206
Views
1
CrossRef citations to date
0
Altmetric
Section B

Computing Green's function of the initial-boundary value problem for the wave equation in a layered cylinder

&
Pages 2514-2534 | Received 15 May 2013, Accepted 03 Dec 2013, Published online: 22 May 2014

References

  • A.I. Abreu, J.A.M. Carrer, and W.J. Mansur, Scalar wave propagation in 2D: A BEM formulation based on the operational quadrature method, Eng. Anal. Bound. Elem. 27 (2003), pp. 101–105. doi: 10.1016/S0955-7997(02)00087-5
  • E.L. Albuquerque, P. Sollero, and M.H. Aliabadi, The boundary element method applied to time dependent problems in anisotropic materials, Int. J. Solids. Struct. 39 (2002), pp. 1405–1422. doi: 10.1016/S0020-7683(01)00173-1
  • G.A. Athanassoulis and K.A. Belibassakis, Coupled made and finite element approximations of underwater sound propagation problems in general stratified environments, J. Comput. Acoust. 16 (2008), pp. 83–116. doi: 10.1142/S0218396X08003506
  • D.E. Beskos, Boundary element methods in dynamic analysis, Appl. Mech. Rev. 40 (1987), pp. 1–23. doi: 10.1115/1.3149529
  • D.E. Beskos, Boundary element methods in dynamic analysis Part II, Appl. Mech. Rev. 50 (1997), pp. 149–197. doi: 10.1115/1.3101695
  • M. Bonnet, Boundary Integral Equation Methods for Solids and Fluids, John Wiley and Sons, New York, 1995.
  • M. Bouchon, A simple method to calculate Green's function for elastic layered media, Bull. Seismol. Soc. Am. 71 (1981), pp. 959–979.
  • J.W. Brown and R.V. Churchill, Fourier Series and Boundary Value Problems, McGraw-Hill, New York, 1993.
  • D. Courant and D. Hilbert, Methods of Mathematical Physics, Wiley-Interscience, New York, 1953.
  • K.M. EL-Morabie and M.A. Sumbatyan, Detection of a single elliptic-shape buried object in stratified elastic media: Anti-plane problem, Eur. J. Mech. A/Solids 37 (2013), pp. 1–7. doi: 10.1016/j.euromechsol.2012.04.003
  • S. Faydaoglu and G.Sh. Guseinov, An expansion result for a Sturm-Liouville eigenvalue problem with impulse, Turk. J. Math. 34 (2010), pp. 355–366.
  • G.B. Folland, Fourier Analysis and Its Applications, Wadsworth & Brooks/Cole, Pacific Grove, California, 1992.
  • N.A. Kampanis and V.A. Dougalis, A finite element code for the numerical solution of the Helmholtz equation in axially symmetric waveguides with interfaces, J. Comput. Acoust. 7 (1999), pp. 83–110. doi: 10.1142/S0218396X99000084
  • A.L. Karchevsky, Reconstruction of pressure velocities and boundaries of thin layers in thinly-stratified layers, J. Inverse ILL-Posed Probl. 18 (2010), pp. 371–388. doi: 10.1515/jiip.2010.015
  • J.T. Katsikadelis and A.J. Yiotis, The BEM for plates of variable thickness on nonlinear biparametric elastic foundation: An analog equation solution, J. Eng. Math. 46 (2003), pp. 313–330. doi: 10.1023/A:1025074231624
  • S. Kobayashi and N. Nishimura, Green's Tensor for Elastic Half Space- An Application of Boundary Integral Equation Method, Kyoto University Press, Japan, 1980.
  • N. Kurt, M. Sezer, A. Celik, Solution of Dirichlet problem for a rectangular region in terms of elliptic functions Int. J. Comput. Math. 81 (2004), pp. 1417–1426. doi: 10.1080/0020716042000261441
  • W.J. Mansur, A time-stepping technique to solve wave propagation problems using the boundary element method, Ph.D. diss., University of Southampton, England, 1983.
  • W.J. Mansur and C.A. Brebbia, Formulation of the boundary element method for transient problems governed by the scalar wave equation, Appl. Math. Model. 6 (1982), pp. 307–311. doi: 10.1016/S0307-904X(82)80039-5
  • D.A. Mitsoudis, N.A. Kampanis, and V.A. Dougalis, Finite element discretization of the Helmholtz equation in an underwater acoustic waveguide, in Effective Computational Methods in Wave Propagation, N.A. Kampanis, V.A. Dougalis, and J.A. Ekaterinaris, eds., Numerical Insights Series, CRC Press/ Taylor and Francis, New York, 2008, pp. 113–134.
  • P.M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, 1953.
  • A.H. Nayfeh, Wave Propagation in Layered Anisotropic Media with Applications to Composites, Elsevier Science B.V., Netherlands, 1995.
  • M.N. Ozisik, Heat Conduction, John Wiley and Sons, New York, 1980.
