Coupled systems mechanics

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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

  • Akbarov, Surkay D. (Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus) ;
  • Ismailov, Meftun I. (Nachicivan State University, Faculty of Mathematics) ;
  • Aliyev, Soltan A. (Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus)
  • Received : 2017.08.15
  • Accepted : 2017.10.07
  • Published : 2017.12.25
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Abstract

The hydro-elastic system consisting of a pre-stretched highly elastic plate, compressible Newtonian viscous fluid, and the rigid wall is considered and it is assumed that on the plate a lineal-located time-harmonic force acts. It is required to investigate the dynamic behavior of this system and determine how the problem parameters and especially the pre-straining of the plate acts on this behavior. The elasticity relations of the plate are described through the harmonic potential and linearized (with respect to perturbations caused by external time-harmonic force) form of these relations is used in the present investigation. The plane-strain state in the plate is considered and the motion of that is described within the scope of the three-dimensional linearized equations of elastic waves in elastic bodies with initial stresses. The motion of the fluid is described by the linearized Navier-Stokes equations and it is considered the plane-parallel flow of this fluid. The Fourier transform with respect to the space coordinate is applied for a solution to the corresponding boundary-value problem. Numerical results on the frequency response of the interface normal stress and normal velocity and the influence of the initial stretching of the plate on this response are presented and discussed. In particular, it is established that the initial stretching of the plate can decrease significantly the absolute values of the aforementioned quantities.

