Phan tich anh hu'dng cua tai trong den mat on dmh dong va dap u'ng phi tuyen dao dong tham so cua tam composite
Effect of load on the dynamic instability and the nonlinear responses parametric vibration of composite plates
Ngay nhan bai: 03/12/2015
Ngay sij^ bai: 13/02/2016 _ Nguyen Thj Hren Lu'ong Ngay chap nhan dang; 29/04/2016 Nguyen Hai, Huynh Quoc Hung
TOM TAT
Viec phan tich hien tifOng mat on dinh dong va dao dong tham so cua ket cau chiu tai trong dpng d o cgng htfdng tham so cd f nghia quan trpng ve ly thuyet va thiJc tiln. Trong nghien cdu nay, sii mat on d m h ddng va dao dgng tham s6 phi tuyen cua tam c h a nhat composite chiu tai trpng dpng dddc phan tich bang phUdng phap do cdng dpng idc. Tac gia trinh bay ket qua thiet lap ma tran do ctfng dpng lilc cho tam chfl nhat dda tren ly thuyet tam Von Karman chiu tai trpng dgng. He philtJng trinh vi phan bac hai vdi he s6 thay doi tuan hoan thupc loai philong trinh phi tuyen Mathieu-Hill md rgng ddcJC thilt lap de xac dinh cac viing mat dn dinh dong va dap dng phi tuyen dao dpng tham sd theo phuong phap Bolotin. Anh htldng cua tai trgng den vimg mat on dinh dong va dac tinh dap dng phi tuyen dao dgng tham sd cua tam composite dugc nghien ciiu va thao luan trong bai bao nay.
Tit khda: dao dpng tham so phi tuyen, mat on dinh dgng, phuong phap do ciing dgng lUc, tam composite.
ABSTRACT
The analysis of the phenomenon dynamic instability and parametric vibration of structures subjected t o dynamic loadings due to the resonance parameter is of both theoretical and practical importance. In this study, the dynamic instability and nonlinear parametric vibrations of composite laminated rectangular plates subjected to period in-plane loads are theoretically analyzed by using the dynamic stiffness method. The authors represent the way to establish the dynamic stiffness matrices of rectangular plates subjected to periodic in-plane forces based on von Karman's plate theory. A set of second-order ordinary differential nonhnear equations of extended Mathieu-Hill type with periodic coefficients is formed to determine the regions of dynamic instability and nonhnear responses parametric vibration based on Bolotin's method. The effect of load on the regions of dynamic instability and the response characteristics nonlinear parametric vibrations of laminated composite plates are investigated and discussed in this paper.
Keywords: nonlinear parametric vibration, dynamic instability, dynamic stiffiiess method, composite plate.
Nguyen Thi Hien LUOng
Khoa Ky Thuat Xay dUng, Trudng DH Bach Khoa TP.HCM NguySn Hai
Khoa Khoa hgc Lfng dung, TrUdng DH Bach Khoa TP.HCM Ths. Huynh Quoc Hiing
TrUdng khoa Xay dUng, TrUdng DH Xay ddng Mien Trung, Phii Yen Email lien lac: [email protected]
0 4 i B « n K i | H l <
I . G i d i t h i ^ u
Ket cau d a n g t l m duoe sd d y n g rat p h o bien t r o n g t h u c t i e n ky t h u a t n h u la ket eau eau, ket eau cong t r i n h xay d u n g d a n d u n g va c o n g n g h i e p , va m o t sd hogt d f i n g ky t h u a t khac. TrUdng h o p t a m chiJ nhat chiu t^i t r o n g t r o n g m a t p h l n g thay d d i d i e u hoa vdi tan s6 kich t h i c h cCia lUe 9: N(t) = Ns + Ndeose(t), vdi eose(t) la ham dieu hda ciia c h u ky T, t a m thUc hien bien d 6 d a o d o n g n g a n g co t h e t S n g m a n h n g o a i m a t p h i n g vUot qua m i e n t h a m so k h o n g gian da b i e t {Ns, Nd, T), n^u khSo sat ket eau t a m t r o n g t r u d n g h a p nay t h i g o i la h i ^ n tUong mat d n d i n h d o n g hoac m a t on d i n h t h a m sd.
