Header Page of 89 i B GIO DC V O TO TRNG I HC XY DNG NGUYN VN M NGHIấN CU BIN PHP NNG CAO N NH KH NG FLUTTER TRONG KT CU CU H TREO LUN N TIN S K THUT H Ni Nm 2015 Footer Page of 89 Header Page of 89 ii B GIO DC V O TO TRNG I HC XY DNG NGUYN VN M NGHIấN CU BIN PHP NNG CAO N NH KH NG FLUTTER TRONG KT CU CU H TREO Chuyờn ngnh: K thut xõy dng cụng trỡnh giao thụng Xõy dng Cu hm Mó s: 62580205-1 LUN N TIN S K THUT TP TH HNG DN KHOA HC PGS TS Phm Duy Hũa GS TS Lờ Xuõn Hunh H Ni Nm 2015 Footer Page of 89 Header Page of 89 iii LI CAM OAN Tụi xin cam oan lun ỏn ny l cụng trỡnh nghiờn cu ca riờng tụi Nhng ni dung, s liu v kt qu trỡnh by lun ỏn l hon ton trung thc v cha cú tỏc gi no cụng b bt k cụng trỡnh no khỏc Tỏc gi lun ỏn Nguyn Vn M Footer Page of 89 iv Header Page of 89 LI CM N Li u tiờn, tụi by t lũng bit n sõu sc nht n th cỏn b hng dn khoa hc: cỏc thy giỏo PGS TS Phm Duy Hũa v GS TS Lờ Xuõn Hunh ó tn tõm hng dn, ng viờn khớch l v cú nhiu úng gúp ý kin khoa hc quý bỏu giỳp tụi hon thnh lun ỏn v nõng cao nng lc khoa hc Tụi cng xin chõn thnh cm n cỏc thy cụ giỏo b mụn Cu v cụng trỡnh ngm ca trng i hc Xõy dng, b mụn Cu-Hm ca trng i hc Bỏch khoa, i hc Nng, trng i hc Giao thụng ti v Vin C hc ó cú nhng ý kin úng gúp giỏ tr v to iu kin thun li tụi hon thnh lun ỏn V tụi cng chõn thnh cỏm n Ban Giỏm hiu trng i hc Xõy dng, Ban Giỏm hiu trng i hc Bỏch khoa v Ban Giỏm c i hc Nng ó h tr v to iu kin thun li giỳp tụi hon thnh cụng trỡnh nghiờn cu ca mỡnh Cui cựng, tụi by t lũng bit n v v cỏc con, ngi thõn gia ỡnh v bn bố ó ng viờn v giỳp tụi vt qua nhng khú khn quỏ trỡnh lm lun ỏn Tỏc gi lun ỏn Nguyn Vn M Footer Page of 89 Header Page of 89 v MC LC LI CAM OAN iii LI CM N iv MC LC v DANH MC CC BNG BIU viii DANH MC CC HèNH V, TH x DANH MC CC T VIT TT V Kí HIU .xiii M U 1 TNH CP THIT CA TI MC CH V NHIM V NGHIấN CU CA LUN N I TNG NGHIấN CU PHM VI NGHIấN CU PHNG PHP NGHIấN CU í NGHA KHOA HC V THC TIN CA LUN N CU TRC CA LUN N Chng 1: TNG QUAN NGHIấN CU DAO NG FLUTTER TRONG 1.1 DAO NG FLUTTER TRONG CU H TREO 1.1.1 Cỏc hin tng khớ ng n hi 1.1.2 Dao ng flutter 1.1.3 Kim soỏt mt n nh flutter 1.2 TNG QUAN NGHIấN CU N NH FLUTTER TRONG CU H 12 1.2.1 Cỏc nghiờn cu v phõn tớch bi toỏn flutter 12 1.2.2 Cỏc nghiờn cu v bin phỏp nõng cao n nh flutter 19 1.2.3 Cỏc nghiờn cu n nh flutter bng phng phỏp hm giú s 29 1.2.4 Thit k khỏng giú cho mt s cu h treo Vit Nam 32 1.2.5 Cỏc nghiờn cu v khớ ng Vit Nam 35 1.3 VN NGHIấN CU 38 1.3.1 Nhng kt qu chớnh ó c cỏc nh khoa hc cụng b 38 1.3.2 Nhng ni dung nghiờn cu ca lun ỏn 39 Kt lun Chng 39 Chng 2: Mễ PHNG S TNG TC GIA KT CU V DềNG 40 2.1 VI NẫT C BN V HM GIể 40 Footer Page of 89 Header Page of 89 vi 2.1.1 Lp biờn ca hm giú 40 2.1.2 Mụ hỡnh hm giú 41 2.2 PHNG PHP HM GIể S 43 2.2.1 Phng trỡnh RANS 43 2.2.2 Phng phỏp tớnh 44 2.2.3 Xỏc nh cỏc tham s khớ ng 45 2.2.4 Thut toỏn mụ phng 48 2.3 KIM NH PHNG PHP HM GIể S CHO MT S KT CU 49 2.3.1 Tit din trũn 50 2.3.2 