Phan tich hien lu'p'ng truyen song trong dam cd vet nirt ngang bang phu'cng phap WSFEM
Analysis Of Wave Propagation Phenomena In Beam With Transverse Crack By WSFEM
Ngay nhan bai: 29/11/2014 Nguyen Thi Hien LiTdng, Ngay sim bai; 18/6/2015 B^,; Qugj. j;„f^^ Nguyin Tiianh Tu, Ngay chap nhan dang: 18/7/2015 ^^^.^ ,^^^„^ ^ j ^ ^
TCMTAT
Bii bao nay trinh bay mpt phuong phap xac dinh vet ncit trong ket cau d i m sii dung phUcmg phap phan tti hflu ban pho Wavelet (Wavelet Spectral Finite Element Method-WSFEM). WSFEM diiac phdt trien de nghifin ciiu hifin tU<?ng truyin song din h6i cho kit c3u dam ID, lim cd sd cho bii toan xac djnh vet mit. Vet nilt trong dam console dUc^c mo hinh h6a bang 16 xo c6 do mem tifdng difdng. NhQng van de chinh lien quan den viec phat hi?n vi tri va dp sau vet nijEt trong dam dUpc trinh bay trong cac tnlcfng h^fp cij the ciia dam Bernoulli m6 rpng vdi ket qua dat dUdc chinh xac va dang tin cay.
TH khda: Truyen sdng, vet ntjtt ngang, xdc dinh vet niit, phUdng phdp phdn ttl hHu han pho Wavelet.
ABSTRACT
This p £ ^ r presents a method for crack identification in beam structure using WSFEM {Wavelet Spectral Finite Element Method).
WSFEM is developed for studying the phenomenon of elastic wave propagation in 1-D beam structure. It is a basis for solving the inverse problem identifying cracks in beams. The cracks in the cantilever beam is modeled as equivalent springs. The main issues regarding crack location and depth detection in beams are discussed in the particular case of Extended Euler-Bernoulli beam with accurate and reliable results.search show that with the same Intent increased.
Keywords: Wave propagation, transverse crack, crack identification, Wavelet spectral finite element method.
PGS.TS. Nguy£n I h i Hien Lifdng
Giing vien, Khoa Ky Thu^t Xay D^ng, Tnfdng Dgi Hpc Bach Khoa - Dai Hoc Quoc Gia Tp.HCM Email: [email protected]. vn
Dien thoai: 0933111792 TS. Bui Qu6c Tinh
D e p t of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan
EmaiL [email protected] ThS. Nguyen Thanh Tii
Giing vi&n, Khoa Ky thugt xiy difng, Tnl6ng Dai hpc Ky thuat - Cong nghe Can Thd, 256 Nguyen Van Cii, Q.Ninh Kieu, TP. Can ThO Email: [email protected]
Difn thogi: 01689952871 NCS. Nguyen I h i n h Vinh
Giing vien, Khoa Khoa Xiy dUng, Tn(6ng Dai hoc Tien Giang, 119 Ap Bac, Phddng 5, My Tho, Tien Giang Email: [email protected]
Di?n thoai: 01668382118
7 6
Giti thieu C d s d i y thuyet:
Bien doi Wavelet mdi duoc surdung trong linh xay dung, mac dCi no dugc
sCrdung Whh pho bien trong nganh ky thuat dien va nganh truyen t h d n g 2.1 Mo hinh dam co mot vet nult de mo Xi dc dgc tinh v^ t6ng hpp cac tin hl^u t h d i gian. Cac cong eg
bi^n ddi Wavelet duoc the hien trong ky thuat ket cau bang each gi^i cac phuong trinh vi phan thu6ng va vi phan neng trong bai toan ddng lUc [1-8].
