HU Yang-fan, WANG Biao. Solution of the Two Dimensional Scattering Problem in Piezoelectric/Piezomagnetic Media by Polarization Method[J]. Applied Mathematics and Mechanics, 2008, 29(12): 1395-1410.
Citation: HU Yang-fan, WANG Biao. Solution of the Two Dimensional Scattering Problem in Piezoelectric/Piezomagnetic Media by Polarization Method[J]. Applied Mathematics and Mechanics, 2008, 29(12): 1395-1410.

Solution of the Two Dimensional Scattering Problem in Piezoelectric/Piezomagnetic Media by Polarization Method

  • Received Date: 2008-09-03
  • Rev Recd Date: 2008-09-18
  • Publish Date: 2008-12-15
  • Using the polarization method,the scattering problem for a two dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated.To achieve the purpose,the polarization method for two-dimensional piezoelectric/piezomagnetic "comparison body" was formulated for the first time.For simple harmonic motion,the kernel of the polarization method reduces to the 2-D time-harmonic Green's function, which is deduced using the Radon transform.The formalism was further simplified under certain conditions(low frequency of the incident wave and small diameter of the inclusion),where some explicit analytical expressions were obtained.The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites were given first,followed by simplified results for piezoelectric composites.Based on the latter results,two numerical results were provided for an elliptical cylindrical inclusion in a PZT-5H-matrices,illustrating the effect of different factors(including size effect,shape effect,effect of the material properties,and piezoelectric effect) on the scattering cross-section.
  • loading
  • [1]
    Pao Y H, Mow C-C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Russak,Crane, 1973.
    [2]
    Auld B A.Acoustic Fields and Waves[M].Vols 1 & 2,New York:John & Wiley, 1973.
    [3]
    Barnett D M.Bulk, surface, and interfacial waves in anisotropic linear elastic solids[J].International Journal of Solids and Structures,2000,37(1/2):45-54. doi: 10.1016/S0020-7683(99)00076-1
    [4]
    Stroh A N. Steady state problems in anisotropic elasticity[J].Journal of Mathematical Physics,1962,41(1):77-103.
    [5]
    Wu K C. Extension of Stroh's formalism to self-similar problems in two-dimensional elastodynamics[J].Proc R Soc London A,2000,456(1996):869-890. doi: 10.1098/rspa.2000.0540
    [6]
    Willis J R. A polarization approach to the scattering of elastic waves—scattering by a single inclusion[J].J Mech Phys Solids,1980,28(5/6):287-305. doi: 10.1016/0022-5096(80)90021-6
    [7]
    Ma H, Wang B. The scattering of electroelastic waves by an ellipsoidal inclusion in piezoelectric medium[J].International Journal of Solids and Structures,2005,42(16/17):4541-4554. doi: 10.1016/j.ijsolstr.2005.01.013
    [8]
    Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion, and related problems[J].Proc R Soc London A,1957,241(1226): 376-396. doi: 10.1098/rspa.1957.0133
    [9]
    Barnett D M, Lothe J. Dislocation and line charges in anisotropic piezoelectric insulators[J].Phys Status Solids, B,1975,67(1):105-111. doi: 10.1002/pssb.2220670108
    [10]
    Pan E, Tonon F. Three-dimensional Green’s functions in anisotropic piezoelectric solids[J].International Journal of Solids and Structures,2000,37(6):943-958. doi: 10.1016/S0020-7683(99)00073-6
    [11]
    Wang C Y.Achenbach J D.Three-dimensional time-harmonic elastodynamic Green’s functions for anisotropic solids[J].Proc R Soc London A,1995,449(1937):441-458. doi: 10.1098/rspa.1995.0052
    [12]
    Helgason S.The Radon Transform[M]. Boston: Birkhauser,1980.
    [13]
    Li X Y, Wang M Z. Three-dimensional Green’s functions for infinite anisotropic piezoelectric media[J].International Journal of Solids and Structures,2007,44(5):1680-1684. doi: 10.1016/j.ijsolstr.2006.06.021
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2746) PDF downloads(640) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return