Calculation of non-axisymmetric vibrations of shells of revolution with liquid by finite element method

Аuthors

Shklyarchuk F. N.^1*, Rei Juhnbum F. ^2**

1. Institute of Applied Mechanics of Russian Academy of Science, IAM RAS, 32a, Leninskii av., Moscow, В-334, GSP-1, 119991, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: shklyarchuk@list.ru
**e-mail: joyfulife@hanmail.net

Abstract

The new variant of finite element method (FEM) is developed for calculation of arbitrary orthotropic elastic shells of revolution partially filled with ideal incompressible liquid. The compound shells are connected with ring ribs. The preliminary axisymmetirc stress-strain state of the shells is taken into account. The displacements of the shell and liquid are considered in the form of the n-th harmonic in the circumferential direction.
The shell is divided on narrow conical belts which together with the contained in them lays of the liquid are considered as finite elements (FE). The tangential displacements of a FE shell are approximated by linear functions of the meridional coordinate and the normal displacement — by a full cubic polynomial.
The axial displacement of a thin FE lay of the liquid is approximated by a power function multiplied by a linear function of the axial coordinate x. The radial and circumferential displacements of the liquid are obtained from the exact solution to the equation of continuity with the kinematic boundary condition on the shell surface and expressed in terms of the elastic shell normal displacement and the axial displacement of the liquid. The axial displacements of the liquid are excluded as cyclic coordinates and the liquid is represented by matrix of apparent masses. The shell pole is replaced by a rigid plate or orifice of rather small radius.
Examples of calculations of the non-axisymmetric mode frequencies of the truncated conical shell and hemispherical shell filled with liquid are considered. The obtained results are in good agreement with the knownanalytical and experimental results.

Keywords:

shell of revolution, shell with liquid, hydro-elastic vibrations, non-axisymmetric vibrations

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