NhOIng b^i toan dong luc trong ket cau cong trinh co hai loai: Loai thiJ nhSt sCrdung tSn so thap, duoc goi la bai to ^n ddng lUc hoc; loai thu"hai la sCrdung Xin so cao va dUpc gpi \h bai toan truyen song. Hau het cac bai toan trong ket cau cong trinh deu thuoc logi t h i l nhat, trong do uhng xCr cua tOcin b d ket cau chi sirdung vai mode dao ddng d^u tien.Truyen song la mpt h i i n tUpng da phuang thUc sCr dung mode dao dong vdi tan so cao C^c cdng cy phSn tfch thong thu'dng n h u phuong phap phan tCr hOu han khdng thi xil ly nhCmg bai toan nay do hgn che ve each md hlnh va tinh toan phiJc tap. Lua chpn duy nhat cho vhn 3i nhy la dUa tren phuong phap bi^n doi.
Phan tich Fourier la k y t h u a t bien doi tin hieu til mien thdi gian sang mien tan so. Vdi nhieu tin hieu, phan tich Fourier rat hQu fch vi noi dung tSn so cCia tin hi^u la rat quan trpng. Phep bien d6i Fourier c6 hieu qud khi phan tich dc tfn hi&u tu3n hoan, thuan ldi cho dc phep chap tin hieu.
Tuy nhien, ph4p bien do! Fourier van c6 nhijng han che. Khi bien doi sang mien tan sd, t h d n g tin t h d i gian da bi mat. Neu mdt thupc tinh tin hieu khdng thay ddi nhieu theo t h d i gian thi nhUpc diem tren khong co anh hudng nhieu.Nhieu tin hi^u co chCra cac thdng sd ddng n h u t r d i , nghieng, bien ddi d ^ t ngdt, thdng tin li^c k h ^ dSu v i ket thOc cua dc sU kien.
Nhiing t h d n g s6 nhy thudng l i phSn quan trpng nhat cua tin hi^u, va phan ttch Fourier khdng thfch hpp 3i phat hi6n chOng
Phuong phap SFEM dUa tren bien doi Fourier Ici phUOng phdp khh pho bien dUdc dCing de gi^i quyet cac bai toan dong lUc hoc cong trinh lien quan d^n kich thfch vdi tan sd cao. Tuy nhien, nd co nhung han che trong viec xCrly Ceic k^tcSu hCru han va cac dieu kien bien hay cac dieu kien ban d i u k h i c khdng, va do dd hp dung phuong phap SFEM dUa tren bien 36i Fourier de g i i i cac bhi t o i n lign quan d^n kich thfch vdi tan so cao bi han che.O^ dap u'ng dUdc yeu cau d d phSn g i i i on djnh vdi cac tin hieu cd nhieu t h l n h p h i n thdi gian va tan so, ta c l n dCing mdt phuang p h l p bien ddi sao cho d d p h i n g i i i thdi glan va tan so c6 the thay doi mpt c i c h thich nghl vdi dac t i n h cCia tin hieu tren mat phSng thdi gian v l tan s d Phan tich Wavelet cho ph^p sil dyng c i c k h o i n g thdi gian dai khi ta can t h d n g tin t i n sd thap chinh x l c han, v l m i l n n g l n hdn doi vdi thdng tin tan so cao.
Cd nhieu loai m d hlnh vet nuit ap dung cho phUdng p h l p PTHH ddpc sCf dung cho dam, m d hlnh vet nut thay doi t i ^ t dien, md hinh vet nut dupc m o t l n h u Id xo, mo hlnh vet ndt dang cUa va chCrV,... Do khd khan trong viec chuyen cac cdng thu'c thiet lap cho c i c md hinh vet ndt t d phUdng phap PTHH sang phUdng p h l p WSFEM, md hinh Id xo tUong dddng dddc sCr dung de k h i o s i t hi&n t u p n g truyen sdng trong d i m cd vet nut bdi tfnh don g i l n cua nd ( h i n h l ) .
Hlnh 1. Md hlnh dam cd mdt v^t nut
Phuang trinh dao ddng cOa d i m c6 vet ndt van dupc giCr nguyen, vet ndt duoc thay bSng Id xo vdi c i c dieu kien tuong thfch Dam dUdc chia t h l n h nhieu doan lien ket vdi nhau tai vet nCrt bdi c i c 16 xo v l n g o l i yeu cau thda man hai dieu kien bien, can p h l i thda man dieu kien tUOng thich tai cac vet ndt [11], [12], [13].