Tit din ngang cu Great Belt 53 2.3.3 Tit din tm mng phng 55 2.3.4 Kt cu nhp cu treo Thun Phc 59 Kt lun Chng 2: 64 Chng 3: NGHIấN CU C CH PHT SINH MT N NH FLUTTER 65 3.1 DAO NG FLUTTER 65 3.1.1 Dao ng flutter xon (1DOF) 65 3.1.2 Dao ng flutter un-xon (2DOF) 66 3.1.3 Phõn tớch nh hng ca cỏc vi phõn khớ ng n dao ng flutter 69 3.2 PHN TCH C CH N NH FLUTTER I VI KT CU NHP 75 3.2.1 Phõn tớch c ch phỏt sinh v ngn chn mt n nh flutter 75 3.2.2 Phõn tớch nh hng ca cỏc tham s cn n n nh flutter 78 3.3 PHN TCH MT BIN PHP CI TIN FAIRING CONG LếM 81 Kt lun Chng 3: 84 Chng 4: PHN TCH V XC NH MIN THAM S HIU QU CA 86 4.1 PHN TCH MIN HIU QU CA GểC FAIRING V V TR MẫP 86 4.1.1 Kho sỏt hiu qu ca gúc fairing 86 4.1.2 Kho sỏt ng thi cỏc tham s gúc fairing v v trớ mộp ún giú 88 4.2 PHN TCH MIN HIU QU CA CHIU DI TM SPOILER 91 4.3 PHN TCH MIN HIU QU CA B RNG KHE SLOT 92 4.4 PHN TCH MIN HIU QU CA GểC FAIRING LếM 95 4.4.1 Phõn tớch hiu qu ca gúc fairing tam giỏc lừm 95 4.4.2 Phõn tớch hiu qu ca gúc fairing cong lừm 101 Kt lun Chng 4: 106 KT LUN 107 Footer Page of 89 Header Page of 89 vii A Nhng ni dung ó c thc hin lun ỏn 107 B Nhng úng gúp mi ca lun ỏn 108 C Hng nghiờn cu phỏt trin 108 DANH MC CC CễNG TRèNH KHOA HC CễNG B 109 TI LIU THAM KHO 111 Ting Vit 111 Ting Anh 111 PH LC I Ph lc A: Phng phỏp step-by-step ca Matsumoto [57[63] I Ph lc B: Cỏc bc phõn tớch n nh flutter ca kt cu nhp cu Thun VII Footer Page of 89 Header Page of 89 viii DANH MC CC BNG BIU Bng 1.1 Cỏc cu h treo nhp ln vi cỏc bin phỏp kim soỏt flutter [27] 12 Bng 1.2 Tit din cỏc mụ hỡnh M1 n M8 21 Bng 1.3 Cỏc dng fairing cho cỏc mụ hỡnh M1 n M8 21 Bng 1.4 Tit din cỏc mụ hỡnh S1 n S12 22 Bng 1.5 Cỏc dng fairing cho cỏc mụ hỡnh S1 n S12 22 Bng 1.6 Mt s cu h treo c thit k chng giú cỏc t nc ngoi 33 Bng 2.1 Cỏc yờu cu t l mụ hỡnh thớ nghim dao ng t [109] 42 Bng 2.2 Cỏc yờu cu i vi mụ hỡnh khớ ng cu hon chnh [109] 42 Bng 2.3 Kim chng cỏc h s lc tnh t mụ phng v thớ nghim hm giú 53 Bng 2.4 Kt qu cỏc vi phõn khớ ng i vi dao ng thng ng 57 Bng 2.5 Kt qu cỏc vi phõn khớ ng i vi dao ng xoay 57 Bng 2.6 Cỏc tham s mụ hỡnh tit din kt cu nhp cu Thun Phc 59 Bng 2.7 Vn tc flutter ti hn ca mụ hỡnh 64 Bng 3.1 S thay i Fi x i theo tc i vi tit din dng khụng thoỏt giú 71 Bng 3.2 S thay i Fi x i theo tc i vi tit din dng thoỏt giú 71 Bng 3.3 Quan h vi phõn khớ ng-vn tc flutter tit din dng khụng thoỏt giú 72 Bng 3.4 Quan h vi phõn khớ ng-vn tc flutter tit din dng thoỏt giú 74 Bng 3.5 Vn tc flutter ti hn i vi nm dng tit din phõn tớch 77 Bng 4.1 Vn tc flutter xon ti hn U cri ng vi gúc v b rng B 87 Bng 4.2 Vn tc flutter un-xon ti hn U cri ng vi gúc v b rng B 87 Bng 4.3 Vn tc flutter xon ti hn U cri ng vi gúc d/h v b rng B 89 Bng 4.4 Vn tc flutter un-xon ti hn U cri ng vi gúc d/h v b rng B 89 Bng 4.5 Vn tc flutter xon ti hn U cri ng vi B v L/B 91 Bng 4.6 Vn tc flutter un-xon ti hn U cri ng vi B v L/B 91 Bng 4.7 Vn tc flutter xon ti hn U cri ng vi gúc v b