Free Vibrations of Heterogeneous Orthotropic Cylindrical Shells Reinforced by Annular Ribs and Filled by Fluid
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FREE VIBRATIONS OF HETEROGENEOUS ORTHOTROPIC CYLINDRICAL SHELLS REINFORCED BY ANNULAR RIBS AND FILLED BY FLUID F. S. Latifov∗ , M. Z. Yusifov, and N. I. Alizade
UDC 539.3
Abstract: Natural vibrations of heterogeneous orthotropic cylindrical shells reinforced by annular ribs and filled with fluid are studied. Dependences of a frequency response on various geometric and physical parameters of the problem are described. Keywords: free vibrations, reinforced inhomogeneous orthotropic cylindrical shell, fluid filling the shell. DOI: 10.1134/S0021894420030219
Shell structures are widely used in construction and engineering. The main permanent load on a shell is its weight. Shell strength can be improved by using light porous materials with low bulk density, but these materials have low strength. To compensate for this drawback, technological heterogeneity is developed. In designing shells, the choice of material is of great importance. Recently, various promising materials have appeared, particularly those obtained using nanotechnologies. Porous aluminum with the addition of polymer, carbon, or metal particles is widely used as a shell material. Heterogeneity is created in the supporting structures by adding another highstrength material to the surface layers of the material by means of diffusion or other technologies. Thus, there is technological heterogeneity in the structure with a clearly manifested front separating hardened and unhardened materials. There is a need to develop methods for calculating the stress–strain state of heterogeneous shells and study the effect of heterogeneity on the frequencies of their own vibrations. Algorithms are required for determining resonant frequencies, leading to the fracture of the initial and hardened materials of inhomogeneous shells. When using polymeric materials in engineering practice, particularly fiberglass, one should account for the anisotropy of elastic properties in studying low-frequency vibrations of shells. The thin-walled part of the shell can be made more rigid by reinforcement with ribs, which significantly improves its strength along with the mass of the structure. It should be noted that, if a shell has geometric and physical nonlinearity, the equations describing its stress– strain state are nonlinear differential equations in partial derivatives. These equations are solved in [1] by a method of successive loads [2, 3]. Both the error caused by linearizing the equation and the calculation time are reduced by a two-step method of successive parameter perturbation [4]. The impact of the conditions of mounting along the contour on the stability of polymer concrete shells is described in [5]. In [6], the Hamilton–Ostrogradsky variational principle is used to study the free vibrations of a longitudinally supported orthotropic cylindrical shell of heterogeneous thickness, which is in contact with a moving fluid. The study of parametric vibrations in a viscoelastic medium of a rectilinear rod made of a nonlinear material of heterogeneous thickness using the Pasternak contact
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