2.2 Ma tran do ciJing cila phan tiled vit ndt ddpc md hinh b i n g 16 xo tdong dddng
Wavelet ddpc sCr dung hieu q u i trong viec xCr ly cac tin hieu v l g i l i c i c phUdng trinh vi phan [1 -4]. Bi^n ddi Wavelet da ddpc dng dung de glai va p h i n tich c i c bai toan trong cd hoc [5-7].Vi6c sd dung wavelet trong co hoc cd t h ^ duoc dng dung nhu phan tich cac dng x d c o hoc di khai t h i c cac t h d n g so md hlnh, khd nhieu, cac glai phap thiet hai vv... Do d d co the g i i i c i c b l l toan ket c l u ddng Idc va c i c bai t o l n truyen sdng b i n g phddng p h l p SFEM dda trfin bi^n doi Wavelet.
Trong b i i b l o nay, WSFEM ddpc phat trien de nghien cdu hien tddng t r u y i n sdng d i n hoi cho k i t c l u dam Euler-Bernounlli m d rdng trong trudng h p p khdng ndt va cd ndt; c i c ket q u i rat d i n g tin cay ddOC so sanh vdi phdOng phap FEM, phdong p h l p LSFEM [9] va md hinh ranh ndt CO be rdng I p dung WSFEM [10].
Hinh 2. Mo hlnh phan t d cd vet ndt Phddng trinh chuyen vi tgi ben t r i i v l ben phai dam (hinh 2)
w,(jc) = C,e-'*''+Cje-'*>'''^^* (1)
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Trong do la chuyen vj dpc true, ^ I I chuyen vj ddng
+Tai vi tri ben trai phan tCr (x = 0):
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Chinh lech chuyin vi doc true:
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LUc dpc ben trai bing Idc dpc ben phli vet ndt:
Vdi W la ma tran 12x12
Ldc pho tie dung tai nut cd the xac dinh bing cle phdong trinh chuyin vj
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Chuyen vi ddng bin trai vet ndt bing chuyen vi ddng ben phli vet ndt:
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Mo men ben trai vet ndt bing md men ben phli vet ndt:
8^w,(x) ^d^w^jx)
Ldc cit ben trai vlt ndt bing ldc cit bin phii vet ndt:
d'w,(x) ^d'w^jx) I dx^ dx^
Chinh lech gdc xoay xac djnh nhd sau:
dwyjx) div^jx) _ d%{x) dx dx dx^
Tgi vi tri ben phli vet ndt (x = L - L,):
dx Til (6) din [12) ddac viet lai
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tran Kd de trdthanh ma tran dp cdng vudng 6 x 6 ma khong Inh hddngtf ket qui bai toan.
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Dd mem tgi vj t r i vet ndt cho phan t d thanh hdu han phd ddpc tinh dda vao d m h |i^ Castlgliano [11]
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S, IS luc tai nut tac dung nen phan tCr Nang luong bien dang d4o U khi CO vet nilt duac viet:
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Vdi n IS he so Poisson. A la dien tich cua vet nUt 1^ IS he so cudng do Ung
suat i(hi hlnh thanh vet ndt dang mode 1 3.1 Khcio sat d a m k h d n g n d t
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(25)Khi phan tfch truyen sdng trong d i m cantilever Euler-Bernoulli m d rdng vdi thdng sd b l i t o l n : E=70GPA, u=0.3, p=2700 K g / m ' , c h i l u d l i d i m
= 0.5m, c h l l u rdng dam b = 0.05m, c h i l u cao dam h = 0.005m. Dam Euler-Bernoulli m d rdng truyen sdng vdi hai trddng hpp song ngang va sdng doc, tai trong xung tac dung tai dau t d do cCia d i m n h d tren hinh 4.Thdngs6 tai trpng t a c d u n g tren hinh 5. H i m wavelet sd dung I I h i m M^ bleu thi moment u6n tai bi tri v l t ndt Daubechies bac N=22.