rng B 96 Bng 4.8 Vn tc flutter un-xon ti hn U cri ng vi gúc v b rng B 97 Bng 4.9 Vn tc flutter xon ti hn U cri ng vi gúc v b rng B 100 Bng 4.10 Vn tc flutter un-xon ti hn U cri ng vi gúc v b rng B 100 Bng 4.11 Vn tc flutter ti hn xon U cri ng vi gúc v b rng B 102 Footer Page of 89 Header Page of 89 ix Bng 4.12 Vn tc flutter un-xon ti hn U cri ng vi gúc v b rng B 102 Bng 4.13 Vn tc flutter xon ti hn U cri ng vi gúc v b rng B 105 Bng 4.14 Vn tc flutter un-xon ti hn U cri ng vi gúc v b rng B 105 Bng 4.15 Tng hp hiu qu ca tham s hỡnh hc tit din 106 Bng B.1 Vn tc flutter ti hn ca mụ hỡnh X Footer Page of 89 Header Page 10 of 89 x DANH MC CC HèNH V, TH Hỡnh 1.1 Quan h gia tn s dao ng riờng nh nht v chiu di nhp ca 40 cu Hỡnh 1.2 S cỏc hin tng khớ ng n hi Hỡnh 1.3 Cỏc chi tit khớ ng [27] 10 Hỡnh 1.4 Nguyờn lý thit b TMD 11 Hỡnh 1.5 S sp cu Tacoma Narrows [66] 12 Hỡnh 1.6 Quỏ trỡnh x lý bi toỏn n nh khớ ng 19 Hỡnh 1.7 Mụ hỡnh tit din cu Tacoma cú gn fairing 20 Hỡnh 1.8 Mụ hỡnh dm kớn v cỏc dng fairing ct 23 Hỡnh 1.9 Mụ hỡnh tit din dm h 23 Hỡnh 1.10 Mt ct ngang cú b trớ cỏc chi tit khớ ng 24 Hỡnh 1.11 Cỏc la chn tit din m bo n nh flutter 25 Hỡnh 1.12 Cỏc dng tit din ban u v cú slot tng ng 26 Hỡnh 1.13 Mụ hỡnh li dao ng 30 Hỡnh 1.14 Cỏc li bin dng vt th dao ng a) un v b) xon 30 Hỡnh 1.15 Dng hỡnh hc ca bn loi tit din ngang cu 30 Hỡnh 1.16 Cỏc loi tit din ngang theo Lin Huang 31 Hỡnh 1.17 Cỏc chia li i vi tit din hỡnh ch nht v hp 31 Hỡnh 1.18 H thng iu khin tm flap 35 Hỡnh 1.19 H thng iu khin ch ng bng tm winglet 36 Hỡnh 1.20 Mụ hỡnh lý thuyt v thớ nghim hm giú vi TMDs 36 Hỡnh 1.21 p dng gii phỏp fairing cho cu Nht Tõn [74] 37 Hỡnh 2.1 S cỏc chia li hm giú s 47 Hỡnh 2.2 S thut toỏn mụ phng bng phng phỏp hm giú s 49 Hỡnh 2.3 Min phõn tớch tit din trũn hm giú s 50 Hỡnh 2.4 To li tớnh toỏn 51 Hỡnh 2.5 Ph ỏp sut tớnh toỏn 51 Hỡnh 2.6 Ph vộc t tc tớnh toỏn 52 Hỡnh 2.7 ng cong h s lc cn v lc nõng theo thi gian ca tit din trũn 52 Hỡnh 2.8 Mt ct ngang cu Great Belt theo t l 1:80 53 Hỡnh 2.9 Min phõn tớch tit din Great Belt hm giú s 53 Hỡnh 2.10 Min to li 54 Hỡnh 11 Ph ỏp sut v ph tc 54 Footer Page 10 of 89 Header Page 132 of 89 118 of Structure under Wind Action, Bach Khoa Publishing House, Hanoi, ISBN 978-604-911-943-9 71 Omenzetter P , Wilde K., Fujino Y (2000), Suppression of wind-induced instabilities of a long span bridge by a passive deck-flaps control system - Part I: Formulation, Journal of Wind Engineering and Industrial Aerodynamics 87 (2000) 61-79 72 Omenzetter P , Wilde K., Fujino Y (2000), Suppression of wind-induced instabilities of a long span bridge by a passive deck-flaps control system - Part II: Numercial simulations, Journal of Wind Engineering and Industrial Aerodynamics 87 (2000) 81-91 73 Permata Robby, Yonamine Kazuhide, Hattori Hiroshi and Shirato Hiromichi , Aerodynamics and Flutter Stability of Slender Bridge Deck with Double Slot and Porous, Proceeding