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115 Tuyen tap cdng trinh Hdi nghi Cff hoc toiin qudc Ky idem 30 ndm Vien Ca hoc vd 30 ndm Tap chi Cff hoc Hd Ndi, ngciy 8-9 74/2009 Phan tfch nhay cam ciia dam co vet mit bang phuong phap bien doi Wavelet Nguyen Thj Hien Luong , Ly VTnh Phan Khoa Xdy dimg, Triedng Dgi hge Bdch khoa - DHQG -HCM Tdm tdt: : Bdi bdo phdn lich nhgy cam cho vdng ciia ddm Eider-Bernoulli cd mdt vit mil bang phuang phdp biin ddi Wavelet kit hgp vdi phuang phdp phdn tic hieu hgn Sic dung mim cue bd phdt sinh vit niet, cdc hi sd cudng icng sudt vd ca cdu niet tuyin dnh, ma tran cimg ciia phdn tic duac thiit lap di tinh todn vong ciia ddm Kit qud cho thdy vdng ciia ddm sau biin ddi Wavelet td nhgy cdm vdi vit niet vd phicang phdp phcin tich Wcn>elet cd thi sic dung hiiu qud bdi todn xdc dinh vet niet kit cdu L Gidi thieu Sir hinh va phat trien ciia cac khuyet tat (dien hinh la cae vet nirt) ket cau lam suy giam kha nang lam viec va tiioi thg ciia ket cau Van de clat la viec cd the sdm xac djnh va danh gia mirc ciia khuyet tat de dua cac bien phap thfch hgp, kjp thdi nham sira chira hay ban che anh hudng ciia ehiing Bai toan chan doan vet niit (xac djnh vi trf va sau) ket cau da va dang dugc rat nhieu nha nghien cuu quan tain [1-7] G Owolabi va cdng sir (2003) sir dung cac tan sd rieng dac thuc nghiem de xac djnh vj trf va chieu sau vet nirt [2] P Saavedra va L Cuitino (2001) nghien ciru viec xac djnh vet mit va irng xir dgng bgc ciia dam cd vet mit [4] N.T.Hien Luong vaN.D Thach (2006) da sir diing phuong phap phan tir bu'u ban ket hop vdi giai thuat di truyen de chan doan vet nirt ket cau dam, dd vet nirt dugc mo phong lam suy giam cung dam theo qui luat tuyen tinh [6] Bai bao nghien cuu kha nang ung dung phan tfch Wavelet bai toan chan doan vet nirt thdng qua phan tich nhay cam cho vong dam nirt Dam cd mdt vet nirt dugc ind phong dua tren phuong phap phan tir huu ban (PTHH) ket hgp cac he sd mem cue bg phat sinh vet mit, cac he so cudng irng suat va ly thuyet co' bgc nirt tuyen tinh Tir do, ma tran cirng ciia ket cau dugc thiet lap lam co sd de phan tfch anh hudng ciia vet nirt den tan so rieng, tim vong dam va danh gia nhay cam ciia vdng S3u thuc hien bien doi Wavelet Qua ket qua thu dugc, ta cd the danh gia kha nang ciia phuong phap bien ddi Wavelet bai toan chan doan vet nirt ket cau Mo hinh PTHH cua dam co vet niit 2.1 Md phdng vet niii Dimarogonas va Gounaris (1998) [3] da mo phong su suy giam cirng cue bd dam vet nut thong qua cac mem cue bd phat sinh tai vj trf vet nirt Chuyen vi phat sinh theo cac hudng tac dung ciia lire Pj theo ly thuyet ciia