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On One Application of the Approach Developed in Chapter 3 on the Dynamics of Pre-strained Hydro-elastic Systems

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Abstract

In the present chapter, according to a paper by Akbarov and Ismailov (CMES: Comput Model Eng Sci 97(4):359–390, 2014a, Int J Mech, 2014b), we consider the problem related to the forced vibration of the system consisting of the pre-stretched plate made of highly-elastic material and half-plane filled by barotropic compressible Newtonian viscous fluid. It is assumed that this forced vibration is caused by the lineal located time-harmonic force acting on the free face plane of the plate. The problem is solved by employing the approach developed in Chap. 3 for the study of the Lamb’s problems for the bi-material pre-strained elastic systems.

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References

  • Akbarov SD (2013) Stability loss and buckling delamination: three-Dimensional linearized approach for elastic and viscoelastic composites. Springer, Berlin

    Book  Google Scholar 

  • Akbarov SD, Guz AN (2000) Mechanics of curved composites. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Akbarov SD, Ismailov MI (2014a) Forced vibrations of a system consisting of a pre-strained highly elastic plate under compressible viscous fluid loading. CMES: Comput Model Eng Sci 97(4):359–390

    Google Scholar 

  • Akbarov SD, Ismailov MI (2014b) Frequency response of a viscoelastic plate under compressible viscous fluid. Int J Mech 8:332–344

    Google Scholar 

  • Bagno AM, Guz AN (1997) Elastic waves in prestressed bodies interacting with fluid (Survey). Int Appl Mech 33(6):435–465

    Article  MathSciNet  Google Scholar 

  • Bagno AM, Guz AN, Shchuruk GI (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

    Article  Google Scholar 

  • Biot MA (1965) Mechanics of incremental deformations. Wiley, New York

    Google Scholar 

  • Charman CJ, Sorokin SV (2005) The forced vibration of an elastic plate under significant fluid loading. J Sound Vib 281:719–741

    Article  Google Scholar 

  • Fu Y, Price W (1987) Interactions between a partially or totally immersed vibrating cantilever plate and surrounding fluid. J Sound Vib 118:495–513

    Article  Google Scholar 

  • Fung YC (1965) Introduction to solid mechanics. Prentice-Hall, New York

    Google Scholar 

  • Guz AN (2004) Elastic waves in bodies with initial (residual) stresses. A.S.K., Kiev (in Russian)

    Google Scholar 

  • Guz AN (2009) Dynamics of compressible viscous fluid. Cambridge Scientific Publishers, Cambridge

    Google Scholar 

  • Jensen FB, Kuperman WA, Porter MB, Schmidt H (2011) Computational Ocean Acoustic. Springer, Berlin

    Google Scholar 

  • Kwak H, Kim K (1991) Axisymmetric vibration of circular plates in contact with water. J Sound Vib 146:216–381

    Article  Google Scholar 

  • Lai-Yu LU, Bi-Xing Z, Cheng-Hao W (2006) Experimental and inversion studies on Rayleigh wave considering higher modes. Chin J Geophy 49(4):974–985

    Article  Google Scholar 

  • Lamb H (1904) On the propagation of tremors over the surface of an elastic solid. Philos Trans R Soc London Ser A 203:1–42

    Article  Google Scholar 

  • Lamb H (1921) Axisymmetric vibration of circular plates in contact with water. Proc R Soc (London) A 98:205–216

    Article  Google Scholar 

  • Rabotnov YuR (1980) Elements of hereditary mechanics of solid bodies. Mir Publishers, Moscow

    Google Scholar 

  • Sorokin SV, Chubinskij AV (2008) On the role of fluid viscosity in wave propagation in elastic plates under heavy fluid loading. J Sound Vib 311:1020–1038

    Article  Google Scholar 

  • Tsang L (1978) Time-harmonic solution of the elastic head wave problem incorporating the influence of Rayleigh poles. J Acous Soc Am 65(5):1302–1309

    Article  MathSciNet  Google Scholar 

  • Tubaldi E, Armabili M (2013) Vibrations and stability of a periodically supported rectangular plate immersed in axial flow. J Fluids Struct 39:391–407

    Article  Google Scholar 

  • Zhao J, Yu S (2012) Effect of residual stress on the hydro-elastic vibration on circular diaphragm. World J Mech 2:361–368

    Article  Google Scholar 

Download references

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Correspondence to Surkay D. Akbarov .

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Akbarov, S.D. (2015). On One Application of the Approach Developed in Chapter 3 on the Dynamics of Pre-strained Hydro-elastic Systems . In: Dynamics of Pre-Strained Bi-Material Elastic Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-14460-3_8

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  • DOI: https://doi.org/10.1007/978-3-319-14460-3_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14459-7

  • Online ISBN: 978-3-319-14460-3

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