Đang tải... (xem toàn văn)
Kinh nghiem thac tien chi ra rang: khi tinh chu ky CO ban ciia dao ddng rieng CLia he, chi cdn dadng cong dang dao ddng gid dinh cd the thda man dieu kien rang budc ciia diem mut th[r]
(1)DIEN DAN KHOA H O C CONG NGHE
^ DAO D O N G CUA NHA VA
C O N G T R I N H KHI C O D O N G DAT
(Tiep theo)
5 Dao dong ci/dng biPc
Dao ddng cadng bac Id chi loai dao ddng sinh dadi tdc dpng ciia mdt lac kich thich ben ngodi lien tuc len vat the' Trong ky thuat cdng trinh, ta thadng gap loai dao dpng dd Vi du, dao ddng cadng bde ciia mdt gian xadng cd the' sinh dadi anh hadng ciia sa van hanh mdy mdc ddt dd; bdi Id mdy mdc quay khdng the tuydt ddi khdng cd dp lech tdm; ma saquay ciia khdi lapng lech tdm dd se sinh lac qudn tinh; td dd, lam cho kdt cau chiu tdc dpng ciia lac kich thich cd tinh chu ky cadng bde kdt cdu sinh dao ddng theo quy luat ciia lac kich thich
Trong thdi gian ngdn ddu tien ciia dao ddng cadng bde cua he ket cdu, tdn tai ddng thdi dao ddng gdy nen bdi lac kich thich va dao dpng ta ciia he Kdt qua ciia sa hpp thdnh ciia hai dang dao ddng ndi tren Id rdt phdc tap Nhung cd tdc ddng cua lac cdn, sau mdt thdi gian nhdt dinh (thdng thadng thi khodng thdi gian ndy rdt ngan), dao dpng ta hodn todn tdt hdn ma dat tdi trang thdi on dinh, chi bidn doi theo quy luat cua lac kich thich Khi lac kich thich bidn thien theo quy luat didu hda thi dao ddng cadng bde trang thdi on dinh dd Id dao ddng didu hda Ndu ta diing B va phdn biet bie'u thi bien dp vd tdn sd ciia nd, thi phaong trinh dao ddng cua dao ddng cadng bde trang thdi on dinh dd cd the bieu dat
X = Bcos et (20) Tan sd cua dao ddng la tan sd ciia lac kich
thich khdng cd quan he ndo vdi tdn sd dao ddng ridng ciia he cd Dp Idn ciia bidn dp B ciia dao ddng cadng bde cd quan he vdi tan sd dao ddng rieng ciia he, lac can tdn sd ciia lac kich thich va tri sd cue dai ciia lac kich thich Qua dien todn, ta thu daoc:
N G U Y E N H O N G HIEP
mco
1 e
CO
2 \
4n'd 2z52
(21)
a> Trong dd:
P- Ld tri sd cac dai cua Igc kich thich n- Ld he sd phan dnh dp Idn ciia lac can
Kdt qud cua thac nghiem vd nghidn ciru vd ly thuydt da chdng niinh: tdn sd ciia lac cadng bde Id chenh lech rdt nhidu vdi tdn sd ciia dao ddng ridng thi bien dp ciia dao dpng cadng bde rdt nhd Khi tidp can vdi , thi bien dp B tang rdt nhanh Khi tdn sd ciia kich thich chenh rdt it va xdp xi bdng tdn sd dao ddng rieng , thi bien dp cua dao ddng cadng bde dat ddn tri s6 cdc dai
Hinh 12
Khi dd, dao ddng trd ndn dd dpi nhdt Hidn tapng gpi la cdng hadng Hinh 12 tren day bieu thj dadng cong bien thien ciia bien dd dao ddng cadng bde theo bien thidn cua tdn sd cua lac kich thich, dapc gpi la dadng cong cdng hadng
taong ong vdi dao Trong hinh 12, dadng cong
dpng cadng bde khdng cd lac cdn, dadng cong td (2) den (5) Idn lapt bieu thi mot sd tradng hpp tang to len ciia lac cdn Td tren bieu dd, ta thdy rd: lac cdn cdng nhd, cdng hadng thi bidn dp cdng to Ndu lac can rat nhd thi dieu kien cdng hadng, trade dao ddng dat ddn trang thai on dinh thi he kdt cdu da cd the' bi pha hoai bdi le dao ddng qua dd dpi