Bai bao dau tien ve k^t cau t a m chCl nhat chiu lUc kieh thich t h o n g sd xuat hien vao nam 1936 d o Einaudi khdi xUdng NhCrng cong t r i n h t i e p t h e o ve de t^i nay sd d u n g ty t h u y e t t u y e n t i n h cua tam de x^c djnh nhCfng v u n g bat on dinh t r o n g mien t h o n g so. M o t trong n h d n g tac gia n g h i e n edu d a u tien ve hien tUcing dn d m h d6ng cOa tam ehu' nhat chiu lUe kich thich t h o n g so la Bolotin [1], YamakI va Nagai [21 phan tieh mat on d i n h d p n g ciia tam v u d n g ehm tai trong dieu hoa bSng p h u o n g phap Galerkin. TakahashI va Konishi [3] k h i o sat on dinh d o n g cua t a m chit nhat chju tai t r p n g flieu hoa sil d u n g phucJng phSp Galerkin. Ramaehandra and Panda [4] nghien CLiu on d i n h d p n g cCia tam composite ehju t i i t r o n g dieu hoa bSng phuang phap Galerkin. Wei-Ren Chen [5] sCf d u n g p h u o n g phap Galerkin phan ti'ch su on d j n h d o n g cua t a m composite t h e o ly thuydt bien d a n g c3t bac nhat.
SCf d u n g ty t h u y e t t a m Von Karman bien dang ldn de nghi&n cUu hien tUOng on djnh d p n g eiia tam g d m eo n h u n g c6ng t r i n h tieu bieu n h u la Nguyen H. va Ostiguy [6-7] sd d u n g phuOng phap giai tich va thUe n g h i g m d l nghidn cdu sU Snh h u d n g cua dieu kien bien len m i t on dinh d p n g va dap dng phi tuyen eCia tam chif nhat. Wu va Shih [8-9] phan tich mat dn dinh d d n g va dap Ung phi t u y e n cua tam chiu t l i t r p n g dieu hoa sCf d u n g p h u o n g phap Galerkin.
SCf d u n g p h u o n g phap phan tCr hflu han de phan tich mat on dinh d d n g cCia tam g o m cd nhUng cdng t r i n h tieu bieu nhU ta Hutt va Salama [10] sd d u n g m d hinh phan t d t a m m d n g b o n nut t i m dupe e l c v i i n g bat o n d j n h d o n g cua t a m . Srivastava va cong s U [ 1 1 - 13] phan t i c h on d i n h d d n g tam cd sUdn gia eUdng chiu t l i trong dieu hda. M o o r t h y va c o n g sU [14] phan tfch mat on dinh d o n g tam composite chiu t l i t r o n g dieu hda sCf d y n g p h u a n g phap phan I d hOfu han. SU m i t on d j n h d d n g cCia t l m sandwich ehiu tai t r o n g dieu hoa duac nghidn cdu b d i Chakrabarti va Sheikh [15-16] sCf d u n g m d hinh t l m ly t h u y l t bien dang e l t bac eao, Noh va Lee [17] sCr d u n g mo hinh t a m ly t h u y e t bien dang cat bac eao de phan tich dn d i n h dpng cua tam xlen composite va t i m dUOc cac v u n g mat on d m h d d n g theo p h u o n g phap nghiem Bolotin. Panda va edng su [18]
nghien cdu mat 6n djnh t h a m sd eiia tam composite bang p h u a n g phap phan tCr hflu han tr§n ca sd ly t h u y e t bien dang cat bac cao
Trong n g h i e n c d u nay, m i l o n d i n h d d n g va dao d o n g t h a m so phi t u y e n eua t a m c o m p o s i t e ducjc p h a n tich bang p h u a n g phap dd edng d d n g lUc m d r o n g (X-DSM), T i c gia t r i n h bay ket q u i t h i e t lap ma t r a n d o cCfng ctpng lUc cho t a m c h f l nhat c o m p o s i t e d i i a tren 1^ t h u y e t t a m V o n K a r m i n He p h u o n g t r i n h vi phan bac hai vfli h f sd thay d o i tuan h o i n t h u d c loai p h u o n g t r i n h p h i t u y e n Mathieu-Hill m d r d n g duac t h i e t l i p de xac d m h eae v u n g m i t on d i n h d d n g va d i p flng phi t u y e n dao d d n g t h e o p h u o n g p h a p n g h i e m B o l o t i n . A n h h u d n g eua tai t r o n g d e n v u n g m a t o n d m h d d n g v l dap dng phi t u y i n dao d d n g cua t a m c o m p o s i t e dUOc p h a n t i e h va t h i o luan
2 . Mo h m h phan t i c h va hi phuomg t r t n h chuydn d o n g Kh . . t l m composite chfl nhat cd chieu dai i, chieu rdng b, V ' h i 4 u day h ehiu tac dung t l i trong ddng d i l u hda N, duoc trinh bay ( ,q Hlnh 1
Hinh I. Mo hmh tarn diunhjt composite va dang tai Irong.
