Một số bài toán truyền sóng trong môi trường phức tạp liên quan đến tỷ số h v​

ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC TỰ NHIÊN _ Trương Thị Thùy Dung MỘT SỐ BÀI TỐN TRUYỀN SĨNG TRONG MƠI TRƯỜNG PHỨC TẠP LIÊN QUAN ĐẾN TỶ SỐ H/V LUẬN ÁN TIẾN SĨ CƠ HỌC Hà Nội - 2020 ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC TỰ NHIÊN _ Trương Thị Thùy Dung MỘT SỐ BÀI TOÁN TRUYỀN SĨNG TRONG MƠI TRƯỜNG PHỨC TẠP LIÊN QUAN ĐẾN TỶ SỐ H/V Chuyên ngành: Cơ học vật rắn Mã số: 9440109.02 LUẬN ÁN TIẾN SĨ CƠ HỌC NGƯỜI HƯỚNG DẪN KHOA HỌC: TS Trần Thanh Tuấn GS TS Phạm Chí Vĩnh Hà Nội - 2020 LÕI CAM OAN Tấi xin cam oan Ơy l cấng trẳnh nghiản cu riảng ca tấi CĂc kát quÊ ềc trẳnh b y luên Ăn l trung thác v cha tng ềc cấng bậ bĐt k cấng trẳnh n o kh¡c Nghi¶n c˘u sinh i LÕI CƒM ÌN Nh˙ng dÃng Ưu tiản luên Ăn, tấi muận gi lèi cÊm ẽn chƠn th nh nhĐt tểi hai thƯy hểng dăn ca tấi, TS TrƯn Thanh TuĐn v GS TS PhÔm Chẵ Vắnh ThƯy  truyÃn cho tấi niÃm am mả nghiản cu khoa hc, tiáp cho tấi thảm la v ẻng lác gip tấi kiản trẳ trản èng nghiản cu, ng thèi thƯy cung cĐp kián thc v ˜a nh˙ng lÌi khuy¶n giÛp tÊi tr˜ ng th nh hẽn quĂ trẳnh hc têp, nghiản cu v ho n th nh luªn ¡n n y TÊi xin gi lèi cÊm ẽn chƠn th nh tểi cĂc thƯy, cÊ gi¡o BỴ mÊn CÏ hÂc, Khoa To¡n - CÏ - Tin hc, PhÃng sau Ôi hc, Trèng Ôi hc Khoa hc Tá nhiản, Trung tƠm Vêt l l thuyát quậc tá ICTP  trang b kián thc, tÔo mấi trèng nghiản cu tật v tÔo iÃu kiằn gip tấi quĂ trẳnh hc têp Tấi xin cÊm ẽn cĂc th nh viản nhm nghiản cu ca thƯy PhÔm Chẵ Vắnh  chia s kinh nghiằm, nhiằt tẳnh gip Ô tÊi TÊi xin b y t‰ s¸ bi¸t Ïn án gia ẳnh tấi  luấn ng hẻ, ẻng viản, gip ễ tấi quĂ trẳnh hc têp v thác hiằn luên Ăn H Nẻi, thĂng 12 nôm 2020 Nghiản c˘u sinh Tr˜Ïng Th‡ ThÚy Dung ii Mˆc lˆc Danh s¡ch b£ng Danh s¡ch h¼nh v³ M– ƒU TÊNG QUAN 1.1 1.2 1.3 GiÓi thi»u ph˜Ïng ph¡p t sË Tẳnh hẳnh nghiản cu và ph luên Ăn nghiản cu giÊi quyá Mc tiảu v cĂc nẻi dung chẵ CặNG THŸC T SÈ H/V C’A SÂNG M ƒT RAYLEIGH TRONG BƒN KHỈNG GIAN TR‹C H ŒNG PH’ MËT LŒP TR‹C H ŒNG 2.1 2.2 2.3 2.4 C¡c ph˜Ïng tr¼nh cÏ b£n Ma trªn chuyºn cıa lÓp b i to¡n s‚ng m°t Ra CÊng th˘c t sË H/V cıa s‚ng m°t Rayleigh 2.3.1 2.3.2 2.3.3 T½nh to¡n minh hÂa sË v b i to¡n ng˜Òc 2.4.1 2.4.2 2.4.3 iii CỈNG THŸC XƒP Xƒ TƒN SÈ CËNG H – NG C’A COMPOSITE LŒP TR‹C H ŒNG 3.1 3.2 3.3 3.4 B i to¡n Phẽng trẳnh xĂc nh tƯn sậ tểi hÔn 3.2.1 3.2.2 T½nh to¡n sË 3.3.1 3.3.2 Kát luên chẽng CỈNG THŸC TƒN SÈ CËNG H – NG CÌ BƒN Vƒ Hƒ SÈ KHUƒCH ƒI C’A LŒP ƒN NHŒT 4.1 4.2 4.3 4.4 GiĨi thi»u v· mÊi tr˜Ìng n nhĨt B i to¡n 4.2.1 4.2.2 T½nh to¡n minh hÂa sË Kát luên chẽng BƒI TOƒN TRUYƒN SÂNG MƒT RAYLEIGH TRONG BƒN KHỈNG GIAN TR‹C H ŒNG MICROPOLAR 5.1 5.2 5.3 5.4 S‚ng Rayleigh v biºu di¹n Stroh Tr˜Ìng hỊp vªt li»u ¯ng h˜Ĩng Tr˜Ìng hỊp tr¸c h˜Ĩng 5.3.1 5.3.2 5.3.3 T½nh to¡n minh hÂa sË 5.4.1 Nakamura's technique", Journal of Physics of the Earth, 42(4), pp 377-397 [29] Lesan, D (2004), Thermoelastic Models of Continua , London: Kluwer Aca-demic Publishers 108 [30] Love A.E.H (1911), Some Problems of Geodynamics , Cambridge University