مروری بر تحلیل انتشار موج SH در عوارض توپوگرافی اورتوتروپ

نوع مقاله : مقاله مروری

نویسندگان

1 دانشجوی دکتری، گروه مهندسی عمران، واحد زنجان، دانشگاه آزاد اسلامی، زنجان، ایران.

2 استادیار، گروه مهندسی عمران، واحد زنجان، دانشگاه آزاد اسلامی، زنجان، ایران.

3 استاد، پژوهشکده‌ی مهندسی ژئوتکنیک، پژوهشگاه بین‌المللی زلزله‌شناسی و مهندسی زلزله، تهران، ایران.

چکیده

در این مقاله، پیشینه‌ی تحقیق حاکم بر انتشار موج مهاجم برون صفحه‌ی SH در یک محیط الاستیک خطی ناهمسان اورتوتروپ با تکیه بر عوارض توپوگرافی به عنوان مطالعه‌ی موردی پرداخته شده است. ضمن اشاره‌ی مختصر به مبانی الاستیسیته‌ی مصالح ناهمسان و معادله‌ی موج اسکالر، در ادامه ادبیّات فنّی توابع گرین مستخرج در حل مسأله مزبور ارائه شده است. با تقسیم‌بندی رویکردهای تحلیل مسأله به سه دسته روش تحلیلی، نیمه‌تحلیلی و عددی، مطالعات مربوطه در هر دسته طبقه‌بندی و به ترتیب توسعه معرفی شده است. به لحاظ تناسب و گسترش روش اجزای مرزی در تحلیل مسائل انتشار موج به ویژه عوارض توپوگرافی، این روش براساس دو فرآیند فرمول‌بندی محیط کامل و نیم‌فضا تمییز شده و ادبیّات منوط به تفکیک در دو محیط ایزوتروپ و اورتوتروپ بسط داده شده است. این نوشته به عنوان نقطه‌ی آغازین به کلیه‌ی محققان و پژوهشگران علاقه‌مند به حوزه‌ی تحلیل لرزه‌ای ساختگاه همسان و ناهمسان پیشنهاد می‌شود.

کلیدواژه‌ها

موضوعات

مراجع

  1. Aki, K. (1988) Local site effects and strong ground motion. In: Proceedings of the Special Conference on Earthquake Engineering and Soil Dynamics 2. Soc. Civil Eng. Park City, UT.
  2. Li, Y.G. (1988) Seismic Wave Propagation in Anisotropic Media with Applications to Denning Fractures in the Earth [Dissertation]. Uni. Southern California.
  3. Babuska, V., Cara, M. (1991) Seismic Anisotropy in the Earth. Kluwer Academic Pub, Dordrecht,

 

