Structural Engineering and Mechanics

  • 제81권4호
  • /
  • Pages.443-459
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Attenuation of quasi-Lamb waves in a hydroelastic system "elastic plate+compressible viscous fluid+rigid wall"

  • Akbarov, Surkay D. (Department of Mechanical Engineering, Yildiz Technical University) ;
  • Negin, Mesut (Department of Civil Engineering, Bahcesehir University)
  • 투고 : 2021.03.25
  • 심사 : 2021.11.16
  • 발행 : 2022.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.

키워드

참고문헌

  1. Akbarov, S.D. (2015), Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach, Springer, Heidelberg, New-York, Dordrecht, London.
  2. Akbarov, S.D. (2018), "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.
  3. Akbarov, S.D. and Huseynova, T.V. (2019), "Forced vibration of the hydro-elastic system consisting of the orthotropic plate, compressible viscous fluid and rigid wall", Couple. Syst. Mech., 8(3), 199-218. https://doi.org/10.12989/csm.2019.8.3.199.
  4. Akbarov, S.D. and Huseynova, T.V. (2020), "Fluid flow profile in the "orthotropic plate+compressible viscous fluid+rigid wall" system under the action of the moving load on the plate", Couple. Syst. Mech., 9(3), 289-309. https://doi.org/10.12989/csm.2020.9.3.289.
  5. Akbarov, S.D. and Ismailov, M.I. (2016), "Dynamics of the oscillating moving load acting on the hydroelastic system consisting of the elastic plate, compressible viscous fluid and rigid wall", Struct. Eng. Mech., 59(3), 403-430. https://doi.org/10.12989/sem.2016.59.3.403.
  6. Akbarov, S.D. and Ismailov, M.I. (2017), "The forced vibration of the system consisting of an elastic plate, compressible viscous fluid and rigid wall", J. Vib. Control, 23(11), 1809-1827. https://doi.org/10.1177/1077546315601299.
  7. Akbarov, S.D. and Kepceler, T. (2015), "On the torsional wave dispersion in a hollow sandwich circular cylinder made from viscoelastic materials", Appl. Math. Model., 39, 3569-3587. https://doi.org/10.1016/j.apm.2014.11.061.
  8. Akbarov, S.D. and Panakhli, P.G. (2017), "On the particularities of the forced vibration of the hydro-elastic system consisting of a moving elastic plate, compressible viscous fluid and rigid wall", Couple. Syst. Mech., 6(3), 287-316. https://doi.org/10.12989/csm.2017.6.3.287.
  9. Akbarov, S.D., Ismailov, M.I. and Aliyev, S.A. (2017), "The influence of the initial strains of the highly elastic plate on the forced vibration of the hydro-elastic system consisting of this plate, compressible viscous fluid, and rigid wall", Couple. Syst. Mech., 6(4), 439-464. https://doi.org/10.12989/csm.2017.6.4.439.
  10. Akbarov, S.D., Kocal, T. and Kepceler, T. (2016a), "Dispersion of Axisymmetric Longitudinal waves in a bi-material compound solid cylinder made of viscoelastic materials", CMC: Comput. Mater. Continua, 51(2), 105-143. https://doi.org/10.3970/cmc.2016.051.105.pdf.
  11. Akbarov, S.D., Kocal, T. and Kepceler, T. (2016b), "On the dispersion of the axisymmetric longitudinal wave propagating in a bi-layered hollow cylinder made of viscoelastic materials", Int. J. Solid. Struct., 100-101(1), 195-210. https://doi.org/10.1016/j.ijsolstr.2016.08.016.
  12. Astaneh, A.V. and Guddati, M.N. (2017), "Dispersion analysis of composite acousto-elastic waveguides", Compos. Part B: Eng., 130, 200-216. https://doi.org/10.1016/j.compositesb.2017.07.040.
  13. Bagno, A.M. (1997), "Elastic waves in prestressed bodies interacting with a fluid (Survey)", Int. Appl. Mech., 33(6), 435-63. https://doi.org/10.1007/BF02700652.
  14. Bagno, A.M. (2015), "The dispersion spectrum of a wave process in a system consisting of an ideal fluid layer and a compressible elastic layer", Int. Appl. Mech., 51(6), 648-653. https://doi.org/10.1007/s10778-015-0721-7.
  15. Bagno, A.M. (2016), "Wave propagation in an elastic layer interacting with a viscous liquid layer", Int. Appl. Mech., 52(2), 133-139. https://doi.org/10.1007/s10778-016-0740-z.
  16. Bagno, A.M. (2017), "Dispersion properties of Lamb waves in an elastic layer-ideal liquid half-space system", Int. Appl. Mech., 53(6), 609-616. https://doi.org/10.1007/s10778-018-0843-9.
