Research Article
BibTex RIS Cite

Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping

Year 2025, Volume: 74 Issue: 1, 130 - 137

Abstract

The plane strain problem for low-frequency forced vibrations of a fluid-loaded thin viscoelastic shell is considered. A small structural damping is incorporated using the concept of a complex Young’s modulus. The two-term asymptotic expansion is derived assuming that the structural damping is of the same order as the small thickness of the shell. It is demonstrated that the effect of the structural damping is remarkably greater than that of the radiation damping and the latter can be neglected in the vast majority of the problems.

References

  • Mouritz, A. P., Gellert, E., Burchill, P., Challis, K., Review of advanced composite structures for naval ships and submarines, Composite Structures, 53(1) (2001), 21–42. https://doi.org/10.1016/S0263-8223(00)00175-6
  • Barabash, M., Pisarevskyi, B. Y., Bashynskyi, Y., Taking into account material damping in seismic analysis of structures, Tehnicki Glasnik, 14(1) (2020), 55–59. https://doi.org/10.31803/tg-20180523192812
  • Kumar, M., Shenoi, R. A., Cox, S. J., Experimental validation of modal strain energies based damage identification method for a composite sandwich beam, Composites Science and Technology, 69(10) (2009), 1635-1643. https://doi.org/10.1016/j.compscitech.2009.03.019
  • Zhou, X. Q., Yu, D. Y., Shao, X. Y., Wang, S., Research and applications of viscoelastic vibration damping materials: A review, Composite Structures, 136 (2016), 460–480. https://doi.org/10.1016/j.compstruct.2015.10.014
  • Song, X., Cao, T., Gao, P., Han, Q., Vibration and damping analysis of cylindrical shell treated with viscoelastic damping materials under elastic boundary conditions via a unified Rayleigh-Ritz method, International Journal of Mechanical Sciences, 165 (2020), 105–158. https://doi.org/10.1016/j.ijmecsci.2019.105158
  • Boily, S., Charron, F., The vibroacoustic response of a cylindrical shell structure with viscoelastic and poroelastic materials, Applied Acoustics, 58(2) (1999), 131–152. https://doi.org/10.1016/S0003-682X(98)00070-X
  • Ruzzene, M., Baz, A., Finite element modeling of vibration and sound radiation from fluid-loaded damped shells, Thin-Walled Structures, 36(1) (2000), 21–46.
  • Paimushin, V. N., Gazizullin, R. K., Static and monoharmonic acoustic impact on a laminated plate, Mechanics of Composite Materials, 53(3) (2017), 283–304.
  • Paimushin, V. A., Firsov, V. A., Gyunal, I., Egorov, A. G., Kayumov, R. A., Theoretical-experimental method for determining the parameters of damping based on the study of damped flexural vibrations of test specimens, 3. identification of the characteristics of internal damping, Mechanics of Composite Materials, 50 (2014), 633–646.
  • Deng, J., Liu, Y., Zhang, Z., Liu, W., Dynamic behaviors of multi-span viscoelastic functionally graded material pipe conveying fluid, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(17) (2017), 3181–3192.
  • Belov, A. V., Kaplunov, J. D., Nolde, E. V., A refined asymptotic model of fluid-structure interaction in scattering by elastic shells, Flow, Turbulence and Combustion, 61(1) (1998), 255–267.
  • Kaplunov, J. D., Kossovich, L. Y., Kossovitch, L. Y., Nolde, E. V., Dynamics of Thin Walled Elastic Bodies, Academic Press, 1998.
  • Norris, A. N., Rebinsky, D. A., Acoustic coupling to membrane waves on elastic shells, The Journal of the Acoustical Society of America, 95(4) (1994), 1809–1829.
  • Rebinsky, D. A., Norris, A. N., Benchmarking an acoustic coupling theory for elastic shells of arbitrary shape, The Journal of the Acoustical Society of America, 98(4) (1995), 2368–2371.
  • Andrianov, I. V., Kaplunov, J., Kudaibergenov, A. K., Manevitch, L. I., The effect of a weak nonlinearity on the lowest cut-off frequencies of a cylindrical shell, Zeitschrift f¨ur Angewandte Mathematik und Physik, 69 (2018), 1–12.
  • Ege, N., Erbaş, B., Kaplunov, J., Asymptotic derivation of refined dynamic equations for a thin elastic annulus, Mathematics and Mechanics of Solids, 26(1) (2021), 118–132.
  • Yücel, H., Ege, N., Erbaş, B., Kaplunov, J., A revisit to the plane problem for low-frequency acoustic scattering by an elastic cylindrical shell, Mathematics and Mechanics of Solids, (2024), 1699–1710.
  • Yücel, H., Forced vibrations of a fgm thin-walled cylinder under fluid loading, Zeitschrift für Angewandte Mathematik und Physik, 76(1) (2025), 1–13.
  • Sorokin, E. S., Theory of Internal Friction in Vibrations of Elastic Systems, Gosstroiizdat, Moscow, 1960.
  • Kaplunov, J., Prikazchikova, L., Shamsi, S., A hierarchy of asymptotic models for a fluid-loaded elastic layer, Mathematics and Mechanics of Solids, 29(3) (2024), 560–576. DOI: 10.1177/10812865231201573
  • Sommerfeld, A., Partial Differential Equations in Physics, Academic Press, 1949.
  • Abramowitz, M., Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Volume 55, US Government Printing Office, 1968.
  • Goldenveizer, A. L., Theory of Elastic Thin Shells: Solid and Structural Mechanics, Volume 2, Elsevier, 2014.
There are 23 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Research Articles
Authors

Hazel Yücel 0000-0001-8769-9173

Publication Date
Submission Date November 28, 2024
Acceptance Date December 20, 2024
Published in Issue Year 2025 Volume: 74 Issue: 1

Cite

APA Yücel, H. (n.d.). Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(1), 130-137.
AMA Yücel H. Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 74(1):130-137.
Chicago Yücel, Hazel. “Forced Vibrations of a Thin Viscoelastic Shell Immersed in Fluid under the Effect of Damping”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74, no. 1 n.d.: 130-37.
EndNote Yücel H Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 1 130–137.
IEEE H. Yücel, “Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 1, pp. 130–137.
ISNAD Yücel, Hazel. “Forced Vibrations of a Thin Viscoelastic Shell Immersed in Fluid under the Effect of Damping”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/1 (n.d.), 130-137.
JAMA Yücel H. Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;74:130–137.
MLA Yücel, Hazel. “Forced Vibrations of a Thin Viscoelastic Shell Immersed in Fluid under the Effect of Damping”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 1, pp. 130-7.
Vancouver Yücel H. Forced vibrations of a thin viscoelastic shell immersed in fluid under the effect of damping. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 74(1):130-7.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.