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Dispersion of the axisymmetric waves propagating in the hydro-elastic system consisting of the pre-strained highly elastic plate, compressible inviscid fluid, and rigid wall

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Abstract

The paper deals with the study of the influence of the homogeneous finite initial strains in a highly elastic plate which is in contact with a compressible inviscid fluid on the dispersion of the axisymmetric waves propagating in the “plate + fluid” and “plate + fluid + rigid wall” systems. It is assumed that the homogeneous finite initial strains in the plate are caused by the radial forces acting at infinity, and the motion of the plate is described by the three-dimensional linearized equations and relations of elastic waves in bodies with initial stresses. The fluid flow is formulated by the linearized Navier–Stokes equations for compressible barotropic inviscid fluids. Elasticity relations for the plate material are presented through the harmonic potential. It is established that as a result of the difference between the initial strain states appearing in the axisymmetric and plane-strain states in the plate, the dispersion equation obtained for the studied dynamic problem does not coincide with the dispersion equation obtained for the corresponding plane-strain state. The dispersion curves are constructed for various values of the initial strains in the case where the material of the plate is soft-rubber, and the fluid is taken as water. From analysis of these curves, in particular, it is established that the initial strains not only quantitatively, but also qualitatively influence the dispersion of the axisymmetric waves propagating in the hydro-elastic system under consideration.

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References

  1. Akbarov, S.D.: Dynamics of Pre-strained Bi-material Elastic Systems: Linearized Three-Dimensional Approach. Springer, Heidelberg (2015)

    Book  Google Scholar 

  2. Akbarov, S.D.: Forced vibration of the hydro-viscoelastic and – elastic systems consisting of the viscoelastic or elastic plate, compressible viscous fluid and rigid wall: a review. Appl. Comput. Math. 17, 221–245 (2018)

    MATH  Google Scholar 

  3. Akbarov, S.D., Agasiyev, E.R., Zamanov, A.D.: Wave propagation in a pre-strained compressible elastic sandwich plate. Eur. J. Mech A/Solids 30, 409–422 (2011)

    Article  MATH  Google Scholar 

  4. Akbarov, S.D., Negin, M.: On the dispersion of waves propagating in “plate+fluid layer” systems. Coupled Syst. Mech. 10(2), 123–142 (2021). https://doi.org/10.12989/csm.2021.10.2.123

    Article  Google Scholar 

  5. Akbarov, S.D., Negin, M.: Attenuation of quasi-Lamb waves in a hydroelastic system “elastic plate+compressible viscous fluid+rigid wall". Struct. Eng. Mech. 81(4), 443–459 (2022). https://doi.org/10.12989/sem.2022.81.4.443

    Article  Google Scholar 

  6. Akbarov, S.D., Bagirov, E.T.: The dispersion of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder with the initial inhomogeneous thermal stresses. Waves Random Complex Media 10, 10 (2021). https://doi.org/10.1080/17455030.2021.1912437

    Article  Google Scholar 

  7. Bagno, A.M.: Dispersion properties of lamb waves in an elastic layer-ideal liquid half-space system. Int. Appl. Mech. 53(6), 609–616 (2017)

    Article  Google Scholar 

  8. Bagno, A.M.: Effect of prestresses on the dispersion of quasi-Lamb waves in the system consisting of an ideal liquid layer and a compressible elastic layer. Int. Appl. Mech. 53(2), 139–148 (2017)

    Article  Google Scholar 

  9. Bagno, A.M.: Dispersion properties of Lamb waves in an elastic layer—ideal liquid half-space system. Int. Appl. Mech. 53(6), 609–616 (2017)

    Article  Google Scholar 

  10. Baggens, O., Ryden, N.: Poisson’s ratio from polarization of acoustic zero-group velocity Lamb mode. J. Acoust. Soc. Am. 138, EL88 (2015)

    Article  Google Scholar 

  11. Bian, C., Wang, J., Xie, L., et al.: The axisymmetric love wave in elastic solids and its special properties. Arch. Appl. Mech. (2022). https://doi.org/10.1007/s00419-021-02082-1

    Article  Google Scholar 

  12. Cès, M., Clorennec, D., Royer, D., Prada, C.: Thin layer thickness measurements by zero group velocity Lamb mode resonances. Rev. Sci. Instrum. 82, 114902 (2011)

