On the Frequency Spectrum of Free Vibrations of Membranes and Plates in Contact with a Fluid

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On the Frequency Spectrum of Free Vibrations of Membranes and Plates in Contact with a Fluid. / Ivanov, D. N.; Naumova, N. V.; Sabaneev, V. S.; Tovstik, P. E.; Tovstik, T. P.

In: Vestnik St. Petersburg University: Mathematics, Vol. 49, No. 1, 01.2016, p. 68-76.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{5b1d3bcd1802465398e1f17cdba98b75,

title = "On the Frequency Spectrum of Free Vibrations of Membranes and Plates in Contact with a Fluid",

abstract = "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.",

keywords = "membrane, plate, incompressible fluid in container, free constraint vibrations",

author = "Ivanov, {D. N.} and Naumova, {N. V.} and Sabaneev, {V. S.} and Tovstik, {P. E.} and Tovstik, {T. P.}",

year = "2016",

month = jan,

doi = "10.3103/S1063454116010076",

language = "Английский",

volume = "49",

pages = "68--76",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - On the Frequency Spectrum of Free Vibrations of Membranes and Plates in Contact with a Fluid

AU - Ivanov, D. N.

AU - Naumova, N. V.

AU - Sabaneev, V. S.

AU - Tovstik, P. E.

AU - Tovstik, T. P.

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

KW - membrane

KW - plate

KW - incompressible fluid in container

KW - free constraint vibrations

U2 - 10.3103/S1063454116010076

DO - 10.3103/S1063454116010076

M3 - статья

VL - 49

SP - 68

EP - 76

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 9177870