Bai toan ket cau tam dUoe p h i n tich dUa Iren ly thuyet tam do vong ldn Von Karman. Phuang trinh c h u y i n dgng phi t u y i n khdng t h d nguyen eua t l m composite duoc t h i l t lap'
L,{F)-Lj(W)+{W,,^ W , „ - W , ; , )r' = 0 (1) L,(W) + L3(F)-L(F,W) + W,„+2EW,, = tJ (2) trong d d d l u phay ki hieu 11 vi p h i n t u a n g flng vdi b i l n cua toa d o
h o l e thdl gian; r - l / b la ty so kich thudc eiia tam, va eac h^ sd khdng t h f l nguyen duac dmh nghTa:
X=x/1, Y=y/b, W = w / h , F=v//E2h\ (3)
A^QlpiV^ih']"^, T=t[EihVpi'']''^
t r o n g do: w(x,y,t)-d6 v o n g cua t a m , \|;-ham flng s u i t , t - t h d i gian, p -khoi luong rieng cua t a m , 9 -tan so kich t h i c h cua t l i t r p n g , Ej- Modulus d i n hoi cCia ldp vat lieu doc theo true 2; e -tham s6 g i l m chan; va c l e ham khdng t h f l nguyen
(4a)
^A;,)(F,„
+ 4 D ; , ( W , ^ )r' +D;,(W,,„y )r°]/E,h' m F ) = [ A ; , [ F „ „ . ) - 2 A ; , ( F , „ „ ) r + ( 2 A ; - 2 A ; , ( F , ^ )r' + A ; , { F „ ^ jr-lE^h L j ( ) = [ B ; , ( ) , x „ x + r ( 2 B ; - B ; , ) ( ) „ „ , + ! + f ^ ( 2 B ; - B ; , ) ( ) , ^ + r ' B ; , i ) , ^ ] / h
L(F,W) - { F , „ Vi^,^, +F„^ VJ,„ - 2 F , , ^ W , | , )r' (4d) trong do: he sd A,„ B,, va D,, (i,j = 1,2,6) - l l n lUpt la dp edng mang
mong hay eon goi la do cflng m d rdng, dd cflng ndi ket gifla mang m6ng-u6n-xoln va do cflng udn eiia t l m , va cac he sd A'= A ' ; B'= - A ' B ; D ' = D - B A ' B ,
T i l trpng khdng t h f l nguyen
Nidl^NB+NwCOsAT, trong do thanh phan tai trong finh Nxi(^[iiND) va t l i trong ddng N«d(=P>iNc,), vh Kr lUc tdi han on dinh tinh efla tam, p^ Pu - he sd t i l trong tTnh va tai trong ddng.
He sd g i l m chan A=27tE/nn., trong d d £ln.=&>m(1-|J=)°*-tln so dao dong neng cua tam, com- t i n sd dao ddng t u do.