Press, Cambridge (republished by Dover, New York, 1967) [31] Lunedei, E., Albarello, D (2010), "Theoretical HVSR from the full wave field modelling of ambient vibrations in a weakly dissipative layered", Earth.Geophys.J.Int 181, pp 1093-1108 [32] Makarov S., Chilla E., Frohlich H.J (1995), "Determination of elastic con-stants of thin films from phase velocity dispersion of different surface acous-tic wave modes", J Appl Phys., 78, pp 50285034 [33] Malischewsky P G., Wuttke F., Ziegert A (2002), "The use of surface acous-tic waves for non-destructive testing", Schriftenreihe Werkstoffwissenschaf- fen 17, Verlag Dr Koster, Berlin , pp 135-140 (in German) [34] Malischewsky P G and Scherbaum F (2004), "Love's formula and H/V-ratio (ellipticity) of Rayleigh waves", Wave Motion, 40, pp 57-67 [35] Malischewsky P G., Schnapp J D., Ziegert A (2006), "The ellipticity of Rayleigh waves and nondestructive testing", ECNDT Berlin 2006, We 2.4.3 [36] Malischewsky P G., Scherbaum F., Lomnitz C., Tuan T T., Wuttke F., and Shamir G (2008), "The domain of existence of prograde Rayleigh-wave particle motion for simple models", Wave Motion, 45(4), pp 556-564 [37] Maurer H R., Van der Veen M., Giudici J., and Springman S (1999), "Determining elastic soil properties at small strains", Proc Sympos on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP) [38] Munirova L M., Yanovskaya T B (2001), "Spectral ratio of the horizontal and vertical Rayleigh wave components and its application to some problems of seinology Izvestiya", Phys Solid Earth, 37, pp 709-716 (Translated from Fizika Zemli 9(2001) 10-18) 109 [39] Mucciarelli, M (1998), "Reliability and applicability of Nakamura's tech-nique using microtremors: an experimental approach", J Earthq Engrg 2, pp 625-638 [40] Nakamura Y (1989), "A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface", Quarterly Report of RTRI, Railway Technical Research Institute (RTRI) , 30 (1), pp 25-33 [41] Nakamura Y (2000), "Clear identification of fundamental idea of Naka-muras technique and its applications", 12WCEE, 2656 [42] Nakamura Y (2008), On the H/V spectrum, Proceedings of the 14th World Conference on Earthquake Engineering , Beijjing, China [43] Nam N.T., Merodio J., Ogden R.W., Vinh P.C (2016), "The effect of initial stress on the propagation of surface waves in a layered halfspace", Inter- national Journal Solids and Structures , 88-89, pp 88-100 [44] Nogoshi, M and T Igarashi, (1970), "On the propagation characteristics of microtremors", J Seism Soc Japan, 23, pp 264-280 [45] Nogoshi, M and Igarashi, T (1971), "On the Amplitude Characteristics of Microtremor (Part 2) (in Japanese with English abstract), Jour Seism Soc Japan, 24, pp 26-40 [46] Nowacki, W (1986), Theory of Asymmetric Elasticity , Oxford: Pergamon Press [47] Ogden R.W and Pham Chi Vinh (2004), "On Rayleigh waves in incom-pressible orthotropic elastic solids", J Acoust Soc Am., 115, pp.530533 [48] Oubaiche E.H., Chatelain J.L., Bouguern A., Bensalem R., Machane D., Hellel M., Khaldaoui F and