Keywords

References

  1. Akbarov, S.D. and Ismailov, M.I. (2016a), "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
  2. Akbarov, S.D. and Ismailov, M.I. (2016b), "Frequency response of a pre-stressed metal elastic plate under compressible viscous fluid loading", Appl. Comput. Math., 15(2), 172-188.
  3. Akbarov, S.D. (2015), Dynamics of Pre-Strained Bi-Material Systems: Linearized Three-Dimensional Approach, Springer.
  4. Akbarov, S.D. and Ismailov, M.I. (2015), "Dynamics of the moving load acting on the hydro-elastic system consisting of the elastic plate, compressible viscous pluid and rigid wall", Comput. Mater. Cont., 45(2), 75-10.
  5. 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. Vibr. Contr., 23(11), 1809-1827. https://doi.org/10.1177/1077546315601299
  6. Akbarov, S.D. and Ismailov, M.I., (2014), "Forced vibration of a system consisting of a pre- strained highly elastic plate under compressible viscous fluid loading", Comput. Model. Eng. Sci., 97(4), 359-390.
  7. Akbarov, S.D. and Panakhli, P.G. (2015), "On the discrete-analytical solution method of the problems related to the dynamics of hydro-elastic systems consisting of a pre-strained moving elastic plate, compressible viscous fluid and rigid wall", Comput. Model. Eng. Sci., 108(2), 89-112.
  8. Akbarov, S.D. and Panakhli, P.G. (2017), "On the particularities of the forced vibration of the hydroelastic system consisting of a moving elastic plate, compressible viscous fluid and rigid wall", Coupled Syst. Mech., 6(3), 287-316. https://doi.org/10.12989/CSM.2017.6.3.287
  9. Amabili, M. (2001), "Vibration of circular plates resting on a sloshing liquid: solution of the fully coupled problem", J. Sound Vibr., 245(2), 267-283.
  10. Amabili, M. and Kwak, M.K. (1999), "Vibration of circular plates on a free fluid surface: Effect of surface waves", J. Sound Vibr., 226(3), 407-424. https://doi.org/10.1006/jsvi.1998.2304
  11. Askari, E., Jeong, K.H. and Amabili, M. (2013), "Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface", J. Sound Vibr., 332, 3064-3085. https://doi.org/10.1016/j.jsv.2013.01.007
  12. Askari, E. and Daneshmand, F. (2010), "Coupled vibrations of cantilever cylindrical shells partially submerged in fluids with continuous, simply connectec and non-convex domain", J. Sound Vibr., 329, 3520-3536. https://doi.org/10.1016/j.jsv.2010.02.027
  13. Askari, E. and Daneshmand, F. (2010), "Free vibration of an elastic bottom plate of a partially fluid-filled cylindrical container with an internal body", Eur. J. Mech. A/Sol., 29, 68-80. https://doi.org/10.1016/j.euromechsol.2009.05.005
  14. Askari, E. and Jeong, K.H. (2010), "Hydroelastic vibration of a cantilever cylindrical shell partially submerged in a liquid", Ocean Eng., 37, 1027-1035. https://doi.org/10.1016/j.oceaneng.2010.03.016
  15. Askari, E., Daneshmand, F. and Amibili, M. (2011), "Coupled vibrations of a partially fluid-filled cylindrical container with an internal body including the effect of free surface waves", J. Flu. Struct., 27, 1049-1067. https://doi.org/10.1016/j.jfluidstructs.2011.04.010
  16. Bagno, A.M. (2015), "The dispersion spectrum of wave process in a system consisting of an ideal fluid layer and compressible elastic layer", Int. Appl. Mech., 51(6), 52-60.
  17. Bagno, A.M. and Guz, A.N. (1997), "Elastic waves in prestressed bodies interacting with fluid (survey)", Int. Appl. Mech., 33(6), 435-465. https://doi.org/10.1007/BF02700652
  18. Bagno, A.M., Guz, A.N. 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. Bauer, H.F. and Chiba, M. (2007), "Viscous oscillations in a circular cylindrical tank with elastic surface cover", J. Sound Vibr., 304, 1-17. https://doi.org/10.1016/j.jsv.2007.01.045
  20. Biot, M.A. (1965), Mechanics of Incremental Deformations,Wiley, New York, U.S.A.
  21. Charman, C.J. and Sorokin, S.V. (2005), "The forced vibration of an elastic plate under significant fluid loading", J. Sound Vibr., 281, 719-741. https://doi.org/10.1016/j.jsv.2004.02.013
  22. Chiba, M. (1994), "Axisymmetric free hydroelastic vibration of a flexural bottom plate in a cylindrical tank supported on an elastic foundation", J. Sound Vibr., 169, 387-394. https://doi.org/10.1006/jsvi.1994.1024
  23. Fu, F. and Price, W. (1987), "Interactions between a partially or totally immersed vibrating cantilever plate and surrounding fluid", J. Sound Vibr., 118(3), 495-513. https://doi.org/10.1016/0022-460X(87)90366-X
  24. Guz, A.N. (2009), Dynamics of Compressible Viscous Fluid, Cambridge Scientific Publishers.
  25. Guz, A.N. and Makhort, F.G. (2000), "The physical fundamentals of the ultrasonic nondestructive stress analysis of solids", Int. Appl. Mech., 36, 1119-1148. https://doi.org/10.1023/A:1009442132064
  26. Guz, A.N. (2004), Elastic Waves in Bodies with Initial (Residual) Stresses, A.C.K., Kiev.
  27. Hashemi, H.S., Karimi, M. and Taher, H.R.D. (2010), "Vibration analysis of rectangular mindlin plates on elastic foundations and vertically in contact with stationary fluid by the ritz method", Ocean Eng., 37, 174-185. https://doi.org/10.1016/j.oceaneng.2009.12.001
  28. Hasheminejad, S.M. and Mohammadi, M.M. (2017), "Hydroelastic response suppression of a flexural circular bottom plate resting on Pasternak foundation", Acta Mech.
  29. Jensen, F.B., Kuperman, W.A., Porter, M.B. and Schmidt, H. (2011), Computational Ocean Acoustic, 2nd Edition, Springer, Berlin.
  30. Jeong, K.H. (2003), "Free vibration of two identical circular plates coupled with bounded fluid", J. Sound Vibr., 260, 653-670. https://doi.org/10.1016/S0022-460X(02)01012-X
  31. Kutlu, A., Ugurlu, B., Omurtag, M.H. and Ergin, A. (2012), "Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid", Ocean Eng., 42, 112-125. https://doi.org/10.1016/j.oceaneng.2012.01.010
  32. Kwak, H. and Kim, K. (1991), "Axisymmetric vibration of circular plates in contact with water", J. Sound Vibr., 146, 381-216. https://doi.org/10.1016/0022-460X(91)90696-H
  33. Lai-Yu, L.U., Bi-Xing, Z. and Cheng-Hao, W. (2006), "Experimental and inversion studies on rayleigh wave considering higher modes", Chin. J. Geophys., 49(4), 974-985. https://doi.org/10.1002/cjg2.919
  34. Lamb, H. (1921), "Axisymmetric vibration of circular plates in contact with water", Proceedings of the Royal Society, London, U.K.
  35. Liao, C.Y. and Ma, C.C. (2016), "Vibration characteristics of rectangular plate in compressible inviscid fluid", J. Sound Vibr., 362, 228-251. https://doi.org/10.1016/j.jsv.2015.09.031
  36. Moshkelgosha, E., Askari, E. and Jeong, K.H. (2017), "Fluid-structure coupling of concentric double FGM shells with different lengths", Struct. Eng. Mech., 61(2), 231-244. https://doi.org/10.12989/sem.2017.61.2.231
  37. Shafiee, A.A., Daneshmand, F., Askari, E. and Mahzoon, M. (2014), "Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid", Struct. Eng. Mech., 50(1), 53-71. https://doi.org/10.12989/sem.2014.50.1.053
  38. Sorokin, S.V. and Chubinskij, A.V. (2008), "On the role of fluid viscosity in wave propagation in elastic plates under heavy fluid loading", J. Sound Vibr., 311, 1020-1038. https://doi.org/10.1016/j.jsv.2007.10.001
  39. Sun, Y., Pan, J. and Yang, T. (2015), "Effect of a layer on the sound radiation of a plate and its active control", J. Sound Vibr., 357, 269-284. https://doi.org/10.1016/j.jsv.2015.07.016
  40. Truesdell, C. and Noll, W. (1965), The Nonlinear Field Theories of Mechanics, Springer, Berlin, New York, U.S.A.
  41. Tsang, L. (1978), "Time-harmonic solution of the elastic head wave problem incorporating the influence of rayleigh poles", J. Acoust. Soc. Am., 65(5), 1302-1309.
  42. Tubaldi, E. and Armabili, M. (2013), "Vibrations and stability of a periodically supported rectangular plate immersed in axial flow", J. Flu. Struct., 39, 391-407. https://doi.org/10.1016/j.jfluidstructs.2013.03.003
  43. Zhao, J. and Yu, S. (2012), "Effect of residual stress on the hydro-elastic vibration on circular diaphragm", World J. Mech., 2, 361-368. https://doi.org/10.4236/wjm.2012.26041