3. Phan t i c h m a t d n d i n h d o n g v l dao d d n g t h a m sd 3.1. Phuang phdp xdc dinh nghiem
Nghiem efla phuong trinh (1) va (2) dupe bleu dien dang tdng q u i t chudi Fourier
W ( X , Y , T ) - £ 2 ^ ™ W ^ m { ' < ) > ' „ ( Y ) (5)
R X , Y , T ) - £ 2 ^ F J i ) Z „ ( X ) S „ ( Y ) - ^ Y ' (6)
trong dd W™ v l Fpo la hhtn khdng t h f l nguyen phu thudc vao t , va X™,, Yn, Zp, v l S« la eac ham dac biet ciia thanh d i m [6] eo dang:
X^(X)-A„(cosh([5„X)-cos(P^X))+B„sinh{p„X) + sin(P^X) (7a) Y„(Y) = A„(cosh{p„Y) - cos[pJ)) + B.sinhip J ) + sin(p„Y) (7b)
05.2016iSnni![|BVI 1 0 5
Zp(X) = coshfa^X) - cos(a„X) - y„(sinh(a„X) - sinta^X)) (7c) S„(Y) = cosh(a,Y) - cos{a„Y) -y„(sinWa,Y) - sin(a J ) ) (7d) trong d d cac he sd p, a«y„ A v l B, phu thude vao dieu kien bien eua tam.
3.2. PhUOng trinh Mathieu-Hill mdrdng
Hiuong trinh (5) va (6) thay vao phuang trinh ( l ) v a (2) v a t h u c h i ^ tac budc tinh toan, cudi eiing nhan ducx: phUOng trinh chuyen ddng phi t u y m la
W , „ +2eW„ -Ktto+a, cos A T ) W + i i W ' + yW' = 0 (8) trong dd ri 11 he sd phi t u y i n bac hai do anh hUdng cua do cung k i t noi
keo-udn vay la he so phi t u y i n bac ba do I n h hudng efla bien dang ldn.
ao=B™r([MX„,y„)] + [L,(Z„,S,)]-'IL3(Z,,S.)][L,(X,,YJ]+Nym) (9a)
cc, -N,,r=n"][S^J-' {9b) n = - [ S _ r ' [ L , ( Z „ , S , ) r ' ( [ L , [ 2 „ , S „ ) ] [ V ] r ' + m ( X „ . Y J ] [ R ] r ' ) (9c)
y =[S,^r'[L,(Z„,S,)r'[R][Vjr' (9d) trong phuong trinh (9) e l c ham dupe xle dinh-
[L,(Z„,SJ] = JjL,(Z„S„)Z,S,dXdY,
7, noa)
[L,(>'m.Yn)] = j|L3(X„Y„)Z,S,dXdY
IV]=JJ(X,„.xx YAY,-YY - ^ n , . . Y „ „ X , „ Y , „ )Z,S,dXdY (10b)
[L,(X,,,YJ] = jJL,{X„YJX,Y,dXdY;
[L,(Zp,SJ]=iJL3(ZpS,)X,Y,dXdY
[fil = Jjl2„S,,„X„,„Y„+Z„,„S,X„Y„,„-2Z„„S,„A„„T„„]X,Y,dXdY (lOd)
[ ^ = 1 jx,„,xx Y/,Y,dXdY ; [S,„J = jjx„Y„X,Y,dXdY [1 Oe) Phuang trinh (8) la phuong trinh vi phan bac hai cd he sd thay doi tuan h o i n thudc loai phuang trinh phi tuyen Mathieu-Hill m d r d n g .
3.3. Phdn tich mat on dinh ddng
Nghiem eua h f phuang trinh (8) I I dang nghiem tuan hoan eiia chu ky T va 2T, trong do T=2n/Q. Bien cua vung mat on dinh dpng v l dap ung phi tuyen cua k i t cau dUoc xle dmh t f l nghiem eua ehu ky 2T la quan trong nhat, cd y nghTa trong ly t h u y l t va thuc nghiem hem nghiem eua ehu kyT.Theo phuang p h i p nghiem Bolotin [1], nghiem cua chu ky 2T cd dang chudi Fourier
W ( t ) = 2 ^ a „ ! kAT
. " J '"'
trong do an, an, la bien do eua he thdng.
Thay nghiem (11) vao phuang trinh (8) v l ehi xet trUdng hop vung chinh m i t dn ^ n h ddng hoSc cdng hUdng tham sd ehinh la quan trpng nhat va dUpe x i y ra trong thue tien, co nghia la 6 = 2Q™ (tuang flng vdi k =1), va khai trien cuoi cung nhan duae phuong trinh la
trong dd bien dd ddng cfla dao ddng tham sd a duoc dinh nghTa
4 . Xac d j n h ma t r a n do cdng d d n g lUc
Thay phuong trinh (9) v i o phuang trinh (12), va thUe h i f n cac bUdc khai t n l n n h l n duoc phuong trinh vi phan b l e bon la
vdi ba dai luang tieh phan Ji, J: va h la
J, = M/jx„X„dX, J, = J(2M/X„,„ y^dX.
J5=f(M,X.,™,+fN„ + ^ l r X , „ !X„dX
trong 6
M , = —iV;( '\:M,- ^ ; M , .
Nghiem cua phuang trinh (13) eo the x i y ra ba trUemg h a p nhung 6 d l y ehi trinh bay trUdng hpp 1: ed hai n g h i f m thuc va hai nghiem l o (r;, - r i , i r ! , - i r i ) , vcri
- 4 J , J , ) , . . - . l ^ - Nghiem phuong trinh vi phan {13) c6 dang Y, (Y) = C, cosh(r,Y) + C, sinh(r,Y) + C, eos{r,Y)+C, sin(r,Y)
Hinhl Mo hinh, flieu kien bien chuyin vivalifcsuy rong cuj mot dai phan tUtam.
Ap dung cac dieu kien bi§n cua vecto ehuyen vj suy rdng d l i niit (Hlnh 2) x l e dinh duac quan he n h u sau
= AC (18b)
trong d d
eh, = eosh(r,b); s „ =sinh(r,b); Cj =eos(r,b); S3 = sin(rjb) (19) Ap dung eac dieu kien bien efla vecta luc suy rpng d l i nflt (Hinh 2) xac dinh duac quan he n h u sau
trong do t , = g , i f + g j r , ; tj=g,r,'
g,=MJx,„X„dX; g, = Ajx.,
106
Tfl hai p h u a n g trinh (18) v l (20), b l n g c i c h khfl vecto h i n g sd C n h l n duae ma tran d d cdng ddng lUc K eiia d l i phan tCf tam
P = K5 • (22) trong d d
K=RA-' (23) Ma tran d d eung ddng luc K cua p h i n t f l t l m cd kich thude 4x4
dugc the hien I I
(24)
ThUc hien tUOng t u nhU phuong p h i p phan t f l hCfu han, b l n g elch l i p gh^p eac ma tran dd cflng dong lUe efla tflng dai p h i n tfl, ta nhan dupe ma tran dd cdng ddng lUc t d n g the cua tam (Hinh 3).
DB¥|
T T
~ p3=l)2 \ - - 05=0 4
•••• p5=0.5 20 30
^4on-dlme^slonal excitalion ^ u e i c y - y
Hinh 3 M6 hinh lapghep tnic tiep cac ma Iran flo ciing flong luc cua dai phan tU tam 5. K h i o sat va phSn tich ket qua so
He so eua v i t lieu t l m composite (Graphlte/epoxy) duae xem xet 11 Ei/b=20; E2=6.96GPa; Gii/E;=0.5; G,3/E,=0.5, Gu/Ei-0.6; h& so Poisson v= 0.25; p = 1580 k g / m ' . Xet ket c l u tam composite vudng co eau tao 4
\6p [0°/9(y/90°/0°] ehiu lien ket tua don v l lien k i t n g i m .
— B — fuloorthy [14]
X-DSM
Excitation frequency/natural frequency -^
Hinh 4. So sanh vOng mil in flinh flong aia tarn composite vuong hon lop [tP/9O°/9t)°/0°l li&i kelUla flon vfli p^O, A=0.0.
Trong Hinh 4 t h l hign true t u n g Pd [^NKd/Ncr) la he so t l i trong ddng, v l true hoanh ^ (=0/tor.) la t y sd t i n sd lUc kich thieh v l tan sd dao ddng ciia t l m . Viing mat on dinh ddng cfla t l m composite lien k i t tUa dan duae trtnh bay trong Hlnh 4 v l dupe so s i n h vdi k i t q u i cua Moothy [14J b l n g phuong ph^p p h i n t f l hflu han. Hai v i i n g mat on djnh ddng la triing khit nhau va k h i la phu hqp.
Ket qua trong Hlnh 5-6 trtnh bSyviec thay ddi l l i trong tinh N«se l i m chuyen djch eac vflng mat 6n dinh ddng eiia he thdng Khi he sd t l i trong tinh pi (^Na/Nc) tang se l i m vflng mat on djnh ddng duoc rdng han v l hau q u i la lam t i n g k h i nSng mat on djnh ddng cfla tam. Ddng thdl, t h l y duae sU I n h hudng cfla vifc thay ddi d d giam chan A len elc vflng mat on dmh ddng. Ta biet duge vi^c A tang tao ra tac dung ed loi n h d viec rut nhd cac vung mat 6n dinh dong xa dan true t u n g tan sd Well thich cua lUe x ( r f l ' { p h / D a ) ' " ) , va cdn ed t h l ngan ngfla kha nang (j- ong cfla mdt v l i dang n i o dd.
Non-dimensKxial excrtation fraqii«icy-j(
Hinh 5. Tac dfing ciia viec thay flfii p, len viing mat on dinh fl5ng cua tam vuong lien ket tUa n,(a|A=0.0,(WA=011.
IV04
al efcilalior liequency-K
i 0 4 '••••.. \
I , ^=0 \ , •'.
^02! ^ = 0 1 ••-, . . ^ , .
I - . - R , = 0 4 \ /^
s 0 - ^' — '•' " - - iO 60 60 100
Non-dimensioiial excitation frequency-^
Hinh fi. Tac flong cOa viec thay floi ^ len vimg mat on ffinh flong ciJa tam vuong hen ket n g a m ; [ a ) A = 0 . 0 , ( b ) A - 0 , 1 l
/ (
OT frequency-«Hz)
E i c i l a t a r frequency - fi(Hi)
Hinh 7 Tac flong cua viec thay doi p, len flap ilng dao dimg tham so cfla tam composite vuong h^n ke'l tua flOn, p . = 0 . 2 , A - 0 1 1 (a) p.=0,3, (b) p,=0.7.
05.2016 enEiinon 1 0 7
Excitation frequency - G(tfe)
Hinh S, Tac dong cua viec thay fldi p> len dap flng dao dong tham so cfla tam composite vuong lien ket ngam, p^^O.Z, A=0.11. (a) p,=0,3; (b) p,=0.7.
Hinh 9 Anh hicflng cua tai trong ffnh len difimg flap ung -bien flo cua lam vuong composite lien ket tua flon vffi A=011 va 9=80Hz, (a) p,=0 3, (b) p,=0.7.
Hinh 10. Anh huiing cua t3t trong finh len difimg flap iJng -bien do cfla tam vuong composite hin ket ngam vfli A=011 va 6=190Hz, (a) p>=0,3; (b) p,=0.7.