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Sau nhdng bien doi don g i l n , m d h l n h dan hoi ci!ia p h i n t d hdu han pho tai t i l t d i f n ndt d hlnh 3 ddpc viet lai
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Khi chiu I d c d p c t r u c , h e s o d d m e m d U O c t i n h : fl^ = Ebhc
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50 100 ISO 200 250Hinh 5 Ri trong xung Kinh 3 Mat cat tiet dien tai VI tri i)i}t
Khi chju lUc c i t v l moment, md hinh d i n hdi cCia p h i n t d hdu han p h 6 tai tiet dien ndt ddac viet lai n h d sau:
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TTKJI gian(s) , io"*
Hinh 6,Ung xii van toe song ngang bJng phuong phap WSFEM tai dau tir do
Hinh 9. Qng x d van toe sdng doc b i n g p h d o n g p h l p LSFEM va FEM [9] t^|
d l u t d d o c O a d a m
Cac hinh 6-9 cho thay hien t d d n g truyen sdng ngang va song d p c ^ m ^ dam b i n g WSFEM v l so s i n h ket q u i vdi FEM, LSFEM. Sd d u n g 2[}--FErti;
dam ddpc chia t h l n h 100 phan t d ket hpp I p d u n g phddng phap Newmarp' tren mien thdi gian d l g i l i bai toan truyen sdng.Trong khi sd dung WSFEM"
chi chia t h l n h 1 phan tCrvdi b i c Daubechies N=22 cd t h e t h u ddpc k l t q l i f ; t d t hdn vdi 2D-FEM. VI vay, WSFEM tfnh cho d i m console vdi thdi glan vh khoi Idpng tinh toan giam d i n g ke so vdi FEM trong cac bai toan truyin sdng.
Ket qua b l l toan thuan cho d a m console sd d u n g WSFEM so sanh vdi bll b l o [9] sd d u n g phdong phap LSFEM va 2D-FEM deu cho thay cd su phu hop chinh x l c (hinh 7, hinh 9).
3.2 K h i o s i t d i m c6 vet ndt thay doi theo do siu
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Fig.l3 Transverse Velocity Response wilh LSEM and FEM ih y.llng xil'van toe song ngang bSng phuong phap 15FEM va FEM [9| lai dau tudo ciia dam
X ^Q^ Song doc trong m i e n thoi gian
Hlnh 10. Dam console covet niit
D i m cantilever Euler-Bernoulli m d rdng cd vet ndt hlnh 10; vdi thong so bll t o l n : E=70GPA. u=0.3. p=2700 Kg/m3, c h i l u d l i dam L = 1 m, chieu rdng b
= 0.05m, chieu cao h = 0.01 m, tai trong tac dung n h d hinh 4 va hinh 5. HJm wavelet sd dung la ham Daubechies bgc N=22. V l t ndt thay ddi theo dp slu tai VI tri L^ = 0.25m vdi 3 trddng h p p : h y h = 10%. hjh = 20%, h y h = 30%.
X lO"" S o n g d o c trong m i e n thoi gian
Thoi gian(s) ^ ^Q"
Hlnh 8 Jng xilvSntoc sfing doc bSrg phumg phap WSFEM lai dau ti/do ciia dam
- Khong nui - h d m = 1 0 % - hd/h=20%
- hd/h=30%
1 V ^
Thoi gian(s}
Hinh 11. Van toe sdng doc theo thtH gian 6 diu tU do cua dam.