  1. Love, A.E.H. (1934) A Treatise of the Mathematical Theory of Elasticity. 4th ed, Cambridge Uni. Press, London.
  2. Hearmon, R.F.S. (1961) An Introduction to Applied Anisotropic Elasticity. Oxford Uni Press, London.
  3. Lekhnitskii, S.G. (1981) Theory of Elasticity of an Anisotropic Elastic Body. Mir Pub, Moscow.
  4. Ting, T.C.T. (1996) Anisotropic Elasticity, Theory and Applications. Oxford Uni. Press, New York.
  5. Swanson, S.R. (1997) Introduction to Design and Analysis with Advanced Composite Materials, Prentice Hall, Upper Saddle River, NJ.
  6. Jones, R.M. (1998) Mechanics of Composite Materials. Taylor & Francis, New York.
  7. Sadd, M.H. (2005) Elasticity: Theory, Applications and Numerics. 10.1016/B978-0-12-374446-3.X0001-6.
  8. Nayfeh, A.H. (1995) Wave Propagation in Layered Anisotropic Media. Elsevier, Amsterdam.
  9. Zheng, Q.S. and Spencer, A.J.M. (1993) Tensors which characterize anisotropes. J. Eng. Sci., 31, 679-693.
  10. Cowin, S.C. and Mehrabadi, M.M. (1995) Anisotropic symmetries of linear elasticity. Mech. Rev., ASME, 48, 247-285.
  11. Kausel, E. (2006) Fundamental Solutions in Elastodynamics. Cambridge University Press, 9780511546112. Massachusetts Institute of Technology. 10.1017/CBO9780511546112.
  12. Zheng, T., Dravinski, M. (1998) Amplification of SH-waves by an orthotropic basin. Eng. Struct. Dyn., 27, 243-257.
  13. Dineva, P., Manolis, G., Rangelov, T., and Wuttke, F. (2014) SH-wave scattering in the orthotropic half-plane weakened by cavities using BIEM. Acta Acustica united Acustica, 100, 266-276.
  14. Eringen, A.C. and Suhubi, E.S. (1975) Elastodynamics. Academic Press.
  15. Stokes, G.G. (1849) On the dynamical theory of diffraction. Camb. Phil. Soc., 9, 1-62.
  16. Benjumea, R. and Sikarskie, D.L. (1972) On the solution of plane orthotropic elasticity problems by an integral method. Appl. Mech., 39(3), 801-808.
  17. Rubio-Gonzalez, C. and Manzon, J.J. (1999) Response of finite cracks in orthotropic materials due to concentrated impact shear load. Appli. Mech., 66, 485-491.
  18. Watanabe, K. and Payton, G.R. (2001) Source of a time‐harmonic SH-wave in a cylindrically orthotropic elastic solid. Geophys J. Int., 145, 709-713.
  19. Chiang C.R. (2016) Problems of polygonal inclusions in orthotropic materials with due consideration on the stress at corners. Appl. Mech., 86, 769-785.
  20. Chiang, C.R. (2018) Further results on Eshelby’s tensor of an elliptic inclusion in orthotropic materials. Acta Mechanica. 10.1007/s00707-018-2254-8.
  21. Rajapakse, R.K.N.D. and Wang, Y. (1991) Elastodynamic Green’s functions of orthotropic half plane. Eng. Mech., ASCE, 117(3), 588-604.
  22. Panji, M., Kamalian, M., Asgari-Marnani, J., and Jafari, M.K. (2013) Transient analysis of wave propagation problems by half-plane BEM. Geophys J. Int., 194, 1849-1865.
  23. Ke, J. (2012) A new model of orthotropic bodies. Mech. Mater., 204, 4418-4421.
  24. Vinh, P.C., Anh, V.T.N., and Nguyen, N.T.K. (2016) Exact secular equations of Rayleigh waves in an orthotropic elastic half-space overlaid by an orthotropic elastic layer. J. Sol. Struct., 83, 65-72.
  25. Gupta, S., Smita, S., and Pramanik, S. (2017a) Refelction and refraction of SH-waves in an orthotropic layer sandwiched between two distinct dry sandy half-space. Procedia Eng., 173, 1146-1153.
  26. Rajak, B.P. and Kundu, S. (2019) Love wave propagation in a sandy layer under initial stress lying over a pre-stressed heterogeneous orthotropic half-space. AIP Conference Proceedings, 2061(1):020015. 10.1063/1.5086637.
  27. Baksi, A., Das, S., and Bera, R. (2003) Impact response of a cracked orthotropic medium-revisited. J. Eng. Sci., 41, 2063-2079.
  28. Vafa, J. and Fariborz, S. (2016) Transient analysis of multiply interacting cracks in orthotropic layers. J. Mech-A/Sol., 60, 254-276.
  29. Selivanov, M. (2019) An edge crack with cohesive zone in the orthotropic body. Reports of the National Acad. Sci. Ukraine, 6, 25-34.