Guillier B (2012), "Experimental relationship between ambient vibration H/V peak amplitude and shearwave velocity contrast", Seismological Research Letters , 83(6), pp 1038-1046 [49] Oubaiche E.H Chatelain, J.L., Hellel M., Wathelet M., Machane D., Ben-salem R and Bouguern A (2016), "The Relationship between Ambient 110 Vibration H/V and SH Transfer Function: Some Experimental Results", Seismological Research Letters , 87(5), pp 1112-1119 [50] Paolucci R (1999), "Shear resonance frequencies of alluvial valleys by Rayleigh's method", Earthquake Spectra, 15(3), pp 503-521 [51] Parolai S, Bormann P, Milkereit C (2001), "Assessment of the natural fre-quency of the sedimentary cover in the Cologne area (Germany) using noise measurements", J Earthq Engrg 5, pp 541564 [52] Poggi, V and Fah, D (2010), "Estimating Rayleigh wave particle motion from three-component array analysis of ambient vibrations", Geophysical Journal International , 180(1), 251-267 [53] Peter M Shearer (2009), Introduction to Seismology , 2nd ed, Institution of Oceanography, University of California, San Diego [54] Rayleigh Lord (1885), "On waves propagated along the plane surface of an elastic solid" Proceedings of the London Mathematical Society , 17, pp 411 [55] Roberto Villarvede (2009), Fundamental Concepts of Earthquake Engineer-ing, CRC Press [56] S¡nchez-Sesma F.J., Rodr½guez M., Iturrarn-Viveros U., Luz‚n F., Campillo M., Margerin L., Garc½a-Jerez A., Suarez M., Santoyo M.A., and Rodr½guez-Castellanos A (2011), "A theory for microtremor H/V spectral ratio: ap-plication for a layered medium", Geophys J Int., 186(1), pp 221-225 [57] Scherbaum F., Hinzen K G., Ohmberger M (2003), "Determination of shal-low shear wave velocity profiles in the Cologue Germany area using ambient vibration", Geophys J Int., 152, pp 597-612 [58] Singh B (2007), "Wave propagation in an orthotropic micropolar elastic solid", International Journal of Solids and Structures , 44(11-12), 3638-3645 [59] Shuvalov A L (2000), "On the theory of anisotropic plates", Proc R Soc Lond A, 456, pp 2197-2222 111 [60] Sotiropolous D.A (1999), "The effect of anisotropy on guided elastic waves in a layered half-space", Mech Mater, 31, pp 215-233 [61] Stephenson W R (2003), "Factors bounding prograde Rayleigh-wave par-ticle motion in a soft-soil layer", Pacific Conference on Earthquake Engi- neering, 13-15 February, Christchurch, New Zealand [62] Stroh A N (1962), "Steady state problems in anisotropic elasticity" Jour-nal of Mathematical Physics , 41, pp 77103 [63] Ting T.C.T (1996), Anisotropic Elasticity, Theory and Applications , Ox- ford Unversity Press NewYork [64] Tolstoy, I., and Usdin, E (1953), "Dispersive properties of stratified elastic and liquid media: A ray theory", Geophysics, 18(4), 844-870 [65] Tuan T T (2009),The ellipticity H/V-ratio of Rayleigh surface waves , Dis-sertation in GeoPhysics, Friedrich-Schiller University Jena, Germany [66] Tuan T T., Scherbaum F., Malischewsky P G (2011), "On the relationship of peaks and troughs of