<h LSEM and FEM
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Tlxiigian(s) ^ m*
Hlnh 12, Van toe sfing ngang theo thirl gian tai diu tUdo cda dSm 3ua hinh 11, hlnh 12 ta thay so v6l bi^u do dam khdng ndt, eae bieu do van :dc sdng t h u dddc tai dau t d d o cua dam cd vet ndt vdi cac trddng hdp dam i d t ciJng vi tri nhdng vdi d d sau vet ndt k h i c nhau cho ra cac tin hieu bi ihieu ciJng 1 thdi gian tren bleu do vol bien d d k h i c nhau. Khi chieu s l u vet i d t tang d i n thi bien dd tin h i l u bj n h i i u do vet ndt gay ra cung tang d i n
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Thoi gian(s) , JQ"' Hinh 14 Van loc song doc lai diu tudo ciia dam vdi vet ndt hd/h=2D% thay doi theo VI tri So vdi bieu do khdng ndt thi cac bleu do van toe sdng t h u ddpc tai d i u t d do khi bi ndt vdi eac trudng hop dam ndt tai cac v i t r i khac nhau cho ra cae tin hieu bl nhieu tai cac k h o i n g thdi gian khac nhau. Oac biet vdi bieu do sdng doc, tai 3 vi tri ndt khac nhau van cho bien dd tin hieu nhieu gan nhU bang nhau.
, ,0^ Song ngang trong mien thoi gian
Hinh 13, Van toe s6ng ngang lai dau tudo ciia dSm theo [10]
jo s i n h 2 bi^u do tren hinh 12 v l hlnh 13 ta t h i y vi tri thdi gian van tdc song i g a n g b l t d l u b! n h i e u d o v ^ t ndt gay r a i l gidng nhau.Taidd s l u vet ndt i y h = 1 0 % k^t q u i b l i b l o [10) cho bieu do nhieu rd r i n g hon Khi chieu s l u lit ndt tang l^n thi m d hinh v^t ndt lo xo cho bieu d d nhieu rO hem v l bleu 3d nhieu cung gidng dang trong b l i bao [10].
t.3 K h i o s i t d Jm c6 vet niJIt thay doi theo vi trf
)3m cantilever Euler-Bernoulli m d rdng ed vet ndt n h u t r e n H.10; vdi thdng d b l l t o l n : E=70GPA, u=0.3, p=2700 Kg/m3, chieu d i l dam L = 1 m, chieu dng b = 0.05m, chieu cao h = 0.01 m, t i l trpng t i c dung n h d hlnh 4 v l hlnh i. Ham wavelet s d d u n g I I h i m Daubechies bac N=22.Vet ndtthay doi theo 'i tri vdi chifiu s i u vit ndt h y h = 20% cho sdng dpc va h y h = 10% cho sdng igang, k h i o s i t 3 trddng hop L^= 0,1m, L^= 0.25m, l^= 0.4m.
Tlioigian(s) , „}-•
Hinh IS. Van toe song ngang tai dau tudo cila dam theo thcri gian v£ VI tri vet nUt thay doi
Hinh 16.Van loc song ngang lai dautu do cda dam theo thoi gian vdi VI tri vet nA thay doi [10]
So sanh 2 bleu do tren hlnh 15 v l hinh 16 ta thay thdi gian v | n tdc sdng
ngang bj nhieu do elc vj t r i ndt gay ra 6 2 bieu d o t u o n g ddi gidng nhau.Vdi d p sau vet ndt h / h = 10% bieu do trong [10] cho ket q u i ro rang han do b l i bao [10] cd xet den be rdng vet ndt = 0.01 m
3.4 K h i o s i t Sd chuyen d p n g cua v a n toe song t r e n d a m CIc g i l t n dac trdng hlnh hoc, vat lieu cua bai t o l n duoc l l y t d bai t o l n 3 vdi cac thdng so: E = 70GPA, u =0.3, p = 2700 Kg/m3, L = 1 m, b = 0.05m, h
= 0.01m.