the 6th Civil Engineering Conference in Asia Region: Embracing the Future through Sustainability, ISBN 978-602-8605-08-3 74 Pham Hoang Kien, Hiroshi Katsuchi (2014), Wind tunnel test and evaluation of aerodynamic stability of Nhat Tan bridge, National Symposium with international participation on Vibration and Control of Structure under Wind Action, Bach Khoa Publishing House, Hanoi, ISBN 978-604-911-943-9 75 Phan Duc-Huynh, Nguyen Ngoc-Trung (2013), Flutter and Buffeting Control of Long-span Suspension Bridge by Passive Flaps: Experiment and Numerical Simulation, Intl J of Aeronautical & Space Sci 14(1), 4657 (2013), DOI:10.5139/IJASS 2013.14.1.46 76 Phongkumsing S., Wilde K., Fujino Y (2001), Analytical study on flutter suppression by eccentric mass method on FEM model of long-span suspension bridge, Journal of Wind Engineering and Industrial Aerodynamics 89 (2001) 515-534 77 Pourzeynali S., Datta T.K (2002), Reliability analysis of suspension bridges againist flutter, Journal of Sound and Vribration (2002) 254 (1) 143-162 Footer Page 132 of 89 Header Page 133 of 89 119 78 Pugsley A (1949), Some experimental work on model suspension bridges, Struct Eng 27 (8) 79 Reinhold T.A., Brinch M., Damsgaard A (1992), Wind tunnel tests for the Great Belt Link, in: A Larsen (Ed.), Aerodynamics of Large Bridges, Balkema, Rotterdam 80 Sarkar Partha P., Caracoglia Luca, Frederick L Haan Jr., Hiroshi Sato, Jun Murakoshi (2009), Comparative and sensitivity study of flutter derivatives of selected bridge deck sections, Part 1: Analysis of inter-laboratory experimental data, Engineering Structures 31 (2009) 158-169 81 Savage M.G., Larsoe G.L (2003), An experimental study of the aerodynamic influence of pair of winglets on a flat plate model, Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 113-126 82 Scanlan R.H (1999), Developments in aeroelasticity for the design of long-span bridges, Springer, Tokyo 83 Scanlan R.H (1992), Wind dynamics of long-span bridges, Aerodynamics of Large Bridges, A.Larsen (ed.) â 1992 Balkema, Rotterdam, ISBN 9054100427 84 Scanlan R.H., Sabzevari A (5/1967), Suspension bridge utter revised, Preprint No 468, Amer Soc Civil Eng., National Meeting on Structural Engineering 85 Shambhu Sharan Mishra, Krishen Kumar, Prem Krishma (2008), Multimode flutter of long-span cable-stayed bridge based on 18 experimental aeroelastic derivatives, Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 83-102 86 Shigeru Watanabe, Koichiro Fumto (2008), Aerodynamic study of slotted box girder using computational fluid dynamics, Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 1885-1894 87 Starossek Uwe, Scheller Jửrn (2014), Novel active mass damper for control of structural vibrations, National Symposium with international participation on Vibration and Control of Structure under Wind Action, Bach Khoa Publishing House, Hanoi, ISBN 978-604-911-943-9 Footer Page 