  30. Shimpi, R. and Patel, H. (2006) A two variable refined plate theory for orthotropic plate analysis. J. Sol. Struct., 43, 6783-6799.
  31. Verma, K. (2008) On the wave propagation in layered plates of general anisotropic media. J. Eng. Appl. Sci., 4, 444-450.
  32. An, C., Gu, J., and Su, J. (2016) Exact solution of bending problem of clamped orthotropic rectangular thin plates. Braz. Soc. Mech. Sci. Eng., 38, 601-607.
  33. Aki, K. and Larner, K.L. (1970) Surface motion of a layered medium having an irregular interface due to incident plane SH-waves, Geophys. Res., 75(5), 933- 954.
  34. Varadan, V.K., Varadan, V.V., and Pao, Y.H. (1978) Multiple scattering of elastic waves by cylinders of arbitrary cross section, I, SH-waves. Acoust. Soc. Am., 63, 1310-1319.
  35. Campillo, M. and Bouchon, M. (1985) Synthetic SH-seismograms in a laterally varying medium by the discrete wavenumber method. Geophys, R. Astr. Soc., 83, 307-317.
  36. Chen, J., Liu, Z.X., and Zou, Z.Z. (2002) Transient internal crack problem for a nonhomogeneous orthotropic strip (mode I). J. Eng. Sci., 40, 1761-1774.
  37. Chen, J. and Liu, Z.X. (2005) Transient response of a mode III crack in an orthotropic functionally graded strip. J. Mech-A/Sol., 24, 325-336.
  38. Rangelov, T.V., Manolis, G.D., and Dineva, P.S. (2010) Wave propagation in a restricted class of orthotropic inhomogeneous half-planes. Acta Mechanica, 210, 169-182.
  39. Bagault, C., Nélias, D., and Baietto, M. (2012) Contact analyses for anisotropic half space: effect of the anisotropy on the pressure distribution and contact area. J. Sol. Struct., 134(3), 031401-031409.
  40. Sanchez-Sesma, F.J., Palencia, V.J., and Luzon, F. (2002) Estimation of local site effects during earthquakes: An overview. ISET J. Earthquake Technol., 39(3), 167-193.
  41. Eidel, B. and Gruttmann, F. (2003) Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation. Mater. Sci., 28, 732-742.
  42. Sladek J., Sladek V., Zhang C., Krivacek J., and Wen P. (2006) Analysis of orthotropic thick plates by meshless local Petrov-Galerkin (MLPG) method. J. Numer. Methods Eng., 67, 1830-1850.
  43. Petrolito, J. (2014) Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements. Math. Model, 38, 5858-5869.
  44. Nguyen, M., Nha, N., Bui, T.Q., and Tich, T.T. (2017) A novel numerical approach for fracture analysis in orthotropic media. Tech. Dev. J., 20, 5-13.
  45. Guler, M.A., Kucuksucu, A., Yilmaz, K., and Yildirim, B. (2017) On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium. J. Mech. Sci., 120(C), 12-29.
  46. Gupta, S., Smita, S., and Pramanik, S. (2017b) SH-wave in a multilayered orthotropic crust under initial stress: A finite difference approach. Math., 4(1), 10.1080/23311835.2017.1284294.
  47. Comez, I., Yilmaz, K., Guler, M., and Yildirim, B. (2019) On the plane frictional contact problem of a homogeneous orthotropic layer loaded by a rigid cylindrical stamp. Appl. Mech., 89, 1403-1419.
  48. Lee, J.K., Han Y.B., and Ahn, Y.J. (2015) SH-wave scattering problems for multiple orthotropic elliptical inclusions. Mech. Eng., 5, 1-14.
  49. Lee, J.K., Lee, H., and Jeong, H. (2016) Numerical analysis of SH-wave field calculations for various types of a multilayered anisotropic inclusion. Eng. Analy. BE, 64, 38-67.
  50. Dominguez, J. (1993) Boundary Elements in Dynamics. Comp. Mech. Pub., Southampton, Boston.
  51. Brebbia, C.A. and Dominguez, J. (1989) Boundary Elements an Introductory Course. Comp Mech Pub, Southampton, Boston.
  52. Cruse, T.A. and Rizzo, F.J. (1968) A direct formulation and numerical solution of the general transient elastodynamic problem. Math. Analy. Applic., 22, 244-259.
  53. Manolis, G.D. and Beskos, D.E. (1987) Boundary Element Methods in Elastodynamics. Unwin and Allen, London.
  54. Nardini, D. and Brebbia, C.A. (1982) 'A new approach to free vibration analysis using boundary elements'. In Brebbia, C.A. (Ed): Boundary Element Methods, 312-326, Springer-Verlag, Berlin.
