Elastik Heterojen Bir Tabakayla Kaplı Heterojen Yarım Uzayda Parlak ve Karanlık Soliter Love Dalgaları

Yıl 2023, Cilt: 5 Sayı: 1, 67 - 78, 30.04.2023

Ekin Deliktaş

https://doi.org/10.46387/bjesr.1242854

Cited By: 1

Öz

Bu çalışmada, dalga yayılımına dik yönde heterojen, elastik bir tabakayla kaplı heterojen yarım uzayda doğrusal olmayan Love dalgalarının yayılması problemi göz önüne alınmıştır. Çoklu ölçekler yöntemi kullanılarak, doğrusal olmayan Love dalgalarının öz etkileşimini karakterize eden, katsayıları ortamın malzeme özelliklerine, dolayısıyla tabaka ve yarım uzayı oluşturan malzemelerin heterojenlik parametrelerine bağlı, doğrusal olmayan bir Schrödinger denklemi türetilmiştir. Ortamın doğrusal olmayan özelliklerinin yanı sıra heterojenliğinin de parlak ve karanlık soliter Love dalgalarının varlığı üzerindeki etkileri nümerik olarak incelenmiştir. Ayrıca hem tabakaya hem de yarım uzaya ait doğrusal olmayan ve heterojen malzeme özelliklerinin parlak ve karanlık dalga evrimi üzerindeki kaydadeğer etkileri grafiksel olarak gösterilmiştir.

Anahtar Kelimeler

Doğrusal Olmayan Elastisite, Soliter SH Dalgaları, Heterojen Tabakalı Yarım Uzay

Bright and Dark Solitary Love Waves in a Heterogeneous Semi-Space Coated with a Heterogeneous Elastic Layer

Öz

The propagation of nonlinear Love waves in an elastic, vertically heterogeneous crust laid upon an elastic, heterogeneous semi-space is considered. By employing the multiple scales method, the amplitude function of Love waves is represented by a nonlinear Schrödinger equation which includes the nonlinear material and heterogeneity parameters of the layered semi-space in its coefficients. This study numerically investigates the influence of heterogeneity as well as the nonlinear properties of the media on the presence of bright and dark solitary Love waves. Moreover, the remarkable effects of nonlinear and heterogeneous material properties of both layer and semi-space on the wave evolution of bright and dark solions are graphically shown.