133 of 89 Header Page 134 of 89 120 88 Starossek Uwe, Aslan Hassan, Lydia Thiesemann (2009), Experinental and numerial indentification of flutter derivatives of nine bridge deck sections, Wind and Structures an International Journal, 12(6) 89 Strommen Einar (2006), Theory of Bridge Aerodynamics, Springer-Verlag Berlin Heidelberg 90 Sukamta, Fumiaki Nagao, Minoru Noda and Kazuyuki Muneta (2008), Aerodynamic Stabilizing Mechanism for a Cable Stayed Bridge with Two Edge Box Girder, BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications, Milano, Italy, July, 20-24 2008 91 Sumiu Emil, Miyata Toshio (2006), Design of Buildings Bridges for Wind, Wiley, John Wiley & Sons, INC 92 Sumiu Emil, Scanlan Roberth (1985), Wind Effects on Structures, John Wiley & Sons 93 Tanaka H (1992), Similitude and modeling in bridge aerodynamics, Aerodynamics of Large Bridges, A.Larsen (ed.), Rotterdam, ISBN 9054100427 94 Tongji University (2003), Wind tunnel study on wind-resistant performance of the Thuan Phuoc bridge in Danang city, Vietnam 95 Tongji University (2/2011), Wind Tunnel Testing of Tran Thi Ly Bridge of Da Nang City, SR Vietnam 96 Tran Dat Anh, Hiroshi Katsuchi, Hitoshi Yamada, Mayuko Nisho (2014), Numerial analysis for effect of flap on the wind flow across box girder section, Journal of Structure Engineering Vol.60A, JSCE (March 2014), 387-396 97 Tubino F (2005), Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridge, Journal of Wind Engineering and Industrial Aerodynamics 93 (2005) 929-950 98 Uejima Hidesaku, Matsuda Kazutoshi, Yabuno Masashi (8/2006), Wind Tunnel Test for Binh Bridge in Vietnam 99 Ukeguchi M., Sakata H (11/1966), An investigation of aeroelastic instability of suspension bridges, Proceedings of the Symposium on Suspension Bridges Footer Page 134 of 89 121 Header Page 135 of 89 100 Versteeg H.K., Malalasekera W (2007), An Introduction to Computational Fluid Dynamics The Finite Volume Method, Second edition, ISBN 978-0-13127498-3, Pearson Education Limited 101 Walther R., Houriet B., Walmar Isler, Pierre Moùa, Jean-Franỗois Klein (1999), Cable stayed bridges, Second edition, ISBN 7277 2773 7, Thomas Telford Publishing 102 Wang Qi, Liao Hai-li, Li Ming-shui, Xian Rong (2009), Wind tunnel study on aerodynamic optimization of suspension bridge deck based on flutter stability, The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan 103 Wardlaw R.L (1992), The improvenment of aerodynamic performance, Aerodynamics of Large Bridges, A.Larsen (ed.) â 1992 Balkema, Rotterdam, ISBN 9054100427 104 Wilde K., Fujino Y., Kawakami T (1999), Analytical and experimental study on passive aerodynamic control of flutter of a bridge deck, Journal of Wind Engineering and Industrial Aerodynamics 80 (1999) 105-119 105 Wolfhard Zahlten, Renato Eusani (2006), Numerial simulation of the aeroelastic response of bridge structures including instabilities, Journal of