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Article information
2022 , Volume 27, ¹ 4, p.15-32
Bochkarev S.A.
Numerical simulation of natural vibrations of a cylindrical shell partially filled with fluid and embedded in an elastic foundation
The paper presents the results of studies on natural vibrations of circular vertical cylindrical shells completely or partially filled with a stationary compressible fluid and embedded in a Pasternak two-parameter elastic foundation. In the meridional direction, the elastic medium is both homogeneous and inhomogeneous, and is an alternation of areas, in which this medium is present or absent. The behavior of the elastic structure and compressible fluid is described within the framework of classical shell theory based on the Kirchhoff — Love hypotheses and the Euler equations. The equations of motion of the shell combined with the corresponding geometric and physical relations are reduced to a system of ordinary differential equations for new unknowns. The acoustic wave equation is also reduced to a system of ordinary differential equations using the straight line method. The formulated boundary value problem is solved by the Godunov orthogonal sweep method involving the numerical integration of differential equations by the fourth order Runge —Kutta method. The natural frequencies of vibrations are calculated using a combination of stepwise procedure and subsequent refinement by the half-division method. The validity of the obtained results is confirmed by comparing them with the known numerical-analytical solutions. The dependences of minimum vibration frequencies versus the level of fluid are analyzed for simply supported, clamped and cantilevered cylindrical shells of various types of inhomogeneity along the length of the body and with different stiffness. It is demonstrated that with increase in the level of filling of shells with fluid, the influence of the elastic foundation on the frequency spectrum of the structure decreases
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Keywords: classical shell theory, compressible fluid, Godunov orthogonal sweep method, method of lines, natural vibrations, elastic Pasternaks medium
doi: 0.25743/ICT.2022.27.4.003
Author(s):
Bochkarev Sergey Arkadiyevich
PhD.
Position: Senior Research Scientist
Office: Institute of Continuous Media Mechanics, Ural Branch of RAS
Address: 614068, Russia, Perm, 1, Acad. Korolev Str.
Phone Office: (342) 237-83-08
E-mail: bochkarev@icmm.ru
SPIN-code: 3804-5025 References:
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Bibliography link:
Bochkarev S.A. Numerical simulation of natural vibrations of a cylindrical shell partially filled with fluid and embedded in an elastic foundation // Computational technologies. 2022. V. 27. ¹ 4. P. 15-32
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