  • J.S. Papadakis, V.A. Dougalis, N.A. Kampanis, E.T. Flouri, B. Pelloni, L. Bjorno, Z. Dong, A. Plaisant, and E. Noutary, Ocean acoustic models for low frequency propagation in 2D and 3D environments, Acta Acust. 84 (1998), pp. 1031–1041.
  • C. Perez-Arancibia and M. Duran, On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide, J. Comput. Appl. Math. 235 (2010), pp. 244–262. doi: 10.1016/j.cam.2010.05.053
  • M.A. Sales and L.J. Gray, Evaluation of the anisotropic Green's function and its derivatives, Comput. Struct. 69 (1998), pp. 247–254. doi: 10.1016/S0045-7949(97)00115-6
  • B. Sjogreen and N.A. Petersson, Perfectly matched layers for Maxwell's equations in second order formulation, J. Comput. Phys. 209 (2005), pp. 19–46. doi: 10.1016/j.jcp.2005.03.011
  • F. Sturm and N.A. Kampanis, Accurate treatment of a general sloping interface in a finite element 3D narrow-angle pe model, J. Comput. Acoust. 15 (2007), pp. 285–318. doi: 10.1142/S0218396X07003366
  • A. Tan, S. Hirose, Ch. Zhang, and C.Y. Wang, A 2D time-domain BEM for transient wave scattering analysis by a crack in anisotropic solids, Eng. Anal. Bound. Elem. 29 (2005), pp. 610–623. doi: 10.1016/j.enganabound.2005.01.012
  • V.K. Tewary, Computationally efficient representation for elastodynamic and elastostatic Green's functions for anisotropic solids Phys. Rev. B 51 (1995), pp. 15695–15702. doi: 10.1103/PhysRevB.51.15695
  • G.P. Tolstov, Fourier Series, Dover Publications Inc., New York, 1962.
  • F. Tonon, E. Pan, and B. Amadei, Green's functions and boundary element method formulation for 3D anisotropic media, Comput. Struct. 79 (2001) pp. 469–482. doi: 10.1016/S0045-7949(00)00163-2
  • V.S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker, New York, 1971.
  • C.Y. Wang, J.D. Achenbach, and S. Hirose Elastodynamic fundamental solutions for anisotropic solids, Geophys. J. Int. 118 (1994), pp. 384–392. doi: 10.1111/j.1365-246X.1994.tb03970.x
  • C.Y. Wang, J.D. Achenbach, and S. Hirose, Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy, Int. J. Solids. Struct. 33 (1996), pp. 3843–3864. doi: 10.1016/0020-7683(95)00217-0
  • K. Watanabe and R.G. Payton, Green's function for SH-waves in a cylindrically monoclinic material, J. Mech. Phys. Solids 50 (2002), pp. 2425–2439. doi: 10.1016/S0022-5096(02)00026-1
  • K. Watanabe and R.G. Payton, Green's function for torsional waves in a cylindrically monoclinic material, Int. J. Eng. Sci. 43 (2005), pp. 1283–1291. doi: 10.1016/j.ijengsci.2005.05.005
  • V.G. Yakhno, Computing and simulation of time-dependent electromagnetic fields in homogeneous anisotropic materials, Int. J. Eng. Sci. 46(5) (2008), pp. 411–426. doi: 10.1016/j.ijengsci.2007.12.005
  • V.G. Yakhno, Computation of dyadic Green's functions for electrodynamics in quasi-static approximation with tensor conductivity, CMC-Comput. Mater. Con. 21 (2011), pp. 1–15.
  • V.G. Yakhno and V.A. Feofanova, Elastic parameters of a laminar mass, Sov. Min. Sci. 26 (1990), pp. 493–500. doi: 10.1007/BF02499444
  • V.G. Yakhno and D. Ozdek, Computation of the time-dependent Green's function for the longitudinal vibration of multi-step rod, CMES-Comp. Model. Eng. 85 (2012), pp. 157–176.
  • V.G. Yakhno and D. Ozdek, The time-dependent Green function of the transverse vibration of a composite rectangular membrane, CMC-Comput. Mater. Con. 33 (2013), pp. 155–173.
  • V.G. Yakhno and H.C. Yaslan Computation of the time-dependent fundamental solution for equations of elastodynamics in general anisotropic media, Comput. Struct. 89 (2011), pp. 646–655. doi: 10.1016/j.compstruc.2011.01.009
  • V.G. Yakhno and H.C. Yaslan, Approximate fundamental solutions and wave fronts for general anisotropic materials, Int. J. Solids Struct. 49 (2012), pp. 853–864. doi: 10.1016/j.ijsolstr.2011.12.010
  • P.S. Yang, S.W. Liu, and J.C. Sung, Transient response of SH waves in a layered half-space with sub-surface and interface cracks, Appl. Math. Model. 32 (2008), pp. 595–609. doi: 10.1016/j.apm.2007.01.006
  • E.C. Zachmanoglu and D.W. Thoe, Introduction to Partial Differential Equations with Applications, Dover Publications Inc., New York, 1986.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.