Wind Engineering and Industrial Aerodynamics 94 (2006) 909-922 106 Xiang Haifan, Ge Yaojun (2007), Aerodynamic challengens in span length of suspension bridges, Front Archit Civ Eng China, 1(2) 153-162 107 Xilaobing Liu, Zhenqing Chen, Zhiwen Liu (6/2012), Direct simulation method for flutter stability of bridge deck, The Seventh International Colloquium on Bluff Body Aerodynamics and Application (BBAA7), Shanghai, China 108 Xinjun Zhang, Bingnan Sun, Wei Peng (2003), Study on flutter characteristics of cable-supprted bridges, Journal of Wind Engineering and Industrial Aerodynamics 91 (2003) 841-854 109 Footer Page 135 of 89 Xu You-Lin (2013), Wind Effects on Cable-Supported Bridges, Wiley 122 Header Page 136 of 89 110 Yang Yongxin, Ge Yaojun, Xiang Haifan (2007), Flutter control effect and mechanism of central-slotting for long-span bridges, Front Archit Civ Eng China, 1(3) 298-304 111 Yokohama National University (9/2007), Final Report on Wind Tunnel Testing and Evaluation of Aerodynamic Stability of Nhat Tan Main Bridge Footer Page 136 of 89 I Header Page 137 of 89 PH LC Ph lc A: Phng phỏp step-by-step ca Matsumoto [57[63] Phng trỡnh chuyn ng ca kt cu phõn tớch flutter un-xon c vit: C h K h U B KH* h KH* B K H* K H* h mh 0h 0h U U B (A.1a) h B h C0 K U B2 KA1* KA*2 K 2A*3 K A*4 (A.1b) I U U B hoc h B h U B KH1* KH*2 K H*3 K H*4 (A.2a) h 20h 0h h 0h h 2m U U B 20 02 ú h B h U B2 KA1* KA *2 K A*3 K A*4 (A.2b) 2I U U B 20h K 0h K ; 20 ; m I (A.3) 0h C0h C 0h C C0 ; 2m0h K 0h m 2I0 K I (A.4) Bc 1: Xỏc nh cỏc thụng s dao ng t theo phng ng v xon Cỏc thụng s ny c xỏc nh t cỏc phng trỡnh dao ng t do; ngha l v phi cỏc phng trỡnh (A.1a,b) bng khụng Khi ú cỏc thụng s dao ng t c xỏc nh cỏc phng trỡnh (A.3) v (A.4) Bc 2: Gii phng trỡnh dao ng phng ng liờn quan n cỏc lc kộp Phng trỡnh dao ng phng ng cú th c vit di dng m rng nh sau: B2 B2 * B3 B3 * h 0h0h h 0h h F H1*h F H h F H *2 F H m m m m hoc B2 * B3 B2 B3 * h 20h0h F H1* h 0h F H h F H*2 F H (A.5) m m m m Footer Page 137 of 89 II Header Page 138 of 89 B3 B3 * * h *h *h h *2 h H F H h m F m (A.6) ú *h v *h l t s cn v tn s vũng ca h kt cu-giú theo phng ng v c xỏc nh nh sau: *2 h 0h B2 * F H m (A.7) B2 F H1* *2 m h B2 * H 20h m F 20h 0h (A.8) chuyn cỏc lc kộp liờn quan n ta xon v phi ca phng trỡnh (A.6) thnh cỏc ngoi lc thun nht, chuyn v xon cú th c vit di dng hm sin nh sau: sin t cos t sin t (A.9) Thay phng trỡnh (A.9) vo (A.6), ta c 3 B B * h *h *h h *2 F H*2 sin t F H sin t h h m m (A.10) v nghim ca nú s l h h h1 h ú (A.11) h l nghim ca phng trỡnh dao ng t do: h 2*h *h h *2 h h (A.12) h1 v h l nghim ln lt ca phng trỡnh dao ng cng bc: B h 2*h *h h *2 F H *2 sin t h h m (A.13) B * h 2*h *h h *2 F H sin t h h m Bc 3: Gii nghim h , h1 v h (i) Gii nghim h ca phng trỡnh (A.12) Nghim h cú dng: Footer Page 138 of 89 (A.14) III Header Page 139 of 89 * h h eh t sin *h t (A.15) Tuy nhiờn, vỡ ban u h khụng dao ng nờn nghim ca h