  17. Bagno, A.M. and Guz, A.N. (2016), "Effect of prestresses on the dispersion of waves in a system consisting of a viscous liquid layer and a compressible elastic layer", Int. Appl. Mech., 52(4), 333-341. https://doi.org/10.1007/s10778-016-0756-4.
  18. Bagno, A.M. and Shchuruk, G.I. (1994), "Influence of fluid viscosity on waves in an initially deformed, compressible, elastic layer interacting with a fluid medium", Int. Appl. Mech., 30(9), 643-649. https://doi.org/10.1007/BF00847075.
  19. Banerjee, S. and Kundu, T. (2007), "Ultrasonic field modeling in plates immersed in fluid", Int. J. Solid. Struct., 44(18-19), 6013-6029. https://doi.org/10.1016/j.ijsolstr.2007.02.011.
  20. Barshinger, J.N. and Rose, J.L. (2004), "Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material", IEEE Tran. Ultras. Ferroelec. Frequen. Control, 51(11), 1547-1556. https://doi.org/10.1109/TUFFC.2004.1367496.
  21. Duan, W. and Kirby, R. (2019), "Guided wave propagation in buried and immersed fluid-filled pipes: Application of the semi analytic finite element method", Comput. Struct., 212, 236-247. https://doi.org/10.1016/j.compstruc.2018.10.020.
  22. Guz, A.N. (2009), Dynamics of Compressible Viscous Fluid, Cambridge Scientific Publishers, Cambridge, England.
  23. Guz, A.N. and Bagno, A.M. (2017), "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. https://doi.org/10.1007/s10778-017-0819-1.
  24. Guz, A.N. and Bagno, A.M. (2018), "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. https://doi.org/10.1007/s10778-018-0877-z.
  25. Guz, A.N. and Bagno, A.M. (2019), "Propagation of quasi-lamb waves in an elastic layer interacting with a viscous liquid half-space", Int. Appl. Mech., 55(5), 459-469. https://doi.org/10.1007/s10778-019-00968-w.
  26. Kauffmann, P., Ploix, M.A., Chaix, J.F., Potel, C., Gueudre, C., Corneloup, G. and Baque, F. (2019), "Multi-modal leaky Lamb waves in two parallel and immersed plates: Theoretical considerations, simulations, and measurements", J. Acoust. Soc. Am., 145(2), 1018-1030. https://doi.org/10.1121/1.5091689.
  27. Kiefer, D.A., Ponschab, M., Rupitsch, S.J. and Mayle, M. (2019), "Calculating the full leaky Lamb wave spectrum with exact fluid interaction", J. Acoust. Soc. Am., 145(6), 3341-3350. https://doi.org/10.1121/1.5109399.
  28. Kocal, T. (2020), "The dynamical behavior of the moving viscoelastic plate in contact with viscous fluid with finite depth under action of time-harmonic forces", Ocean Eng., 215, 107840. https://doi.org/10.1016/j.oceaneng.2020.107840.
  29. Neciunas, A., Patasius, M. and Barauskas, R. (2018), "Calculating dispersion relations for waveguide immersed in perfect fluid", Math. Model. Anal., 23(2), 309-326. https://doi.org/10.3846/mma.2018.019.
  30. Negin, M. and Akbarov, S.D. (2019), "On attenuation of the seismic Rayleigh waves propagating in an elastic crustal layer over viscoelastic mantle", J. Earth Syst. Sci., 128(7), 181. https://doi.org/10.1007/s12040-019-1202-x.
  31. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications.
  32. Selvamani, R. and Ponnusamy, P. (2013), "Wave propagation in a generalized thermo elastic circular plate immersed in fluid", Struct. Eng. Mech., 46(6), 827-842. https://doi.org/10.12989/sem.2013.46.6.827.
  33. Sharma, J.N. and Pathania, V. (2003), "Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid", J. Sound Vib., 268(5), 897-916. https://doi.org/10.1016/S0022-460X(02)01639-5.
  34. Shukla, K., Carcione, J.M., Hesthaven, J.S. and L'Heureux, E. (2020), "Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method", J. Acoust. Soc. Am., 147(5), 3136-3150. https://doi.org/10.1121/10.0001170.
  35. Su, Z. and Ye, L. (2004) "Selective generation of Lamb wave modes and their propagation characteristics in defective composite laminates", Proc. Inst. Mech. Eng., Part L: J. Mater.: Des. Appl., 218(2), 95-110. https://doi.org/10.1177/146442070421800204.
  36. Viktorov, I.A. (1967), Rayleigh and Lamb Waves, Physical Theory and Applications, Acoustics Institute, Academy of Science of the USSR, Moscow, Russia.
  37. Yu, L., Tian, Z. and Zhao, L. (2012), "Gas accumulation detection in a water tank using Lamb waves", Smart Mater., Adapt. Struct. Intel. Syst., 45097, 807-815. https://doi.org/10.1115/SMASIS2012-8110.