Abstract
The paper presents the results of studies of natural vibrations of circular vertical layered cylindrical shells completely or partially filled with a quiescent compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells, together with the corresponding geometric 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 generalized differential quadrature method. The formulated boundary-value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of the vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of the lowest vibration frequencies on the ply angle and the fluid level for simply supported, rigidly clamped, and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of lay-up scheme and the ply angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.
REFERENCES
M. S. Qatu, R. W. Sullivan, and W. Wang, “Recent research advances on the dynamic analysis of composite shells: 2000–2009,” Compos. Struct. 93, 14–31 (2010). https://doi.org/10.1016/j.compstruct.2010.05.014
M. Qatu, E. Asadi, and W. Wang, “Review of recent literature on static analyses of composite shells: 2000–2010,” Open J. Compos. Mater. 2, 61–86 (2012). https://doi.org/10.4236/ojcm.2012.23009
D. B. Muggeridge and T. J. Buckley, “Flexural vibration of orthotropic cylindrical shells in a fluid medium,” AIAA J. 17, 1019–1022 (1979). https://doi.org/10.2514/3.61270
M. D. Nurul Izyan, Z. A. Aziz, and K. K. Viswanathan, “Free vibration of anti-symmetric angle-ply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory,” Compos. Struct. 193, 189–197 (2018). https://doi.org/10.1016/j.compstruct.2018.03.034
M. D. Nurul Izyan, Z. A. Aziz, R. Ghostine, J. H. Lee, and K. K. Viswanathan, “Free vibration of crossply layered circular cylindrical shells filled with quiescent fluid under first order shear deformation theory,” Int. J. Pressure Vessels Piping 170, 73–81 (2019). https://doi.org/10.1016/j.ijpvp.2019.01.019
M. D. Nurul Izyan and K. K. Viswanathan, “Vibration of symmetrically layered angle-ply cylindrical shells filled with fluid,” PLoS ONE 14, e0219089 (2019). https://doi.org/10.1371/journal.pone.0219089
Z. C. Xi, L. H. Yam, and T. P. Leung, “Free vibration of a laminated composite circular cylindrical shell partially filled with fluid,” Compos. B Eng. 28, 359–374 (1997). https://doi.org/10.1016/S1359-8368(96)00047-9
Z. C. Xi, L. H. Yam, and T. P. Leung, “Free vibration of a partially fluid-filled cross-ply laminated composite circular cylindrical shell,” J. Acoust. Soc. Am. 101, 909–917 (1997). https://doi.org/10.1121/1.418049
K. Okazaki, J. Tani, and M. Sugano, “Free vibrations of a laminated composite coaxial circular cylindrical shell partially filled with liquid,” Trans. Jpn. Soc. Mech. Eng. C 68, 1942–1949 (2002). https://doi.org/10.1299/kikaic.68.1942
K. Okazaki, J. Tani, J. Qiu, and K. Kosugo, “Vibration test of a cross-ply laminated composite circular cylindrical shell partially filled with liquid,” Trans. Jpn. Soc. Mech. Eng. C 73, 724–731 (2007). https://doi.org/10.1299/kikaic.73.724
S. A. Bochkarev and S. V. Lekomtsev, “Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells,” Struct. Eng. Mech. 81, 769–780 (2022). https://doi.org/10.12989/sem.2022.81.6.769
M. H. Toorani and A. A. Lakis, “Shear deformation in dynamic analysis of anisotropic laminated open cylindrical shells filled with or subjected to a flowing fluid,” Comput. Methods Appl. Mech. Eng. 190, 4929–4966 (2001). https://doi.org/10.1016/S0045-7825(00)00357-1
M. H. Toorani and A. A. Lakis, “Dynamic analysis of anisotropic cylindrical shells containing flowing fluid,” J. Press. Vessel Technol. 123, 454–460 (2001). https://doi.org/10.1115/1.1401023