Anahtar Kelimeler

Nonlinear Elasticity, Solitary SH Waves, Heterogeneous Layered Semi-Space

Kaynakça

• A.E.H. Love “Some Problems of Geodynamics”, Cambridge University Press, 1911.
• S. Kundu, S. Gupta, and S. Manna “Propagation of Love wave in fiber-reinforced medium lying over an initially stressed orthotropic half-space”, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 38, no. 11, pp. 1172–1182, 2014.
• J.D. Achenbach “Wave Propagation in Elastic Solids”, Amsterdam: North Holland Publ. Co., 1973.
• K. Bataille, and F. Lund “Nonlinear waves in elastic media”, Physica D: Nonlinear Phenomena, vol. 6, no. 1, pp. 95-104, 1982.
• T. Boxberger, M. Picozzi, and S. Parolai “Shallow geology characterization using Rayleigh and Love wave dispersion curves derived from seismic noise array measurements”, Journal of Applied Geophysics, vol. 75, no. 2, pp. 345-354, 2011.
• A.C. Eringen, and E.S. Suhubi “Elastodynamics”, New York: Academic Press, vol. 1, 1974.
• W.M. Ewing, W.S. Jardetzky, F. Press, and A. Beiser “Elastic waves in layered media”, Physics Today, vol. 10, no. 12, pp. 27, 1957.
• Y. Fukao, and K. Abe “Multi-mode Love waves excited by shallow and deep earthquakes”, Bull Earthq. Res. Inst, vol. 49, pp. 1-12, 1971.
• S.V. Kuznetsov “Love waves in nondestructive diagnostics of layered composites”, Survey Acoustical Physics, vol. 56, no. 6, pp. 877-892, 2010.
• E. Meissner “Elastische Oberflachenwellen mit Dispersion in einem inhomogenen Medium”, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, vol. 66, pp. 181-195, 1921.
• S.C.D. Gupta “Note on Love waves in a homogeneous crust laid upon heterogeneous medium”, Journal of Applied Physics, vol. 23, no. 11, pp. 1276-1277, 1952.
• S.N. Bhattacharya “Love wave dispersion in a homogeneous crust overlying a continuous mantle with vertical in-homogeneity”, Geophysical Journal International, vol. 19, no. 4, pp. 335-349, 1970.
• K. Watanabe “Plane SH-waves in harmonically in-homogeneous elastic media”, Wave motion, vol. 6, no. 5, pp. 477-488, 1984.
• S. Majhi, P.C. Pal, and S. Kumar “Propagation of SH waves in a visco-elastic layer overlying an in-homogeneous isotropic half-space”, Ain Shams Engineering Journal, vol. 9, no. 4, pp. 675-680, 2018.
• S. Manna, S. Kundu, and S. Gupta “Effect of reinforcement and in-homogeneity on the propagation of Love waves”, International Journal of Geomechanics, vol. 16, no. 2, 2016.
• C.D. Wang, C.S. Tzeng, E. Pan, and J.J. Liao “Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space”, Int. J. Rock Mech. Min. Sci. vol. 40, no. 5, pp. 667–685, 2003.
• R.S. Sidhu “Propagation of love waves in a two-layered heterogeneous half space”, Pure and Applied Geophysics, vol. 91, pp. 76-94, 1971.
• S.N. Chatterjee “Propagation of Love waves in a medium containing a heterogeneous layer lying over a heterogeneous half space”, Pure and Applied Geophysics, vol. 90, pp. 53-60, 1971.
• M. Chatterjee, S. Dhua, A. Chattopadhyay and S. A. Sahu “Seismic waves in heterogeneous crust-mantle layers under initial stresses”, Journal of Earthquake Engineering, vol. 20, no. 1, pp. 39-61, 2016.
• S. Gupta et al. “Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space”, Applied Mathematics and Mechanics, vol. 34, no. 2, pp. 249–258, 2013.
• A.M. Abd-Alla, and S.M. Ahmed “Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium”, Applied Mathematics and Computation, vol. 106, no. 2, pp. 265-275, 1999.
• M. Teymur “Nonlinear modulation of Love waves in a compressible hyperelastic layered half-space”, Int. J. Eng. Sci., vol.26, pp. 907-927, 1988.
• E. Deliktas-Ozdemir, S. Ahmetolan, and D. Tuna “Existence of solitary SH waves in a heterogeneous elastic two-layered plate”, Z. Angew. Math. Phys., vol. 73, pp. 220, 2022.
• E. Deliktas-Ozdemir “Nonlinear Love-type waves in a heterogeneous layer sandwiched between two semi- infinite media”, Z. Angew. Math. Phys., vol. 74, pp. 1-7, 2023.
• J.K. Knowles “The finite anti-plane shear field near the tip of a crack for a class of in-compressible elastic solids”, International Journal of Fracture, vol. 13, no. 5, pp. 611-639, 1977.
• E. Deliktas-Özdemir, and M. Teymür “Nonlinear surface SH waves in a half-space covered by an irregular layer”, Z. Angew. Math. Phys., vol. 73, no. 4, pp. 1-18, 2022.
• A. Jeffrey, and T. Kawahara “Asymptotic Methods in Nonlinear Wave Theory”, Boston Pitman, 1982.
• A. Chattopadhyay, S. Gupta, V.K. Sharma, and P. Kumari “Effect of point source and heterogeneity on the propagation of SH-waves”, Int. J. of Appl. Math and Mech., vol. 6, no. 9, pp. 76-89, 2010.
• P. Avtar “Love waves in a two-layered crust overlying a vertically in-homogeneous halfspace”, I. pure and applied geophysics, vol. 66, no. 1, pp. 48-68, 1967.