Khi cd ddng ddt, nha vd cdng trinh chiu tac ddng ciia lac quan tinh ddng dat sinh ma tao ndn dao ddng cadng bde Vi thdi gian dpng ddt rdt ngdn, phan dao ddng ta chaa kip tat, cho nen nghien cdu dao ddng ddng dat gay nen ddi vdi nhd va cdng trinh, ta phai ddng thdi xet den ca dao ddng ta vd dao ddng cadng bde
6 Khai niem ve dang dao dong
Tren ddy, ta da thao ludn vd dao ddng ciia he ket cdu cd bac ta don, chi cd mdt tdn sd dao ddng rieng Taong dng vdi loai tdn sd ndy, chi cd mdt dang dao ddng nha hinh 13 bieu thi
Dao dpng cua he cd nhieu bac ta phdc tap hon dao ddng cua he cd bac ta don rdt nhidu, Ket qua nghien ciru da chimg minh: he ed nhidu bac ta do, tdn tai nhieu tdn sd dao ddng rieng Sd tdn sd dao ddng rieng ciia he bdng sd bac ta ciia he Vi du, he cd n bde ta do, tdn tai n tan sd dao ddng ridng dapc xdp theo thdta Idn nhd theo hang dadi day:
CJ < CO2 < < CO, < < OJn
Trong dd, mdt tdn sd nhd nhdt gpi la tdn sd thd nhdt hoac tdn sd Hinh 13 cobdn Cdc tdn sd khdc theo thdta
(2)gpi Id tdn sd tha tha i, thd n - gpi chung Id tdn sd cao Tong hpp ciia tdt cd cdc tan sd sdp hdng theo thd ta Idn nhd dapc gpi Id tdn sd dao ddng rieng
Ket qua nghien ciru cung da chdng minh: taong dng vdi mdt tan sd co, nao dd, gida cac chuyen vi dao ddng ciia nhung chat diem ciia he deu tdn tai mdi quan he ty Id xdc dinh; dd hinh thdnh mdt dang dao ddng khdng doi taong img vdi tdn sd co, gpi Id dang dao ddng He cd n bac ta thi cd n tan sd dao ddng rieng vd tacmg img se cd n dang dao ddng Dao ddng thac te ciia he Id dao ddng phdc hpp hinh bang each cdng n dang dao dpng dd
Hinh 14 dadi day Id so dd dao ddng ciia he cd bac ta
Hinh 15 dadi day la so dd dao ddng cua he cd bde ta
Dang dao ddng la chi kieu ddng dao ddng eua he, khdng cd quan he gi vdi dp Icfm cua chuyd'n vi ciia dao ddng
Hinh 14
Khi he dao ddng, chuyen vi dao ddng ciia chdt diem bien thien theo thdi gian Khi chuyen vi ciia nhCmg chdt die'm tang hoac gidm deu mdt bdi sd ndo dd, dang dao ddng ciia nd khdng doi md chi cd mdt dang dao ddng xdc dinh
Bdi le ket cau thac td khdng trdnh khdi satdn tai ciia lac cdn, dang dao ddng cao taong ung vdi tdn sd cao va tat rdt nhanh; ngodi bidn dp ciia dang dao ddng cao lai rdt nhd nen thac sa cd gid tri dng dung chi Id mdt vdi dang dao ddng phia trade ma thdi Do dd, ddi vdi cdc kdt cdu cdng trinh ndi chung, ta chi cdn xet dang dao ddng thd nhdt Id cd the thda man dp chinh xdc tinh todn rdi Ddi vcfri mdt sd kdt cdu cdng trinh quan trpng hoac cao, mdm, ta mdi cdn xet den dang dao ddng thd vd thd
7 Ap dung phuong phap gdn dung de tinh toan chu ky co ban cua he co nhidu bac t a
Chu ky dao dpng ridng cua kdt cdu phdn anh ddc trung ddng lac vdn cd ciia nd Khi xdy ddng ddt, dp
\dn eiia lac ddng ddt md kdt cdu phai chiu cd quan he vd\ chu ky dao ddng rieng cua nd Khi tinh todn dao ddng eiia kdt cdu, trade tidn ta phdi tinh chu ky dao ddng rieng ciia nd Ddi vdi he cd bac ta dan vide tinh toan chu ky dao ddng rieng khdng khd khdn vd cd the tien hdnh bang each trac tiep dung bieu thdc td (15) den (18) Nhung thac td, kdt cdu cdng trinh ddu la nhdng he ed nhieu bde ta hoac bac ta vd han, vide tinh toan chinh xac chu ky dao ddng rieng ciia nd Id rdt phae tap