the ellipticity (H/V) of Rayleigh waves and the transmission response of single layer over half-space models", Geophys J Int., 184, pp 793-800 [67] Tuan T T and Trung T N., The dispersion of Rayleigh waves in or-thotropic layered half-space using matrix method, Vietnam J Mech, 38:1 (2016), 2738 [68] Tuan T.T., Vinh P.C., Ohrnberger M., Malischewsky P and Aoudia A (2016), "An improved formula of fundamental resonance frequency of a lay-ered half-space model used in H/V ratio technique", Pure and Applied Geo-physics, 173(8), pp 28032812 [69] Tuan T T., Vinh P C., Malischewsky P., and Aoudia A (2016), "Approx-imate formula of peak frequency of H/V ratio curve in multilayered model and its use in H/V ratio technique", Pure and Applied Geophysics , 173(2), pp 487-498 112 [70] Truesdell, C., and Noll, W (1965) The Nonlinear Field Theories of Mechan- ics, In S Flugge (Ed.), Handbuch de Physik (vol III/3), Berlin: Springer-Verlag [71] Van Der Baan M (2009), "The origin of SH-wave resonance frequencies in sedimentary layers", Geophys J Int, 178.3, pp 1587-1596 [72] Valerio Poggi, Donat Fah, Jan Burjanek, Domenico Giardini (2012), "The use of Rayleigh-wave ellipticity for site-specific hazard assessment and mi-crozonation: application to the city of Lucerne, Switzerland", Geophysical Journal International , Volume 188, Issue 3, March 2012, Pages 11541172 [73] J Verbeke, L Boschi, L Stehly, E Kissling, A Michelini (2012), "High-resolution Rayleigh-wave velocity maps of central Europe from a dense ambient-noise data set", Geophysical Journal International , Volume 188, Issue 3, March 2012, pp 11731187 [74] Vinh P C and Ogden R.W (2004), "On formulas for the Rayleigh wave speed", Wave Motion, 39, pp 191-197 [75] Vinh P.C., and Ogden R.W (2004), "Formulas for the Rayleigh wave speed in orthotropic elastic solids", Ach Mech., 56, pp 247-265 [76] Vinh P C and Ogden R W (2005), "On a general formula for the Rayleigh wave speed in orthotropic elastic solid", Meccanica, 40, pp 147-161 [77] Vinh P C, Malischewsky Peter G (2007), "An improved approximation of Bergmann form for the Rayleigh wave velocity", Ultrasonics, 47, 49-54 [78] Vinh P C, Malischewsky P.G (2007), "An approach for obtaining approx-imate formulas for the Rayleigh wave velocity", Wave Motion, 44, 549-562 [79] Vinh P C, Malischewsky P.G (2008), "Improved approximations of the Rayleigh wave velocity", J Thermoplast Comp Mater , 21, pp 337-352 [80] Vinh P.C (2009), "Explicit secular equations of Rayleigh waves in elastic media under the influence of gravity and initial stress", Appl Math Compt., 215, pp 395-404 113 [81] Vinh P C (2010), "On formulas for the velocity of Rayleigh waves in pre-strained incompressible elastic solids", ASME J Appl Mech., 77, 021006 (7 pages) [82] Vinh P C and Giang P T H (2010), "On formulas for the Rayleigh wave velocity in pre-strained elastic materials subject to an isotropic internal constraint", Int J Eng Sci., 48, pp 275-289 [83] Vinh P C (2011), "On formulas for the Rayleigh wave velocity in pre-stressed