Khao s i t sd chuyen ddng cCia van tdc sdng tren d i m trong trddng hop dam khong co vet ndt v l dam cd vet ndt h y h = 50% tai vi t r i L_, = 60% L
Bieu d o van toe s o n g ngang truyen frong dam
Bieu do van toe s o n g d o c t m y e n trong d a m
Hinh 17 Van loc song ngang tmy^n trong dam khfing nut Bieu do van toe s o n g ngang t m y e n trong dam
0 0 1 O.Z 0 3 0 4 0.5 0.6 0 7 0 8 0 9 1 chieu dai dam (m)
Hlnh IS. Anh hufimg ciJa vet ndt (hd/h=50%)l^ bi& ^ van toe song ngang truyen trong dim theo thcri gian
Trong trddng hop d i m khdng cd vet ndt n h u hlnh 17, van tdc sdng lan truyen trong dam d^n d i u ngam mdi cd sdng p h i n xa lai nen ta thay tai k h o i n g t h d i gian 600-700|is tai dau p h l i cua d i m b i t dau nhgn ddac tin hieu bl nhiSu ddpc rd r i n g do van tdc sdng ngang lan tmyen ve Trong trddng hop d i m cd vet ndt nhd hinh 18, tai vj tri L^ /L- 60% chieu d l i dam thi ngay k h o i n g thdi gian 400-500 [is tin hieu van tdc sdng bi nhieu do vet ndt g l y ra ddOc truyen v^ d i u d i m . Do dd chi c l n do van toe sdng ngang tai d i u t d do cOa dam console sau khi t m y ^ n sdng ta cd the biet ddpc VI tri do sau v^t nilt m l khdng c i n phai khao sat tren t o l n d i m
Hinh 19 Van toe songdoctruy^n trong dim Bieu do v?i toe song doc truyen trong dam
as a* as oe diieu dai ctsrrKm)
Kinh 20. Anh hudng cua vet ndt len van toe song dot truyen trong dim (hd/h=5a%) Trong trddng hop d i m khdng cd vet ndt n h d hinh 19, sdng doc lan truydn khdng bi tan sic, tin hieu do Idc xung truyen v i o van g i d hinh dang theo thdi gian.Dda v i o hlnh 19 cd the d ^ d i n g x l c dinh ddpc v l n tfic sdng dgc lan truydn trong dam.
Trong trddng hdp d i m cd vet ndt thi i n h hddng cda vet ndt len van tfic lan truyen sdng (hlnh 20) tai vi tri 60% chieu d l i d i m cho ta t h i y ngoli tin hieu do Idc xung truyen vao cdn cd tin hieu nhieu nhd hdn chay trong dim dupc hinh thanh khi tin hieu v | n toe sdng doc chgy qua vet ndt va tin hi^u bi n h i i u do I n h hddng cila vit nilt nay Idn d i n theo thdi gian 4 . K £ t l u a n :
Vi6c s d d u n g Wavelet dda vao trong S F E M d l nit gon cac phdOng trinh vi p h i n rieng t h l n h eac phuong trinh vi phan thddng gidp g i l i b l i tohn m^l c i c h don g i l n , nhanh chong. ^ • WSFEM t d ra la mpt phdong p h l p hieu q u i , thay the cho phdOng p h l p FW 3i phan tich c i c bai toan truydn song vcfi khfii Idpng t i n h t o l n g i l m d i f l j
ke so vcfi FEM.. nth Anh hddng cila v^t niit ngang tren d i m d^n cac d i e trdng truyen s6ng
ddpc khao sat dUa v i o bi^u do van toe sdng ngang v l bieu do van tdc s6n9 dpc. Cle ket q u i thu ddpc phij h o p va chinh xac.
Sd dyng bieu do van toe sdng dpc de chan d o l n h u hai k i t c l u se cho kft q u i chfnh xac va rd rang hon so vdi bieu d6 v l n tfic sdng ngang.
Bli t o l n d i m ddpc gan vet ndt b i n g m d hinh Id xo cho thay ddpc c i c Mftl d i n g , t i n h chat cua bieu d d van tdc sdng lan truyen qua d i m bj n d t Trong bai t o l n t r u y i n sdng, viec thu tin hieu tgi 1 nut d i u t d d o cOadlmCfi the giOp ta xac d m h ddpc vi tri vh d p sSu vit ndt. Bhi t o l n ngdOc nay s6 ti4p tuc ddpe trinh bay trong c i c b l i b^o sau.