cú th b qua (ii) Gii nghim h1 ca phng trỡnh (A.13) Nghim h1 cú dng: h1 h1 sin t h1 B3 F0 H *2 m *2 h 2 *2 h B3 F0 H*2 m *2 h (A.16) *2 h (A.17) *2 h *2 *2 h h 2*h *h tan *2 h (A.18) thun tin quỏ trỡnh tớnh toỏn, cú th vit li nh sau: B3 F0 H *2 m h1 *2 h (A.19) *2 h *2 *2 h 4h h1 h1 sin t (A.20) vi H*2 v H*2 (iii) Gii nghim h ca phng trỡnh (A.14) Nghim h cú dng: h h sin t h2 B3 F H *3 m *2 h 2 *2 h B3 F0 H *3 m *2 h (A.21) *2 h *2 *2 h h 2*h *h tan *2 h thun tin quỏ trỡnh tớnh toỏn, cú th vit li nh sau: Footer Page 139 of 89 (A.22) *2 h (A.23) IV Header Page 140 of 89 B3 F0 H *3 m h2 *2 h (A.24) 02 *2 h *2 *2 h h h h sin t (A.25) vi H*3 v H*3 Nh vy, nghim ca phng trỡnh dao ng thng ng s l h h1 h h1 sin t h sin t h h h h10 cos t h cos t Trin khai h v h v chỳ ý rng sin t v cos0 t , ta c h h1 sin t h sin t h1 sin t cos1 h1 sin 1cos t h sin t cos h sin cos t h1 cos1 h1 sin h cos2 h sin (A.26) h h10 cos t h 20 cos t h10 h1 cos1 h10 sin h cos2 h sin cos1 h10 sin h cos2 h sin (A.27) Bc 4: Gii phng trỡnh dao ng xon Ta cú phng trỡnh dao ng xon: 20 02 h B h U B2 KA1* KA*2 K A*3 K A*4 2I U U B v c vit li nh sau: B4 B4 * B3 B3 * 20 02 F A*2 F A3 F A1*h F A 4h (A.28) I I I I Trin khai thnh phn lc t kớch theo phng ng v phi nh sau: B3 B3 * F A1*h F A 4h I I Footer Page 140 of 89 V Header Page 141 of 89 B3 F A1* h1 cos1 h10 sin h cos2 h sin I B3 * sin h cos2 h sin F A h1 cos1 h1 I B3 B3 2F m I *2 h *2 h 2 *2 h *2 h A1* H *2 cos1 F A1* H *3 cos2 FA*4 H *2 sin1 2F * * * * * * * * A H sin1 *2 A1 H sin1 F A1 H sin2 F A H cos1 2F A*4 H*2 cos (A.29) Thay phng trỡnh (A.29) vo (A.28), chỳ ý rng i vi mt n nh xon tn s flutter cú th c tớnh gn ỳng bng tn s xon F , ta cú B3 B3 F2 m I *2 h B B * 20 02 F A*2 F A I 2 I *2 *2 4h *2 h h A* H* cos A* H* cos A* H* sin A* H* sin F F F F A F * H*2 sin1 2F A1* H*3 sin 2F A*4 H*2 cos1 2F A*4 H*2 cos2 (A.30) Phng trỡnh (A.30) cú th c vit li di dng chun nh sau: 2* * *2 ú * 0 B2 B4 2F F m I *2 h B4 F A*2 A1* H *2 cos1 2 I 2 *2 *2 4h *2 h h A1* H *3 cos2 A*4 H*2 sin1 A*4 H *3 sin1 Footer Page 141 of 89 (A.31) (A.32) VI Header Page 142 of 89 *2 B2 B4 2F F m I *2 h B4 * A1* H *2 sin1 F A3 I 02 *2 h *2 *2 h h A1* H3* sin2 A*4 H*2 cos1 A*4 H*2 cos2 (A.33) Bc 5: Tỡm iu kin mt n nh xon Mt n nh xon xy ch t s gim chn * Hn na, gim logarit c tớnh * 2* nờn iu kin mt n nh xon s l * , ngha l B2 B4 2F B * m 2I *2 h A A1* H *2 cos1 2 2I 02 *2 h *2 *2 h h A1* H *3 cos2 A*4 H *2 sin1 A*4 H *3 sin1 / *2 Footer Page 142 of 89 (A.34) VII Header Page 143 of 89 Ph lc B: Cỏc bc phõn tớch n nh flutter ca kt cu nhp cu Thun Phc bng hm giú s (1) Xỏc nh cỏc thụng s ng lc c bn ca kt cu: m, I, , 0h , , 0h v , Re; sau ú tớnh cỏc thụng s ng lc ca mụ hỡnh mụ phng; (2) Khi ng GAMBIT, to cỏc im, cnh v mt, v chia cỏc on thng theo t l thớch hp to li (Hỡnh B.1); Hỡnh B.1 To mụ hỡnh GAMBIT (3) To li v cỏc iu kin biờn (Hỡnh B.2); Hỡnh B.2 Min to li GAMBIT Footer Page 143 of 89 VIII Header Page 