Castigliano: d u, = • — dp \j{y)dy (1) Ngu}>in Thi Hiin Luong, Ly VTnh Phan 116 J(y) dugc ggi la ham mat nang lugng bien dang: (2) V V / V I vdi: K|, Kn, Km Ian lugt la cac he sd cudng iing suit (Stress intensity factor- SIF) irng vdi ba mode co bgc nut tuyin tfnh ([5]).Cdn mddun E'=l trudng hgp iing suat phang va E ' ' E = ^ trudng hop bien dang phang, ( a = 1+v) Do mem cue bd phat sinh duge dinh 1-v" nghTa nhu sau: C ^ ^ = ^1 (3) |j(y)dy Ket hgp cae phuong trinh tren suy ra: d' b llh.iK, ^'. ^l Eb dP-.d?, „, ,=0 (4) dz dy y=0 do: ei„=a cho mode in=I va e.^ =1 cho mode in=II hoac m= III 2.2 Ma trdn cirng cua phdn td ddm cd vet nirt IVIi M'^i TH Hinh Can bang luc phan tir dam cd vet nirt Vdi trudng hgp dam phang chi ed hai phan lire tac dung la lire cat va mdmen (bo qua anh hudng eiia lire dgc) thi dieu kien can bang lire cua phan tu nut cd the bieu dien nhu sau: (T, M; T,,, M;„)"=[T](T,„ M„,7 (5) vdi L la chieu dai phan tir thi ma tran chuyen doi [T] cd dang: -1 -L [T] = - 1 (6) Ma tran cirng eiia phan tir dam cd vet nirt dugc djnh nghTa nhu sau [5]: [Ke] = [T]'[Cr[T] (V) Tir cac phuong trinh tren ta tim dugc cac phan ciia ma tran mlm phat sinh: C „ = — + B , ( B , L ^ + B h ^ - ) , C , = C „ = — - + L B , B , , C , , = - ^ + 72B,B, (8) phdn tich nhgy cdm ciia ddm cd vit niet bdng phuang phdp bien ddi Wavelet 17 TC(I-V') dd:B| =——-——, B^ = fsF,(s)ds, B3 = fsF„(s)ds Ebli (9) vdi s = — la ti le giua chieu sau vet mit va chieu cao dam h Cuoi ciing ta tim dugc ma tran cung ciia phan tir dam cd mdt vet nirt nhu sau: C C 22 [Kc] = c C -C c L-C 22 ^^' 2'' ''' I ^^ 27 ^ — L^22 -C 21 IT*-' 21 ~ ^ 2 ^ I C c 22 ^ I L-C V—•,., L T" V— J , C 21 V—• , I ! _ V— j (10) -C 22 -C 21 c Ma tran khdi lugng ciia phan tir cd vet nut gia djnh la khdng ddi so vdi trudng hgp khong cd vet nirt, va dugc xac djnh theo cdng thuc: M = 22L 4L^ 4L" 54 -13L" mL 156 22L 13L -3L' 420 54 13L 156 -22L -13L -3L' -22L 4L- (11) Tan so rieng ciia dam cd vet nut dugc xac dinh tir phuong trinh tim trj rieng: (12) det(K,-(D'M)=0 Co" sd phan tich Wavelet Phan tich Wavelet dugc bat dau bdi viec lira chgn mdt ham Wavelet co ban (Mother Wavelet) \(/(x), nd se dugc keo gian hoac nen bdi ty le a, va djeh chuyen khdng gian bdi djeh mirc b de tao mdt tap hgp cac ham \\i^^ ( x ) : M^a.l Va- (13) V Bien ddi Wavelet lien tuc la tdng tren toan mien thdi gian ciia tin hieu dugc nhan bdi phien ban ty le va djeh miic cua Wavelet co ban tao tap hgp cac he so: C(a,b) = - ^ ff(x)M; ^^— dx= ff(x)vi;,,(x)dx (14) vdi a va b la cac sd thuc va a phai la sd duong Cac he sd C(a,b) cho biet mu'c tuong quan giu'a mdt ham Wavelet va tin hieu dugc phan