M. H. Toorani and A. A. Lakis, “Dynamics behavior of axisymmetric and beam-like anisotropic cylindrical shells conveying fluid,” J. Sound Vib. 259, 265–298 (2003). https://doi.org/10.1006/jsvi.2002.5161
R. D. Firouz-Abadi, H. Haddadpour, and M. A. Kouchakzadeh, “Free vibrations of composite tanks partially filled with fluid,” Thin-Walled Struct. 47, 1567–1574 (2009). https://doi.org/10.1016/j.tws.2009.05.007
S. Yao, Y. Zhang, J. Xue, F. Jin, and Z. He, “Free vibration of non-shallow, laminated cylinders submerged in a fluid with general boundary conditions,” Appl. Ocean Res. 125, 103232 (2022). https://doi.org/10.1016/j.apor.2022.103232
T. I. Thinh and M. C. Nguyen, “Dynamic stiffness method for free vibration of composite cylindrical shells containing fluid,” Appl. Math. Model. 40, 9286–9301 (2016). https://doi.org/10.1016/j.apm.2016.06.015
V. Q. Hien, T. I. Thinh, and N. M. Cuong, “Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid,” Vietnam J. Mech. 38, 249–265 (2016). https://doi.org/10.15625/0866-7136/6954
H.-Z. Zhu and J.-H. Wu, “Free vibration of partially fluid-filled or fluid-surrounded composite shells using the dynamic stiffness method,” Acta Mech. 231, 3961–3978 (2020). https://doi.org/10.1007/s00707-020-02734-3
E. I. Grigolyuk and F. N. Shklyarchuk, “Equations of perturbed motion of a body with a thinwalled elastic shell partially filled with a liquid,” Prikl. Mat. Mekh. 34, 401–411 (1970).
S. A. Bochkarev, S. V. Lekomtsev, and A. N. Senin, “Natural vibrations and stability of loaded cylindrical shells partially filled with fluid, taking into account gravitational effects,” Thin-Walled Struct. 164, 107867 (2021). https://doi.org/10.1016/j.tws.2021.107867
A. G. Gorshkov, V. I. Morozov, A. T. Ponomarev, and F. N. Shklyarchuk, Aerohydroelasticity of Structures (Fizmatlit, Moscow, 2000) [in Russian].
S. K. Godunov, Ordinary Differential Equations with Constant Coefficient (Novosib. Gos. Univ., Novosibirsk, 1994; American Mathematical Society, Providence, R.I., 1997).
S. A. Bochkarev, S. V. Lekomtsev, and V. P. Matveenko, “Natural vibrations of truncated conical shells containing fluid,” Mech. Solids 57, 1971–1986 (2022). https://doi.org/10.3103/S0025654422080064
I. Sheinman and S. Greif, “Dynamic analysis of laminated shells of revolution,” J. Compos. Mater. 18, 200–215 (1984). https://doi.org/10.1177/002199838401800301
A. V. Karmishin, V. A. Lyaskovets, V. I. Myachenkov, and A. N. Frolov, The Statics and Dynamics of Thin-Walled Shell Structures (Mashinostroenie, Moscow, 1975) [in Russian].
N. A. Alfutov, P. A. Zinov’ev, and V. G. Popov, Analysis of Multilayer Composite Plates and Shells (Mashinostroenie, Moscow, 1984) [in Russian].
C. Shu, Differential Quadrature and Its Application in Engineering (Springer-Verlag, London, 2000).
S. A. Bochkarev and S. V. Lekomtsev, “Stability analysis of composite cylindrical shell containing rotating fluid,” J. Phys.: Conf. Ser. 1945, 012034 (2021). https://doi.org/10.1088/1742-6596/1945/1/012034
Funding
The work was performed within the framework of a state task; state registration no. AAAA-A19-119012290100-8.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Translated by E. Seifina
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Bochkarev, S.A., Lekomtsev, S.V. & Matveenko, V.P. Natural Vibrations of Composite Cylindrical Shells Partially Filled with Fluid. Vestnik St.Petersb. Univ.Math. 56, 435–445 (2023). https://doi.org/10.1134/S1063454123040052
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063454123040052