compressible solids", Wave Motion, 48, pp 613-624 [84] Vinh P.C., Linh N T K (2012), "An approximate secular equation of Rayleigh waves propagating in an orthotropic elastic halfspace coated by a thin orthotropic elastic layer", Wave Motion, 49, pp 681-689 [85] Vinh P C., Linh N T K., Anh V T N (2014), "Rayleigh waves in an incompressible orthotropic half-space coated by a thin elastic layer", Arch Mech, 66, pp 173-184 [86] Vinh P C., Hue T T T (2014), "Rayleigh waves with impedance boundary conditions in anisotropic solids", Wave Motion, 51(7), 1082-1092 [87] Vinh P C., Tuan T T., and Capistran M A (2015), "Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers", Wave Motion, 54, pp 134-144 [88] Vinh P.C., Anh V.T.N., Linh N T K (2016), "On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer", Waves in Random and Complex Media , 26, pp 176-188 [89] Vinh P C., Aoudia A., Giang P T H (2016), "Rayleigh waves in orthotropic fluid-saturated porous media" Wave Motion, 61, 73-82 [90] Vinh P C., Tuan T T., Anh V., Hue L T (2018), "Formulas for the H/V ratio of Rayleigh waves in compressible prestressed hyperelastic half-spaces", Journal of Mechanics of Materials and Structures , 13(3), 247-261 114 [91] Vinh P C., Tuan T T., Hue L T (2018), "Formulas for the H =V ratio of Rayleigh waves in incompressible pre-stressed half-spaces", Archives of Mechanics, 70(2), 131-150 [92] Vinh P.C., Tuan T.T., Hue L.T (2019), "Formulas for the H =V ratio (el- lipticity) of Rayleigh waves in orthotropic elastic half-spaces", Waves in Random and Complex Media , 29(4), pp 759-774 [93] Xiao X., and You X.-Y (2007), "The determination for the adhesion of film and substrate by surface acoustic waves", Surf Coat Technol., 201, pp 9594-9597 [94] Wang Y and R K N D Rajapakse (1994), An exact stiffness method for elastodynamics of a layered orthotropic half-plane, J Appl Mech, 61:2 , pp 339348 [95] Zaslavsky, Y., G Ataev, M Gorstein, M Kalmanovich, N Perelman and A Shapira, ()2008), "Assessment of site specifc earthquake hazards in urban areas A case study: the town Afula, Israel, and neighbouring settlements", Bollettino di Geofsica Teorica ed Applicata , 49, 93-108 [96] Zschau, J and S Parolai, (2004), "Studying earthquake site effects in urban areas: the example of Cologne (Germany)", Taller Humboldt para la Coop- eraci‚n M²xico-Alemania (Humboldt-Workshop) , Juriquilla, Qto., Mexico 2004 115 ... ĐẠI H? ??C QUỐC GIA H? ? NỘI TRƯỜNG ĐẠI H? ??C KHOA H? ??C TỰ NHIÊN _ Trương Thị Thùy Dung MỘT SỐ BÀI TỐN TRUYỀN SĨNG TRONG MƠI TRƯỜNG PHỨC TẠP LIÊN QUAN ĐẾN TỶ SỐ H/ V Chuyên ngành: Cơ h? ??c vật... t trản bĂn khấng gian) hoc mấi trèng ẽn giÊn c tẵnh chĐt n hi ng h? ??ng Vểi nhng mấ h? ??nh phc tÔp h? ??n hoc mấi trèng c tẵnh chĐt phc tÔp h? ??n nh˜ d‡ h? ?Ĩng, n nhĨt, n h? ?i micropolar th¼ nh˙ng b i toĂn... sng SH l sng mẻt th nh phƯn, n ch gƠy dao ẻng theo phẽng nơm ngang Tuy nhiản sng nhiạu o Ôc l sng hai th nh phƯn, cĂc dao ẻng c‚ c£ th nh ph¦n theo ph˜Ïng ngang v ph˜Ïng th¯ng ˘ng º gi£i th½ch vi»c