  55. Cheng, A.H.D., Young, D.L., and Tsai, C.C. (2000) Solution of Poisson’s equation by iterative DR-BEM using compactly supported positive definite radial basis functions. Analy. BE, 24, 549-557.
  56. Patridge, P.W., Brebbia, C.A., and Wrobel, L.C. (1992) The Dual Reciprocity Boundary Element Method. Comp. Mech. Pub., Southampton.
  57. Mansur, W.J. and Brebbia, C.A. (1982a) Formulation of the boundary element method for transient problems governed by the Scalar wave equation. Math. Model, 6(4), 307-311.
  58. Mansur, W.J. and Brebbia, C.A. (1982b) Numerical implementation of the boundary element method for two-dimensional transient scalar wave propagation problems. Math. Model, 6(4), 299-306.
  59. Mansur, W.J. (1983) A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method. Ph.D. Dissertation, University of Southampton.
  60. Karabalis, D.L. and Beskos, D.E. (1984) Dynamic response of 3D rigid surface foundations by time-domain boundary element method. Eng. Struct. Dyn., 12, 73-93.
  61. Manolis, G.D. and Beskos, D.E. (1981) Dynamic stress concentration studies by boundary integrals and Laplace transforms. J. Numer. Methods Eng., 17(4), 573-599.
  62. Antes, H. (1985) A boundary elements procedure for transient wave propagation in two-dimensional isotropic elastic media, FEl Analy. Des., 1, 313-322.
  63. Banerjee, P.K., Ahmad, S., and Manolis, G.D. (1986) Transient elastodynamic analysis of 3D problems by boundary element method. Eng. Struct. Dyn., 14, 933-949.
  64. Beskos, D.E. (1987) Boundary element methods in dynamic analysis. Mech. Rev., 40(1), 1-23.
  65. Beskos, D.E. (1997) Boundary element methods in dynamic analysis: Part II (1986-1996). Mech. Rev., 50(3), 149-197.
  66. Schanz, M. and Antes, H. (1997) Application of operational quadrature methods in time domain boundary element methods. Meccanica, 32, 179-186.
  67. Ahmad, S. and Banerjee, P.K. (1988) Multi-domain BEM for two-dimensional problems of elastodynamics. J. Numer. Methods Eng., 26(4), 891-911.
  68. Heymsfield, E. (1997) Infinite domain correction for anti-plane shear waves in a two-dimensional boundary element analysis. J. Numer. Methods Eng., 40, 953-964.
  69. Friedman, M.B. and Shaw, R. (1962) Diffraction of pulses by cylindrical obstacles of arbitrary cross section. Appl.Mech., 29(1), 40-46.
  70. Cole, D.M., Kosloff, D.D., and Minster, J.B. (1978) A numerical boundary integral method for elastodynamics. Seism. Soc. Am., 68, 1331-1357.
  71. Antes, H. and Von Estorff, O. (1988) Seismic response amplification due to topographic influences. 9th World Conference on Earth Eng., Tokyo-Kyoto, 3, 411-416.
  72. Demirel, V. and Wang, S. (1987) An efficient boundary element method for two-dimensional transient wave propagation problems. Math. Modeling, 11(6), 411-416.
  73. Yu, G., Mansur, W.J., Carrer, J.A.M., and Gong, L. (2000) Stability of Galerkin and collocation time-domain boundary element methods as applied to the scalar wave equation. Struct., 74(4), 495-506.
  74. Soares, J.D. and Mansur, W.J. (2009) An efficient time-truncated boundary element formulation applied to the solution of the two-dimensional scalar wave equation. Anal. BE., 33(1), 43-53.
  75. Niwa, Y., Fukui, T., Kato, S., and Fujiki, K. (1980) An application of the integral equation method to two-dimensional elastodynamics. Appl. Mech., 28, 281-290.
  76. Manolis, G.D. (1983) A comparative study on three boundary element method approaches to problems in elastodynamics. J. Numer. Methods Eng., 19, 73-91.
  77. Karabalis, D.L. and Beskos, D.E. (1962) Diffraction of pulses by cylindrical obstacles of arbitrary cross section. Appl. Mech., 29(1), 40-46.
  78. Von Estorff, O., Pais, A.L., and Kausel, E. (1990) Some observations on time domain and frequency-domain boundary elements. J. Numer. Methods Eng., 29, 785-800.
