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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 Giểi thiằu phẽng phĂp t sậ Tẳnh hẳnh nghiản cu và ph luên Ăn nghiản cu giÊi quyá Mc tiảu v cĂc nẻi dung chẵ 1.1 1.2 1.3 CỈNG THŸC T SÈ H/V C’A SÂNG MƒT 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 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 B i to¡n Ph˜Ïng tr¼nh 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 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˜Óng 5.3.1 5.3.2 5.3.3 T½nh to¡n minh hÂa sË 5.4.1 5.4.2 iv 101 vªn tËc s‚ng v t sË H/V cıa s‚ng m°t Rayleigh v o tham sË micropolar cıa b¡n khÊng gian ˜Ịc th¸c hi»n C¡c giĂ tr tẵnh toĂn sậ cho thĐy rơng ẻ lằch t˜Ïng Ëi lĨn nh§t gi˙a gi¡ tr‡ cıa t sË H/V cıa tr˜Ìng hỊp b¡n khÊng gian c‚ t½nh micropolar so vĨi tr˜Ìng hỊp b¡n khÊng gian khÊng c‚ t½nh micropolar c giĂ tr xĐp x bơng vểi giĂ tr cıa h» sË micropolar " C¡c cÊng th˘c x§p x¿ chẵnh xĂc nhên ềc chẽng n y c th ˜Ịc s˚ dˆng º t½nh to¡n h» sË micropolar cıa mấi trèng t cĂc sậ liằu o Ôc ca t sậ H/V v Kát quÊ liản quan án trèng hềp b¡n khÊng gian micropolar ¯ng h˜Ĩng cıa Ch˜Ïng ¢ ềc ông trản Tuyn têp Hẻi ngh Cẽ hc to n quậc lƯn th X, H Nẻi TrƯn Thanh TuĐn, Trẽng Th Thy Dung, Nguyạn Th Loan v ẩ XuƠn TÚng (2017), "T sË H/V (ellipticity) cıa s‚ng m°t Rayleigh bĂn khấng gian micropolar ng hểng", Tuyn têp Hẻi ngh‡ CÏ hÂc to n quËc l¦n th˘ X, H Nẻi, Têp 3, Quyn 2, pp 1381-1387 102 KT LUN B¬ng vi»c kh£o s¡t b i to¡n truy·n s‚ng m°t Rayleigh v truy·n s‚ng khËi SH c¡c mÊi tr˜Ìng phc tÔp hẽn mấi trèng n hi ng hểng, c thº l c¡c mÊi tr˜Ìng n hÁi tr¸c h˜Ĩng, n nhểt v n hi micropolar, luên Ăn  thu ềc mẻt sậ kát quÊ chẵnh sau: Tẳm ềc cấng th˘c t sË H/V cıa s‚ng m°t Rayleigh b¡n khấng gian trác hểng nn ềc ph mẻt lểp trác h˜Ĩng n²n ˜Ịc CÊng th˘c n y ˜Ịc s˚ dˆng b i to¡n ng˜Òc º ¡nh gi¡ tham sË ca vêt liằu trác hểng t d liằu o Ôc gi£ ‡nh cıa t sË H/V T¼m ˜Ịc cÊng thc xĐp x ca ca tƯn sậ im Ôi cıa ˜Ìng cong phÍ t sË H/V cıa s‚ng m°t Rayleigh mấ hẳnh phƠn lểp trác hểng Cấng thc n y ˜Ịc s˚ dˆng º ¡nh gi¡ t¦n sË cỴng h˜ ng Ëi vĨi s‚ng SH cıa composite lĨp trác hểng Tẳm ềc cấng thc xĐp x ca tƯn sậ cẻng h ng cẽ bÊn v hằ sậ khuách Ôi ca composite lểp n nhểt t trản bĂn khấng gian c tẵnh án hằ sậ cÊn nhểt T¼m ˜Ịc ph˜Ïng tr¼nh t¡n sc v cÊng th˘c t sË H/V cıa s‚ng m°t Rayleigh truy·n b¡n khÊng gian n hi micropolar trác hểng CĂc kát quÊ nghiản cu luên Ăn l cĂc kát quÊ mểi v c‚ thº ˜Ịc ¡p dˆng v o mỴt sË b i toĂn thác tá vẵ d nh b i to¡n ng˜Ịc x¡c ‡nh tham sË vªt li»u, b i to¡n ¡nh gi¡ ˜Ĩc l˜Ịng £nh h˜ ng cıa s‚ng Îng §t KIƒN NGHÀ Vƒ NH⁄NG NGHIƒN CŸU TIƒP Trong quan iºm cıa Nakamura v· h m ph£n ˘ng ca lểp a tƯng mÃm ch xt án sng SH iÃu n y l hềp l vẳ cĂc nghiản cu tẵnh toĂn sậ ậi vểi mấ hẳnh mẻt lểp thẳ hằ sậ khuách Ôi sng P ca lểp a tƯng mÃm c giĂ tr gƯn bơng mẻt v ềc coi l hơng sậ Tuy nhiản mấ hẳnh nhiÃu lểp, hằ sậ khuách Ôi sng P c th c giĂ tr bián i Ăng k xung quanh tƯn sậ cẻng h ng nản cƯn c nhng nghiản cu xt án £nh h˜ ng cıa s‚ng P Do ‚, luªn ¡n c th phĂt trin hểng tẳm cĂc cấng thc xĐp x ca tƯn sậ cẻng h ng ca lểp c x²t th¶m b i to¡n truy·n s‚ng P cÚng vĨi b i to¡n truy·n s‚ng SH Khi ‚ c¡c k¸t quÊ s c thảm hằ sậ Ênh h ng án t¯ gi¡ tr‡ cıa h» sË Poisson cıa vªt li»u Danh mˆc cÊng tr¼nh khoa hÂc cıa t¡c gi£ liản quan án luên Ăn P.C Vinh, T.T Tuan, L.T Hue, V.T.N Anh, T.T.T Dung, N.T.K Linh, P Malischewsky (2019), "Exact formula for the H/V ratio of Rayleigh waves in compressible orthotropic half-space coated by an orthotropic elastic layer", The Journal of the Acoustical Society of America , 146(2), 1279-1289 T.T.T Dung, T.T Tuan, P.C Vinh and G.K Trung (2020), "An approximate formula of first peak frequency of ellipticity of Rayleigh surface waves in orthotropic layered half-space model", Journal of Mechanics of Materials and Structures, Vol 15, No 1, pp 61-74 T.T Tuan, P.C Vinh, A 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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... d‡ch theo ph˜Ïng ngang, ph˜Ïng th¯ng ˘ng v ˜Ìng cong phÍ t sË H/ V (Nakamura, 2000) H? ?nh 1.2: H? ?nh minh h? ?a v· ph˜Ïng ph¡p t sË H/ V (Nakamura, 2008) 10 H/ V ca sng nhiạu chẵnh l o h? ?? sậ khuách Ôi... 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? ??ng, n nhểt, n hi micropolar thẳ nhng b i toĂn văn cÃn ng