On the frequency spectrum of free vibrations of membranes and plates in contact with a fluid
Tóm tắt
A parallelepiped-shaped container, which is completely filled with a perfect incompressible fluid, is considered. The container is covered with an elastic lid, which is modeled by a membrane or a constant-thickness plate. The other faces of the container are nondeformable. The frequency spectrum of small free vibrations of the lid has been obtained taking into account the apparent mass of the fluid the movement of which is assumed to be potential. The main specific feature of the problem formulation is that the volume of the fluid under the cover remains unchanged in the course of vibrations. As a result, the shape of the deflection of the lid should satisfy the equation of constraint, which follows from the condition of preservation of the volume of the fluid under the lid.
Tài liệu tham khảo
M. A. Il’gamov, Vibrations of Elastic Shells, Containing Fluid and Gas (Nauka, Moscow, 1969) [in Russian].
A. S. Vol’mir, Shells in Fluid and Gas Flow. Problems of Hydroelasticity (Nauka, Moscow, 1979) [in Russian].
A. K. Pertsev and E. G. Platonov, Dynamics of Shells and Plates (Sudostroenie, Leningrad, 1987) [in Russian].
A. L. Popov and G. N. Chernyshev, Mechanics of Acoustic Radiation of Plates and Shells (Nauka, Moscow, 1994) [in Russian].
J. Rayleigh, “On waves propagation along the plane surface of an elastic solid,” Proc. London Math. Soc. 17, 4–11 (1885).
H. Lamb, “On the vibrations of an elastic plate in contact with water,” Proc. R. Soc. London, Ser. A 98, 205–216 (1921).
L. A. Tkacheva, “Plane problem of vibrations of an elastic floating plate under periodic external loading,” J. Appl. Math. Tech. Phys. 45, 420–427 (2004).
A. A. Lakis and S. Neagu, “Free surface effects on the dynamics of cylindrical shell partially filled with liquid,” J. Sound Vib. 207, 175–205 (1997).
Y. Kerboua, A. A. Lakis, M. Thomas, and L. Marcouiller, “Vibration analysis of rectangular plates coupled with fluid,” Appl. Math. Model. 32, 2570–2586 (2008).
A. Kaczor and R. Sygulsky, “Analysis of free vibrations of a plate and fluid in container,” Civ. Environ. Eng. Rep., No. 1, 75–83 (2005).
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1 (Springer, Berlin, 1931; GTTI, Moscow, 1951).