tich Vi the, cac thay ddi dot nggt f(x) se tao cac he so Wavelet co bien Idn, day chinh la dac diem de dua co' sd cua phuang phap nhan dang vet nirt Bien doi ngugc ciia Wavelet cho phep tai tao tin hieu tii' cac he sd C (a, b) nhu sau: fW = ^ K \\i I jC(a,b)v|/ a=-co -00 a,b da (x)db- (15) Nguyin Tin Hiin Luang, Ly VTnh Phan 118 Sii' dung cac gia trj rdi rac ciia ty le va djeh miic: a=2j, b=k.2j d l thuc hien bien doi Wavelet rdj rac (Discrete Wavelet Transform - DWT): q , =2-J'' jf(x)M;(2-Jx-k)dx= (16) |f(x)t[(j_,(x)dx Tin hieu dugc tai tao lai tii' cac he sd thdng qua biin ddi Wavelet ngugc (Inverse discrete Wavalet transform- IDWT): f(x)=XXq,2-^"v|;(2-^x-k) (17)' j=:-COk = -CO Xet d d p phan tfch la J, sii' dung phuong trinh (16) ta thu dugc tap hgp cac he so chi tilt: CO cDj(lc)= jf(x)r|/.,,(x)dx • (18) -co Sii' dung ty le diadic d d p J, phuong trinh (18) cho ta tap hgp cac he sd xap xi: CO c A , ( k ) = jf(x)^j,,(x)dx (19) — CO Phien ban rai rac cua dang tai tao tra thanh: fW = Z | Z^Di(l^)^^.k« 1+ ScAj(K)(^j,,(x) j=-co\k=-co J (20) k=-oo Qh xac djnh vet nut ket cau ta chi can quan tam den cac chi tiet ciia tin hieu Anh hu'ong cua vet nut den tan so rieng (bai toan thuan) De xem xet tin cay cua chuang trinh PTHH viet tren Matlab, ta se so sanh ket qua tfnh toan bai toan thuan ciia dam cd cac dae trung hinh hge, vat lieu tir [2] vdi ket qua thuc nghiem Dim nhdm ngam hai dau vdi cac dac trung: h = 25.4inm, b = 25.4inin, E = 70 kN/min2, p = 26.96 X 10-13 kN/inin3, ^ = 0.35, L = 650inm Dat Lcr la khoang each tir diu ngam ben trai din vj tri vet mit Ket qua tinh toan tan so rieng the hien d hinh va bang dudi day [7] s u I'H.'W D>;ii cvjA r.'XN St) ntv.'-.' vi m i v.-\ cTiutn; S.MJ v u r m n 1,000'j UTHAYlX;ir l.'.'M'.'i.MS-.'.-'TH O V I T R I VA CHTBl • o - a=0.2h i - + - 0=0 3h ! •1 a=0 ih j •-» 9395 O530 i z '''\ / ' • \ ~~.' -^ n flsas VFH >:i T r ~' '~^-""/'' ,-^ '""""/ S.M ', * / \' ;' tf.ysi) \ ,.' f= 9975 ' 0.S97 0.9065 n.M6 0.99i5 Hinh Anh hudng ciia vet nut den tan so thir 0,1 0.1' 0.-J t O.b a.i0.4 Vl 111 I •1 m i l ' c-l, (1.' uu Tur^AJN^ 3.74 9.28 a.e2 s.se 7".9 7.44 e.ss e.52 e.oG 5.6 S.1-4 4.e8 22 76 3.3 © 2.3S &2 46 SO -t O O l i m e < o r s p a c e ) t» SO ioo t i m e (or s p a c e ) b Hinh Phan tfch CWT bdi Wavelet bior6.8, vet nirt a = 0.1 h d Lcr = 700inm tjj-icjT^'^ci-cj::!'.'" ui-:.''\Jvi 9.74 9.2S e.s2 - a.62 6.3G 7.9 7.44 e.98 s.se e.52 7.9 7.44 G,9S 6.52 e.oe e.os 5.6 5.14 4.68 4.22 7S 3 84 2.36 92 46 5.6 5.14 4.6a 4.22 3.76 3.3 S4 2.3S 1.92 46 SO 100 t i m e ( o r s p a c e ) bi J;VJ, »} I •' 50 t i m e
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