    Article  Google Scholar 

  13. Grünsteidl, C., Murray, T.W., Berer, T., et al.: Inverse characterization of plates using zero group velocity Lamb modes. Ultrasonics 65, 1–4 (2016)

    Article  Google Scholar 

  14. Guz, A.N.: Elastic waves in bodies with initial (residual) stresses. A.C.K. Kiev (in Russian) (2004)

  15. Guz, A.N.: Dynamics of Compressible Viscous Fluid. Cambridge Scientific Publishers, Cambridge (2009)

    MATH  Google Scholar 

  16. Guz, A.N., Bagno, A.M.: Effect of liquid viscosity on dispersion of quasi-Lamb waves in an elastic-layer–viscous-liquid-layer system. Int. Appl. Mech. 53(4), 361–367 (2017)

    Article  Google Scholar 

  17. Guz, A.N., Bagno, A.M.: Effect of prestresses on the dispersion of lamb waves in a system consisting of a viscous liquid layer and a compressible elastic layer. Int. Appl. Mech. 54(3), 249–258 (2018). https://doi.org/10.1007/s10778-018-0902-2

    Article  Google Scholar 

  18. Guz, A.N., Bagno, A.M.: Propagation of quasi-lamb waves in an elastic layer interacting with a viscous liquid half-space. Int. Appl. Mech. 55(5), 459–469 (2019). https://doi.org/10.1007/s10778-019-00968-w

    Article  MATH  Google Scholar 

  19. John, F.: Plane strain problems for a perfectly elastic material of harmonic type. Commun. Pure Appl. Math. 13(2), 239–296 (1960)

    Article  MATH  Google Scholar 

  20. Ottenio, M., Destrade, M., Ogden, R.W.: Acoustic waves at the interface of a pre-stressed incompressible elastic solid and a viscous fluid. Int. J. Non-Linear Mech. 42(2), 310–320 (2007)

    Article  Google Scholar 

  21. Othmani, C., Zhang, H., Kamali, A.R., et al.: Propagating, evanescent and ZGV Lamb modes in high-performance anisotropic Cu–Al–Ni alloy plates. Arch. Appl. Mech. 92, 21–43 (2022). https://doi.org/10.1007/s00419-021-02040

    Article  Google Scholar 

  22. Prada, C., Clorennec, D., Royer, D.: Zero-group velocity modes and local vibrations of an elastic plate. J. Acoust. Soc. Am. 123, 3156 (2008)

    Article  MATH  Google Scholar 

  23. Paimushin, V.N., Gazizullin, R.K.: Free and forced vibrations of a composite plate in a perfect compressible fluid, taking into account energy dissipation in the plate and fluid. Lobachevskii J. Math. 42(8), 2016–2022 (2021)

    Article  MATH  Google Scholar 

  24. Paimushin, V.N., Tarlakovskii, D.V., Firsov, V.A., Gazizullin, R.K.: Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account. Z. Angew. Math. Mech. (2020). https://doi.org/10.1002/zamm.201900102

    Article  Google Scholar 

  25. Tofeldt, O., Ryden, N.: (2017) Zero-group velocity modes in plates with continuous material variation through the thickness. J. Acoust. Soc. Am. 141(5), 3302–3311 (2017). https://doi.org/10.1121/1.4983296

    Article  Google Scholar 

  26. Wijeyewickrema, A.C., Ushida, Y., Kayestha, P.: Wave propagation in a pre-stressed compressible elastic layer with constrained boundaries. J. Mech. Mater. Struct. 3(10), 1963–1976 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 3349, Besiktas, Istanbul, Turkey

    Surkay D. Akbarov

  2. Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences, Az141, Baku, Azerbaijan

    Surkay D. Akbarov & Emin T. Bagirov

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  1. Surkay D. Akbarov
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Akbarov, S.D., Bagirov, E.T. Dispersion of the axisymmetric waves propagating in the hydro-elastic system consisting of the pre-strained highly elastic plate, compressible inviscid fluid, and rigid wall. Arch Appl Mech 93, 861–879 (2023). https://doi.org/10.1007/s00419-022-02304-0

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