V 1/ la cac ma Iran dudne eheo
CHl/ONG 3 CAC PHlTONG TRINH CO BAN CUA HIEN Tl/ONG FLUTTER
3.2. Phirang trinh vi phan ehuyen dgng cua phan to dam trong đng kh
Xet dfim cau cd chi6u dai kha Idn nam ngang trong đng khf dn dinh, van tdc U, ta cd the xei dai dien phan ung mot phan id dam trong đng khf. Phan to chieu dai dam cdu CO the gia su la cung tuyet đi (khong cd bien dang cue bg). Luc tac dung ciia đng khf len phan to gdm luc nang L^ phan bd d^u dgc dam va cd phuang vuong gdc vdi van tdc đng khf va mo men ^odn A/^cung phan bd deu dgc dam cd phuang dgc theo true dan hdi ciia ket caụ Nhu vay phan to dam dieh ehuyen trong đng khf vdi 2
bae tu do: ehuyen vi thang dung h va ehuyen vi gdc xoay a (hinh 3.1).
Hinh 3.1. Sa đ dieh ehuyen ciia phan id dam trong done khf on dinh
Toa d(^ tuyet đi la OXVZ va toa d(^ cue bd k'l CXoV,, Zp (phuong ^'. ^V la tim true doe dam). Lire nane L,, vuone ede vdi hueine eua \an ide gid Í . He sd do cung va
Chon hai true toa do suy rong mo ta ehuyen dong cua phan to dam la h va :c Phuang trinh Lagrange loai II viet vai he hai bae tu do nhu sau :
d f di] cL
dt = Q, (3.2.1)
Trong do: L la ham Lagrange ( L = T - 11)
T, n , Q, lan lugt la dong nang,the nang ciia he v a luc suy rong
f/, la cac toa do suy rong {h,a)
Viet rieng cho hai toa do suy rong a dang sau:
dt dt ydhj yd a J dh = a dL oa = Q. (3.2.2) (3.2.3)
Toa do tuyet đi eiia diem s bat ky lay tren liet dien duge xae dinh theo cdng thue sau (hinh 3.1):
.v^ =.v,3 cosa +1^ sin a
z -h \ r,. cosa +A- sin a
Do ede a be nen cosa ^I; sina ^ a , la duoc :
z , = /; - .v„cf + z„
Dong nang ehuyen dong cCia phan to dam eo the tfnh nhu sau:
(3.2.4)
1
T = — mu 2
. "* . ** (3.2.5)
Trone đ : ọ A la mat do khdi krone cua dam va dien tfch lay tfch phan
43 .r, = z,,d\ z ^ = h - x^d .r, = z,,d\ z ^ = h - x^d T = -\[^lci - + (/7 - x,d ) - ]pdx ,dz , ^ A ^ " 7 ^ ' j t o + -^0 )pdx,dz , +-h' ^p dx ,dz ,^ -ha \x^dx ,dz , •« ^ A
Ta co: I = J (.rj + z j ) pdx ^dz ^ : momen quan tfnh khdi lugng theo true yo m = \ pdx ^dz fj : khdi lugng ciia phan to
A
S ,^ = [ x^dx ^dz Q : Momen linh khdi lugng theo true ZQ
Thay vao bien doi eua dgng nang chuyeMi dgng la duoe cdng thue riit eon sau:
r = i / a - + - / ; / / / - - 5 . hd (3.2.6)
2 2
The nang ehuyen dgng ciia he do thanh phan dan hdi K^, Á^ gay ra tfnh iheo;
n - -(A,//-+Á,,a-) (3.2.7) Ham Laeranee :
L ^T ~n =-I á + -mil- - S . ha - ~K Id- - -K á (3.2.8)
2 2 "' 2 2
Lue suy rgng tfnh theo nguyen ly eong kha dl gdm 2 thanh phan lire khf dgng
L(,, .\f ^ va hai thanh phan lire can nhu sau : ólC = ^ Q Sq,
Ta duac : Q„ = L„ -C h ^3 2.9)
Tliay (3.2.8). (3.2.9) vao phuong trinh Lagrange II (3.2.2). biin doi ta duge:
mh-S^d + C„.h + K,.h = L„ (3.2.10)
Tmnm tir phuoui: trinh Lasraniie II voi ti>a 66 suv rone a (3.2.2). ta dugc:
Vay phuang trinh vi phan chuyan dgng Fluller cua he 2 D 0 F co dan^^:
mh " S.d + CJi + K^h = L^
Sj-Id ^ C^^d ^K^a = M^ ^^--^-^
Vdi mat cat dam cau chat đi xung theo Iriic tim thang dung ciia tiet dien nen tam udn va tam xodn cua tiet dien nam tren cung mot true tim thang dune nen md men
tmh khdi lugng cua phan to bang khong (S^ = 0 do jx^dx^dz^ = 0 ) , phuang trinh vi
A
phan ehuyen dgng Flutter cua he 2D0F dugc viet lai d dang long quat nhu sau:
Id + C „ a + K^a = M^ ^^-'^^^
i3. Ciic thanh luc khi đng tir kich
Do ngudn gdc cac lire tu khf dgng la cac lue tu kfeh ncn cd dae diem sau: phu thugc vao eae thanh phan ehuyen vi va cac dao ham cap 1 va cap 2 eiia ehuyén vi
{h,ujj,d,h,d). Trong thue tien phan tfch d6u sir dung huang tiep can luyen ifnh trong
viec tfnh loan cae thanh phan luc khf done, do he kei eau dane xet la he dan hdi luven linh \a tu ket qua thiJe nghiem md hinh [5], [7]. Nhu \a_\' cac lire khf dgng lu kfeh phu thuge luyen tfnh vao cac thanh phan ehuyen vi va cac dao ham eua eae ehu\ en \ i na>. lire la bao gdm 3 thanh phan: lire dan hdi khf dgng ( phu thugc/;,a ), lire ean khf dgng (phu lhuge,/;,a ) va luc quan tfnh khf dgng ( phu thugc/?,a ).
3.3.1. Mo hinh lire khi đng theo cac he sd thue nghiem cua Scanlan
Do khdi lucrne ciia dam cau duoe xem la rat nane trone đne khf nen thanh phan lue quan imh khf diMig trong tuong uic giua dam va đng khi phu thude vao dao ham
cap 2 eiia dieh ehuyen xji bi bd quạ Han nua, bang ihire nghiem ihay rang thanh phan lire khf đng phu ihude vao dieh ehuyen thang dung h cung kha nho nen eung
-45
L;, = m[Hj: +hLd + HM J
M^ -^ I[A, h + AM + A,a\ (3.3.1.1)
Trong do: H,, A, fi =l,2,3j la cac he .so dugc xac dinh theo thue nghiem
Theo each bien d6i co dién cac he so H,A, (i=l .2,3) bieu di^n la ham eua
i&n sd chiet giam khong thu nguyen ^=-j— (U la van tdc gid, oj la tan sd gdc dao
dgng va B la bd rgng mat cau) can bien doi ra dang khdng thu nguyen H*Â (i=1.2,3),
la cd cac bien doi sau:
/ / / / : / / : 2m pB-cj H, ^ , = pB'co ' ' ^ / / , pB'oj pB'oj pB'co Á--^^A (3.3.1.2)
Liic nay cac thanh phan luc khf dgng tu kfeh co the bieu dien duoi dang sau: