### LONGITUDINAL-RADIAL VIBRATIONS OF A VISCOELASTIC CYLINDRICAL THREE-LAYER STRUCTURE

**DOI Number**

**First page**

**Last page**

#### Abstract

The paper considers a cylindrical three-layer structure of arbitrary thickness made of viscoelastic material. It consists of two external bearing layers and a middle layer, the materials of which are generally different. The problem of nonstationary longitudinal-radial vibrations of such a structure is formulated. Based on the exact solutions in transformations of the three-dimensional problem of the linear theory of viscoelasticity for a circular cylindrical three-layer body, a mathematical model of its nonstationary longitudinal-radial vibrations is developed. Equations are derived that allow, based on the results of solving the vibration equations, to determine the stress-strain state of a cylindrical structure and its layers in arbitrary sections. The results obtained allow for special cases of transition into cylindrical viscoelastic and elastic two-layer structures, as well as into homogeneous single-layer cylindrical structures and round rods.

#### Keywords

#### Full Text:

PDF#### References

Liang, W., Liu, T., Li, Ch., Wang, Q., 2023, Three-Dimensional Vibration Model of Cylindrical Shells via Carrera Unified Formulation, Materials, 16, 3345.

Naeem, M.N., Khan, A.G., Arshad, Sh.H., Abdul, G.Sh., Gamkhar, M., 2014, Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions, World Journal of Mechanics, 4(11), pp. 315–331.

Ye, T., Jin, G., Shi, S., Ma, X., 2014, Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations, International Journal of Mechanical Sciences, 84, pp.120–137.

Banks, H.T., Hu, S., Kenz, Z.R., 2011, A Brief Review of Elasticity and Viscoelasticity for Solids, Advances in Applied Mathematics and Mechanics, 3(1), pp. 1–51.

Khudoynazarov, Kh.Kh., 2006, Transversal vibrations of thick and thin cylindrical shells, interacting with deformable medium, Proceedings of the 8th international conference on shell structures SSTA 2005, Jurata, Gdansk, Poland, Shell Structures: Theory and Applications, London: Taylor & Francis Group, pp. 343–347.

Mofakhami, M.R., Toudeshky, H.H., Hashemi, S.H., 2006, Finite cylinder vibrations with different end boundary conditions, Journal of Sound and Vibration, 297, pp. 293–314.

Sahoo, R., Grover, N., Singh, B.N., 2021, Random vibration response of composite–sandwich laminates, Archive of Applied Mechanics, 91, pp. 3755–3771.

Ghamkhar, M., Naeem, M.N., Imran, M., Soutis, C., 2019, Vibration Analysis of a Three-Layered FGM Cylindrical Shell Including the Effect Of Ring Support, Open Physics, 17(1), pp.587-600.

Shah., A.G., Mahmood, T., Naeem, M.N., Zafar, A.Sh., Arshad, Sh.H, 2010, Vibrations of functionally graded cylindrical shells based on elastic foundations, Acta Mechanica, 211(30), pp. 293–307.

Sayyad, A.S., Ghugal, Y.M., 2015, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite Structures, 129, pp. 177–201.

Altukhov, E.V., Fomenko, M.V., 2010, Elastic equalization of a three-layer plate with imperfect layer contact, Bulletin of Donetsk National University, Series A, Natural Sciences, 1, pp.78-87.

Altukhov, E.V., Fomenko, M.V., 2011, Vibrations of three-layer plates in the case of boundary conditions of the flat end and slipping of layers, Bulletin of Donetsk National University, Series.A, Natural Sciences, 2, pp. 34–41.

Iqbal, Z., Naeem, M.N., Sultana, N., 2009, Vibration characteristics of FGM circular cylindrical shells, Acta Mechanica, 208, pp. 237–248.

Sofiyev, A.H., Deniz, A., Akçay, I.H., Yusufoğlu, E.,2006, The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load, Acta Mechanica, 183, pp. 129–144.

Dimitrienko, Yu.I., Gubareva, E.A., Yakovleva, D.O., 2014, Asymptotic theory of viscoelasticity of multilayer thin composite plates, Science and Education of Bauman Moscow State Technical University, Electron Journal, 14, pp. 359–382.

Khudoynazarov, Kh., Abdurazakov, J., Kholikov, D., 2022, Nonlinear torsional vibrations of a circular cylindrical elastic shell, AIP Conference Proceedings, 2637, 020003.

Milić P., Marinković D., Klinge S., Ćojbašić Ž., 2023, Reissner-Mindlin Based Isogeometric Finite Element Formulation for Piezoelectric Active Laminated Shells, Tehnicki Vjesnik, 30(2), pp. 416 - 425.

Vyachkin E.S., Kaledin V.O., Reshetnikova E.V., Vyachkina E.A., Gileva A.E., 2018, Mathematical modeling of static deformation of a layered construction with incompressible layers, Tomsk State University Journal of Mathematics and Mechanics, 55, pp.72–83.

Khudoynazarov Kh.Kh., Khalmuradov R.I., Yalgashev B.F., 2021, Longitudinal-radial vibrations of a elastic cylindrical shell filled with a viscous compressible liquid, Tomsk State University, Journal of Mathematics and Mechanics, 69, pp. 139-154.

Filippov, I.G., Filippov, S.I., 2007, Vibratory and wave processes in continuous compressible media, Moskow: VINITI, 429 p.

Brekhovskikh, L., 2012, Waves in Layered Media, Elsevier, 574.

Khudayarov, B.A., Turaev, F.Z., 2019, Mathematical simulation of nonlinear vibrations of viscoelastic pipelines conveying fluid, Applied Mathematical Modelling, 66, pp. 662–679.

Netrebko, A.V., Pshenichnov, S.G., 2015, Some problems of dynamics of linear-viscoelastic cylindrical shells of finite length, Problems of strength and ductility, 77(1), pp. 67–74.

Rama G., Marinkovic D., Zehn M., 2018, High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates, Composites Part B: Engineering, 151, pp. 118 - 126.

Safaei, B., Chukwueloka Onyibo, E., Goren, M., Kotrasova, K., Yang, Z., Arman, S., Asmael, M., 2023, Free vibration investigation on rve of proposed honeycomb sandwich beam and material selection optimization, Facta Universitatis-Series Mechanical Engineering, 21(1), pp. 31-50.

Zhao, Z., Yuan, X., Zhang, W., Niu, D., Zhang, H., 2021, Dynamical modeling and analysis of hyperelastic spherical shells under dynamic loads and structural damping, Applied Mathematical Modelling, 95, pp. 468-483.

Khudoynazarov, Kh., 2023, A mathematical model of physically nonlinear torsional vibrations of a circular elastic rod, Tomsk State University Journal of Mathematics and Mechanics, 84, pp. 152–166.

DOI: https://doi.org/10.22190/FUME231219010K

### Refbacks

- There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4