  79. Sladek, V. and Sladek, J. (1992) Time marching analysis of boundary integral equations in two-dimensional elastodynamics. Anal. Bound. Elem., 9, 21-29.
  80. Wang, C.C., Wang, H.C., and Liou, G.S. (1996) Two-dimensional elastodynamic transient analysis by QL timedomain BEM formulation. J. Numer. Methods Eng., 39, 951-958.
  81. Birgisson, B., Siebrits, E., and Peirce, A.P. (1999) Elastodynamic direct boundary element methods with enhanced numerical stability properties. J. Numer. Methods Eng., 46, 871-888.
  82. Israil, A.S.M., Banerjee, P.K., and Wang, H.C. (1992) Time-domain formulations of BEM for two-dimensional, axisymmetric and three-dimensional scalar wave propagation, Chapter III in Advanced Dynamic Analysis by BEM, Eds Banerjee P.K. and Kobayashi S.K. Appl. Sci., London, 75-114.
  83. Banerjee, P.K. (1994) Boundary Element Methods in Engineering. McGraw-Hill Book Co, New York.
  84. Kamalian, M., Gatmiri, B., and Sohrabi-Bidar, A. (2003) On time-domain two-dimensional site response analysis of topographic structures by BEM. Seism. Earthq. Eng., 5(2), 35-45.
  85. Israil, A.S.M. and Banerjee, P.K. (1990) Advanced time-domain formulation of BEM for two-dimensional transient elastodynamics. J. Numer. Methods Eng., 29(7), 1421-1440.
  86. Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., Razmkhah, A., and Gatmiri, B. (2006) Time-domain two-dimensional site response analysis of non-homogeneous topographic structures by a hybrid FE/BE method. Soil Dyn. Earthq. Eng., 26(8), 753-765.
  87. Kamalian, M., Gatmiri, B., Sohrabi-Bidar, A., and Khalaj, A. (2007) Amplification pattern of 2D semi-sine shaped valleys subjected to vertically propagating incident waves. Numer. Methods Eng., 23(10), 871-887.
  88. Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., and Razmkhah, A. (2008a) Seismic response of 2D semi-sines shaped hills to vertically propagating incident waves: Amplification patterns and engineering applications. Spectra, 24(2), 405-430.
  89. Kamalian, M., Sohrabi-Bidar, A., Razmkhah, A., Taghavi, A., and Rahmani, I. (2008b) Considerations on seismic microzonation in areas with two-dimensional hills. Earth Syst. Sci., 117(2), 783-796.
  90. Sohrabi-Bidar, A., Kamalian, M., and Jafari, M.K. (2009) Time-domain BEM for three-dimensional site response analysis of topographic structures. J. Numer. Methods Eng., 79, 1467-1492.
  91. Alielahi, H., Kamalian, M., Marnani, J., Jafari, M.K., and Panji, M. (2013) Applying a time-domain boundary element method for study of seismic ground response in the vicinity of embedded cylindrical cavity. J. Civil Eng. (IJCE), 11, 45-54.
  92. Alielahi, H., Kamalian, M., and Adampira, M. (2015) Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM, Soil Dyn. Earthq. Eng., 71, 63-79.
  93. Alielahi, H., Kamalian, M., and Adampira, M. (2016) A BEM investigation on the influence of underground cavities on the seismic response of canyons. Acta Geotechnica, 11, 391-413.
  94. Alielahi, H. and Adampira, M. (2018) Evaluation of 2D Seismic Site Response due to Hill-Cavity Interaction Using Boundary Element Technique. Earthq. Eng., 22(6), 1137-1167.
  95. Panji, M., Kamalian, M., Asgari-Marnani, J., and Jafari, M.K. (2014a) Analysing seismic convex topographies by a half-plane time-domain BEM. J. Int., 197(1), 591-607.
  96. Panji, M., Kamalian, M., Asgari-Marnani, J., and Jafari, M.K. (2014b) Antiplane seismic response from semi-sine shaped valley above embedded truncated circular cavity: A time-domain half-plane BEM. J. Civil Eng., 12(2-B), 160-173.
  97. Panji, M., Mojtabazadeh-Hasanlouei, S., and Yasemi, F. (2020) A half-plane time-domain BEM for SH-wave scattering by a subsurface inclusion. Geosci., 10.1016/j.cageo.2019. 104342.
  98. Panji, M., Mojtabazadeh-Hasanlouei, S., and Habibivand, M. (2021) Seismic response of the trapezoidal alluvial hill located on a circular cavity: Incident SH-wave. Amirkabir J. Civ. Eng., 53(9), 12-12. 10.22060/ceej.2020.18113.6772.