Trong Hinh 7-8 cho thay c l e dudng dap Cfng dao ddng tham so theo t i n sd kich thich cua lUc deu xien ve b^n p h l i , tflc la tieu b i l u cho he sd phi tuyen bac ba ed t i c ddng cua mdt Id xo eflng, Ddng thdi, khi dang dao ddng tang thi h& so phi tuyen tuang flng cung tang theo, Khi thanh p h i n t l i trpng N<, tang se lam giam tan sd dao dpng rieng cfla he thdng v l l i m eac vung m i t on dinh ddng v l dudng dap flng dao ddng t h a m sd e h u y i n dieh lai g i n nhau hem. V l n de nay cd nghia I I viee thay ddi
t h i n h phan t l i trong tTnh ed the lam cho m d t tam dang d n dinh t r d nen mat dn dinh. N l u t h e m vao d d v i f e tSng t h a n h p h i n d d n g cfla t l i trong se t l m cac vflng mat on dinh ddng t r d nen rpng hon, k i t q u i I I l^lrn tang bien d o d i p dng dao d d n g t h a m sd v l dong thdi cflng lam tang k h i nang cdng hUdng efla h f t h d n g .
Khao s i t I n h hfldng eiia viec thay ddl thanh phan t l i t r g n g tTnh len d i p flng tham sd cua t l m dugc the hien trong Hinh 9-10 vdi true t u n g a la bien d p ddng va tryc hoanh ^(=Pd/2(1-P0 I I tham so t l i t r p n g chuan hoa, Mdt lan nfla cho biet r i n g v i f e tang thanh phan t l i trpng tTnh cd t h l lam thay doi dang dap flng cfla he t h d n g va lam cho bien do dao d d n g tang, dong thdi cdn co v l i t r u d n g hap, ed t h e tang t h e m sd cflng hudng t h a m sd. Van d l nay cd nghTa la v i f c tang t h i n h phan tai trpng tinh la lam tang bien d d dao d d n g t h a m sd va d d n g t h d i eung lam t i n g k h i nang edng hUdng dao d d n g tham sd efla he t h d n g
6. Ket luan
Tac g i l m d rdng phucmg p h i p d p efl^g d d n g luc de p h i n ti'ch h i f n tUOng mat on dinh d d n g va dap dng dao ddng t h a m so phi tuyen ciia k i t e l u tam composite. Phucfng phap nay dua tren nen t i n g cua tieu chuan d d n g lUe hoc v l each thflc thuc hien t u t m g t u n h u phUc^g p h i p p h i n tdhCfu han.
Nghien eflu n i y d l g d p p h i n giflp ehung ta h i l u rd t h e m v l hien t u p n g dao d d n g tham sd v l m i t 6n dinh d d n g eiia ket cau tam composite ehiu t l i trong kich thich tham sd, va dao d g n g tham sd chinh hay ta edng hudng tham sd chinh se x i y ra mdi khi tan sd lyc kieh thich b l n g gan hai lan tan so dao d d n g rl^ng efla h f t h o n g .
Thanh phan t l i trpng tTnh t i n g se lam g i l m tan so dao d d n g rieng cfla he t h o n g v l l i m cac vflng m i t on djnh dpng rdng hem, chuyen dieh d i n t i n sd lUe kich thich n h d hon, va lam d f l d n g d i p dng dao ddng t h a m sd c h u y i n djch lai gan nhau hon. Do dd, l i m t i n g bien d p dap Ungva lam tang k h i nang cdng hUdng dao d o n g t h a m sd eiia he thdng, k i t q u i la CO the l i m eho m d t k i t eau tam dang d n dinh t r d nen mat dn djnh d p n g ,
Anh hudng eua viec thay ddi do g i l m chan Ien cac vung mat on
^ n h d d n g da dUOc phan tich. Ta biet dUOc viec A tang tao ra t i c dung cd loi n h d vi^e rflt nhd c l e v i i n g mat on dlnh d d n g xa d i n true tung tan sd luc kich thich.
D u d n g dap Cfng dao d o n g t h a m so phi t u y i n theo t i n sd kich thich ciia t l i trong deu xien ve ben p h l i , tflc la tieu bieu cho he sd phi tuyen b l e ba cd t i e ddng cua m d t Id xo cdng. Dong t h d i , khi dang dao ddng t i n g t h i he sd phi tuyen tUong dng ciing t i n g theo.
TAI UEU THAM KHAO
[1|6oloIin,V.V,(1964),1heDyn^KstAiliiyofelastksystenis',Saniiancisa]'HoMen-Dav.
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i 0 8 ^'1'*^'*°^ 05.2016
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