ZHOU Wei-jian, CHEN Wei-qiu. Surface Effect on Propagation of Surface Waves in a Dielectric Elastomer Half Space Subject to Biasing Fields[J]. Applied Mathematics and Mechanics, 2015, 36(2): 119-127. doi: 10.3879/j.issn.1000-0887.2015.02.001
Citation: ZHOU Wei-jian, CHEN Wei-qiu. Surface Effect on Propagation of Surface Waves in a Dielectric Elastomer Half Space Subject to Biasing Fields[J]. Applied Mathematics and Mechanics, 2015, 36(2): 119-127. doi: 10.3879/j.issn.1000-0887.2015.02.001

Surface Effect on Propagation of Surface Waves in a Dielectric Elastomer Half Space Subject to Biasing Fields

doi: 10.3879/j.issn.1000-0887.2015.02.001
Funds:  The National Natural Science Foundation of China(11272281;11321202)
  • Received Date: 2014-11-20
  • Publish Date: 2015-02-15
  • The thin surface layer model was used to establish the 1st-order equivalent boundary conditions to account for the surface effect of dielectric elastomers. Based on the linear incremental theory of infinitesimal motions superimposed on the finite deformation of an electroelastic body, the equivalent boundary conditions were rigorously derived with the Stroh formula and the Ting method. The Stroh formalism was further used to deduce the governing equations for surface waves involving the surface effect. For compressible Neo-Hookean dielectric elastomers, the dispersion equations for the Love waves and generalized Rayleigh waves were derived and investigated numerically. It is found that the two types of waves are decoupled from each other, as in the classical cases. Different from the classical Rayleigh waves, the generalized Rayleigh waves with surface effect are size-dependent and uniqueness of the Rayleigh wave no longer exists. Numerical results indicate that it is possible to regulate and optimize the surface acoustic wave devices through application of appropriate biasing fields.
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  • [1]
    Mindlin R D. High frequency vibrations of plated, crystal plates[C]//Breuer S, Budiansky B, Demir H, Drucker D C, Alexander J M eds.Progress in Applied Mechanics: The Prager Anniversary Volume.The Macmillan Company, 1963: 73-84.
    [2]
    Tiersten H F. Elastic surface waves guided by thin films[J].Journal of Applied Physics,1969,40(2): 770-789.
    [3]
    Gurtin M E, Murdoch A I. A continuum theory of elastic material surfaces[J].Archive for Rational Mechanics and Analysis,1975,57(4): 291-323.
    [4]
    Rokhlin S I, Wang Y J. Analysis of boundary conditions for elastic wave interaction with an interface between two solids[J].The Journal of the Acoustical Society of America,1991,89(2): 503-515.
    [5]
    Bovik P. On the modelling of thin interface layers in elastic and acoustic scattering problems[J].The Quarterly Journal of Mechanics and Applied Mathematics,1994,47(1): 17-42.
    [6]
    Niklasson A J, Datta S K, Dunn M L. On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions[J].The Journal of the Acoustical Society of America,2000,108(3): 924-933.
    [7]
    Niklasson A J, Datta S K, Dunn M L. On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers[J].The Journal of the Acoustical Society of America,2000,108(5): 2005-2011.
    [8]
    Chen W Q. Surface effect on Bleustein-Gulyaev wave in a piezoelectric half-space[J].Theoretical and Applied Mechanics Letters,2011,1(4): 041001.
    [9]
    Ting T C T. Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies[J].Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science,2007,463(2085): 2223-2239.
    [10]
    Ting T C T. Steady waves in an anisotropic elastic layer attached to a half-space or between two half-spaces—a generalization of Love waves and Stoneley waves[J].Mathematics and Mechanics of Solids,2009,14(1/2): 52-71.
    [11]
    Gurtin M E, Murdoch A I. Effect of surface stress on wave propagation in solids[J].Journal of Applied Physics,2008,47(10): 4414-4421.
    [12]
    Murdoch A I. The effect of interfacial stress on the propagation of Stoneley waves[J].Journal of Sound and Vibration,1977,50(1): 1-11.
    [13]
    Murdoch A I. The propagation of surface waves in bodies with material boundaries[J].Journal of the Mechanics and Physics of Solids,1976,24(2): 137-146.
    [14]
    Chuang M Y. Green’s function for an anisotropic piezoelectric half-space bonded to a thin piezoelectric layer[J].Archives of Mechanics,2014,66(1): 3-17.
    [15]
    Dorfmann A, Ogden R W. Nonlinear electroelastostatics: incremental equations and stability[J].International Journal of Engineering Science,2010,48(1): 1-14.
    [16]
    Stroh A N. Dislocations and cracks in anisotropic elasticity[J].Philosophical Magazine,1958,3(30): 625-646.
    [17]
    Stroh A N. Steady state problems in anisotropic elasticity[J].Journal of Mathematical Physics,1962,41(2): 77-103.
    [18]
    Barnett D M, Lothe J. Free surface (Rayleigh) waves in anisotropic elastic half-spaces: the surface impedance method[J].Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences,1985,402(1822): 135-152.
    [19]
    Lothe J, Barnett D M. Existence of surface wave solutions for anisotropic elastic half-spaces with free surface[J].Journal of Applied Physics,1976,47(3): 428-433.
    [20]
    Lothe J, Barnett D M. Integral formalism for surface waves in piezoelectric crystals. Existence considerations[J].Journal of Applied Physics,1976,47(5): 1799-1807.
    [21]
    Ting T C T.Anisotropic Elasticity: Theory and Applications [M]. Oxford University Press, 1996.
    [22]
    Li W Y, Landis C M. Deformation and instabilities in dielectric elastomer composites[J].Smart Materials and Structures,2012,21(9): 094006.
    [23]
    Holzapfel G A.Nonlinear Solid Mechanics: A Continuum Approach for Engineering [M]. Wiley, 2000.
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