  99. Panji, M. and Ansari, B. (2017a) Modeling pressure pipe embedded in two-layer soil by a half-plane BEM. and Geotech., 81(C), 360-367.
  100. Panji, M. and Ansari, B. (2017b) Transient SH-wave scattering by the lined tunnels embedded in an elastic half-plane. Analy. BE., 84, 220-230.
  101. Panji, M. and Ansari, B. (2020) Anti-plane seismic ground motion above twin horseshoe-shaped lined tunnels. Infrastruct. Solut., 5, 7.10.1007/s41062-019-0257-5.
  102. Panji, M. and Habibivand, M. (2020) Seismic analysis of semi-sine shaped alluvial hills above subsurface circular cavity. Earthq. Eng. & Eng. Vib., 19(4), 903-917.
  103. Panji, M. and Mojtabazadeh-Hasanlouei, S. (2018) Time-history responses on the surface by regularly distributed enormous embedded cavities: Incident SH-waves. Sci., 31, 1-17.
  104. Panji, M. and Mojtabazadeh-Hasanlouei, S. (2019) Seismic amplification pattern of the ground surface in presence of twin unlined circular tunnels subjected to SH-waves. Transport Infrast. Eng., 5(3), 111-134. 10.22075/jtie.2019.16056.1342.
  105. Panji, M. and Mojtabazadeh-Hasanlouei, S. (2020a) Transient response of irregular surface by periodically distributed semi-sine shaped valleys: Incident SH-waves. Earthq. Tsu., 10.1142/ S1793431120500050.
  106. Panji, M. and Mojtabazadeh-Hasanlouei, S. (2020b) Transient response of the surface by twin underground inclusions subjected to SH-waves. Earthq. Sci. Eng., 7(3), 29-51.
  107. Panji, M. and Mojtabazadeh-Hasanlouei, S. (2021) Surface motion of alluvial valleys subjected to obliquely incident plane SH-wave propagation. Earthq. Eng., 10.1080/13632469. 2021.1927886.
  108. Mojtabazadeh-Hasanlouei, S., Panji, M., and Kamalian, M. (2020) On subsurface multiple inclusions model under transient SH-wave propagation. Wave Rand Compl. Media., 10.1080/17455030.2020.1842553.
  109. Ohkami, T., Ichikawa, Y., and Kawamoto, T. (1991) A boundary element method for identifying orthotropic material parameters. J. Numer. Analy. Meth. Geomech., 15, 609-625.
  110. Fujiwara, H. and Takenaka, H. (1994) Calculation of surface waves for a thin basin structure using a direct boundary element method with normal modes. Geophys J. Int., 117, 69-91.
  111. Sollero, P. and Aliabadi, M.H. (1995) Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Composite Struct., 31(3), 229-233.
  112. Zhang, C. (2002) A 2D time-domain BIEM for dynamic analysis of cracked orthotropic solids. Model Eng. Sci., 3, 381-398.
  113. Chuhan, Z., Yuntao, R., Pekau, O.A., and Feng, J. (2004) Time-domain boundary element method for underground structures in orthotropic media. Eng. Mech., ASCE, 130(1), 105-116.
  114. Leung, K.L., Vardoulakis, I.G., Beskos, D.E., and Tasoulas, J.L. (1991) Vibration isolations by trenches in continuously nonhomogeneous soil by the BEM. Dyn. Earthq. Eng., 10, 172-179.
  115. Hisada, J. (1992) The BEM based on the Green’s function of the layered half-space and the normal mode solution. In Proceedings of Conference on Effects of Surface Geology, Odawara.
  116. Rajapakse, R.K.N.D. and Gross, D. (1995) Transient response of an orthotropic elastic meduim with a cavity. Wave Motion, 21, 231-252.
  117. Zheng, T. and Dravinski, M. (1999) Amplification of waves by an orthotropic basin: Sagittal plane motion. Eng. Struct. Dyn., 28, 565-584.
  118. Ahmad, S., Leyte, F., and Rajapakse, R.K.N.D. (2001) BEM analysis of two-dimensional elastodynamic problems of anisotropic solids. Eng. Mech., ASCE, 27(2), 149-156.
  119. Ge, Z. (2010) Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary direction using boundary element method: SH-case. Sci., 23, 149-155.
  120. Saez, A. and Dominguez, J. (1999) BEM analysis of wave scattering in transversely isotropic solids. J. Numer. Methods Eng., 44, 1283-1300.

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  • تاریخ دریافت: 07 آذر 1399
  • تاریخ بازنگری: 01 خرداد 1400
  • تاریخ پذیرش: 11 خرداد 1400

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