144 of 89 (4) Khi to ANSYS FLUENT v a li ó chia GAMBIT vo FLUENT (Hỡnh B.3) v kim tra li; Hỡnh B.3 a to li t GAMBIT vo FLUENT (5) Cỏc thit lp chung cho bi toỏn, mụ hỡnh dũng chy khụng khớ, cỏc c tớnh ca vt liu, iu kin vo; (6) nh ngha hm dao ng xon, un; (7) Thit lp li ng; (8) Thit lp tin kt qu tớnh toỏn cỏc h s lc tnh CLv CM; (9) Khi to cỏc iu kin gii nghim; (10) Chy chng trỡnh v lu kt qu; (11) Xỏc nh cỏc h s lc tnh CL v CM ng vi mt tc dũng Ui theo N bc thi gian phõn tớch; v iu chnh bng phng phỏp bỡnh phng ti thiu S liu di õy c phõn tớch vi N bc thi gian (t=10 -3s): Footer Page 144 of 89 Thi gian tớnh toỏn Giỏ tr CL(t) Giỏ tr CM(t) 1.00E+00 1.00E+00 -3.16E-02 -3.15E-02 -1.33E-03 -1.34E-03 1.01E+00 -3.11E-02 -1.39E-03 1.01E+00 1.50E+00 -3.10E-02 1.95E-03 -1.40E-03 -3.42E-03 1.50E+00 1.18E-03 -3.47E-03 IX Header Page 145 of 89 2.00E+00 8.25E-03 -2.28E-03 2.00E+00 8.32E-03 -2.36E-03 (12) Thit lp cỏc ma trn F v C phng trỡnh (2.7c,d) Vớ d: Ma trn {F} Ma trn {C} -0.03160260 -0.00133034 0.00435200 0.00000000 0.00359941 0.00000000 0.00000000 0.00435200 0.00000000 0.00359941 -0.03151410 -0.00134064 -0.03143580 0.00430394 0.00000000 0.00425509 0.00365673 0.00000000 0.00371347 0.00000000 0.00430394 0.00000000 0.00000000 0.00365673 0.00000000 (13) Tớnh toỏn cỏc vi phõn flutter theo phng trỡnh (2.6) ng vi mt tc dũng Ui v kt qu l: Giỏ tr cỏc vi phõn khớ ng A*i, H*i H*1 -0.829 H*4 0.465 [X]i A*1 0.102 A*4 -0.048 Giỏ tr cỏc vi phõn khớ ng A*i, H*i H*2 -0.870 -0.183 H*3 [X]i A*2 0.009 0.044 A*3 (14) Thc hin li t bc (8) n (13) ng vi cỏc tc dũng Ui khỏc Kt qu tớnh toỏn c th hin hỡnh B.4 (15) Theo Ph lc A v hỡnh 3.1, tin hnh xỏc nh quan h tng cn h kt cudũng khớ ng vi cỏc mt tc dũng Ui T ú tc flutter ti hn Ucri c xỏc nh ng vi tng cn bng khụng Hỡnh B.5 th hin quan h gia tng cn kt cu-dũng giú vi tc dũng ng vi gúc ti 0o T õy, tc flutter ti hn ca kt cu nhp Thun Phc c xỏc nh (16) Thc hin t bc (1) n (15) ng vi cỏc gúc ti ca dũng khỏc Bng B.1 th kt qu tc flutter ti hn theo cỏc gúc ti -3 o, 0o v +3o Footer Page 145 of 89 X Header Page 146 of 89 Hỡnh B.4 Cỏc vi phõn flutter theo tc giú trit gim Hỡnh B.5 Quan h tng cn vi tc dũng ng vi gúc ti 0o Bng B.1 Vn tc flutter ti hn ca mụ hỡnh Gúc ti +3 -3 Footer Page 146 of 89 Vn tc giú mụ hỡnh (m/s) Flutter xon Flutter un-xon (1DOF) (2DOF) 15.4 12.4 15.5 12.8 15.2 13.4 ... TỔNG QUAN NGHIÊN CỨU ỔN ĐỊNH FLUTTER TRONG CẦU HỆ 12 1.2.1 Các nghiên cứu phân tích toán flutter 12 1.2.2 Các nghiên cứu biện pháp nâng cao ổn định flutter 19 1.2.3 Các nghiên cứu ổn. .. Chương 1: TỔNG QUAN NGHIÊN CỨU DAO ĐỘNG FLUTTER TRONG CẦU HỆ TREO NHỊP LỚN CHỊU TÁC ĐỘNG CỦA GIÓ 1.1 DAO ĐỘNG FLUTTER TRONG CẦU HỆ TREO 1.1.1 Các tượng khí động đàn hồi Cầu hệ treo loại kết cấu phận... trình cầu hệ treo thời gian tới đặt cần thiết nghiên cứu chuyên sâu vấn đề kiểm soát ổn định khí động flutter ngành xây dựng cầu Việt Nam Vì vậy, đề tài Nghiên cứu biện pháp nâng cao ổn định khí động