Stability of layered cylindrical shells filled with fluid

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Abstract

The paper investigates the stability of circular vertical layered cylindrical shells completely filled with a quiescent compressible fluid subjected to hydrostatic and external static loads. The behavior of the elastic structure and the fluid medium is described within the framework of the classical shell theory and Euler equations. The linearized equations of motion of the shell and the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is reduced to the calculation of natural vibration frequency in terms of Godunov's orthogonal sweep method. For this purpose, a stepwise procedure is applied in combination with a subsequent refinement by the Muller method. The reliability of the obtained results is verified through a comparison with known numerical solutions. The dependence of the critical external pressure on the ply angle of simply supported, rigidly fixed and cantilevered two-layer and three-layer cylindrical shells is analyzed in detail. The influence of the combined static pressure on the optimal ply angle providing an increase of the stability boundary is evaluated.

About the authors

Sergey A. Bochkarev

Institute of Continuous Media Mechanics, Ural Branch Russian Academy of Sciences

Author for correspondence.
Email: bochkarev@icmm.ru
ORCID iD: 0000-0002-9722-1269
https://www.mathnet.ru/person31691

Cand. Phys. & Math. Sci.; Senior Researcher; Lab. of Functional Materials Mechanics

Russian Federation, 614068, Perm, Acad. Korolev st., 1

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Supplementary files

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2. Figure 1. Computational scheme of the loaded composite cylindrical shell with fluid

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3. Figure 2. Comparison of natural frequencies of vibrations $\omega$ of the rigidly fixed empty shell (CC) subjected to internal pressure $P$: $\boldsymbol{\square}$ — [47] (experiment); $\boldsymbol{\bullet}$ — [7] (FEM, 2D); $\tiny\boldsymbol{\times}$ — [13] (FEM, 3D); solid line — calculation

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4. Figure 3. Dependences of the lowest natural frequencies of vibration $\omega$ on the pressure parameter $\xi$ obtained for empty (a) and completely filled (b) three-layer cantilevered (CF) shells at different values of the ply angle $\alpha$: 1 — $\alpha=0$, 2 — $\alpha=15^\circ$, 3 — $\alpha=30^\circ$, 4 — $\alpha=45^\circ$, 5 — $\alpha=60^\circ$, 6 — $\alpha=75^\circ$, 7 — $\alpha=90^\circ$

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5. Figure 4. Dependences of the lowest natural frequencies of vibration $\omega$ on the pressure parameter $\xi$ obtained for empty (a) and completely filled (b) two-layer rigidly clamped (CC) shells at different values of the ply angle $\alpha$: 1 — $\alpha=0$, 2 — $\alpha=15^\circ$, 3 — $\alpha=30^\circ$, 4 — {$\alpha=45^\circ$, 5 — $\alpha=60^\circ$, 6 — $\alpha=75^\circ$, 7 — $\alpha=90^\circ$

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6. Figure 5. Isosurfaces of critical values of the external static pressure $\xi$ as the functions of circumferential mode $j$ and ply angle $\alpha$ obtained for two-layer and three-layer shells completely filled with fluid under different boundary conditions

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7. Figure 6. Dependences of the pressure parameter $\xi$ on the ply angle $\alpha$ obtained for empty two-layer (a) and three-layer (b) shells under different boundary conditions

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8. Figure 7. Dependences of the pressure parameter $\xi$ on the ply angle $\alpha$ obtained for completely filled two-layer (a) and three-layer (b) shells under different variants of boundary conditions

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