of a plate and fluid in container”, Civil and Envir. Eng. Rep. (1), 75–83 (2005).

11. Courant R., Gilbert D., Methoden der mathematischen Physik (B. 1, Berlin, 1931) [in German].

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Published

2020-10-19

How to Cite

Ivanov, D. N., Naumova, N. V., Sabaneev, V. S., Tovstik, P. E., & Tovstik, T. P. (2020). On the frequency spectrum of free vibrations of membranes and plates in contact with fluid. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(1), 1. https://doi.org/10.21638/11701/spbu01.2016.110

Issue

Vol. 3 No. 1 (2016)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.