Dd' tien tinh todn thidt kd cdng trinh vdi muc dich thac dung, ta thadng dimg nhung phaong phap gan dimg ddy, chiing tdi se gidi thieu hai phucjng phdp gdn dung de' tinh chu ky co ban ciia dao ddng ridng ciia ket cdu,
(1) Phuang phap nang luqng
Trdn day da ndi he dao ddng ta do, ndu khdng xet den tae ddng ciia lac cdn, thi ndng lacpng ciia he khdng bi tieu hao Trong qud trinh dao ddng, ddng nang vd thd nang ciia he chuyen hda lan va tong gid tri ciia nang laong ciia nd khdng doi, tdc la tai mdt thdi diem bat ky, tong ciia ddng nang U va the ndng ciia he la mdt bang sd:
U -I- n = constant = hang sd
Khi he dao ddng den vi tri can bang, vi du nha vi tri C hinh 16, he chaa cd bidn dang nen thd nang ciia nd bang 0; nhung dd, van tdc chuyen ddng ciia chat die'm Id \qn nhdt, vi vay ddng nang ciia nd dat tdi gid tri cac dai \J^^ Cdn he dao ddng ddn vi tri cd chuyen vi cue dai, vi du nha cdc vi tri B vd D hinh 16, van tdc ciia chdt die'm bdng 0; dd, ddng nang ciia nd cung bang Nhung dd, bidn dang ciia he Id Idn nhdt; dd, thd ndng ciia nd dat tdi gia tri cue dai
Flmax-Td dd ta cd:
U„,ax = n „ ^ (22)
Tdc Id, ddng nang cac dai ciia he dao ddng tai vi tri can bang bang thd nang cue dai he ndm tai vi tri cd chuyd'n vi cue dai Can cd vdo ly le dd, ta cd the tinh tdn sd co bdn vd chu ky co ban ciia he Od chinh Id phacmg phdp ndng lacpng
Ddi vdi he cd bac ta don nhu hinh 16 bieu thi, gia sd khdi lapng ciia chdt diem la m, td cac bieu thdc (10) va (11), ta cd chuyen vi dao ddng x,,, va van tdc v„) bdng:
x„) = A cos tot V|„ = - coA sin cot
Tri so cac dai ciia chuyd'n vi vd tri sd cac dai ciia van tdc lan lacpt Id:
X - A Vmax = WA
Td mdn vat ly ta bidt, dpng ndng bang 1/2 tich ciia khdi lapng nhdn vdi binh phaong ciia van tdc; dd, ta thu dapc tri sd cue dai ciia ddng ndng bang:
1 ,
U„ - —mv_ = —m [coAf
Hinh 16
(3)T d mdn ca hpc kdt cdu ta lai bidt, thd nang ciia he bdng cdng dapc sinh la tdi trpng tac ddng len kdt cdu Idm tren chuyen vi tTnh hpc tao nen Ndu ta cho rang bidn dp dao dpng he dao dpng la chuyen vi tinh hpc sinh ha\ trpng lapng W cua chdt diem thi tri sd cac dai cua the nang Id:
n \mgA
Thd vdo bieu thire (22) ta c6 — micoAY =
-2 ^ ^ -2 -m{coAy = —mgA Vdy: 0) =
(24)
(25)
(26)
Ddy chinh la cdng thdc tinh todn tdn sd vd chu ky dao dpng ridng ciia he cd bac ta den ma ta da riit bdng phaong phdp ndng lapng Do dd bieu thdc trdn, A chinh Id chuyen vi tTnh hpc A,;„f, trpng lapng ciia chdt die'm sinh ra, ndn bieu thdc tren day thac chat Id bieu thac (18) bdi dd ddng sd tap chi thdng trade
Tidp sau ddy, ta lai dung phaong phdp ndng lapng de' riit cdng thdc tinh todn tan sd vd chu ky dao ddng rieng cua he cd nhidu bac ta
Hinh 17 dadi day bieu thi mdt he ddn hdi cd n chat diem Ta dung m;, x,,^,,, x, Idn lapt bieu thi khdi lapng, chuyen vi dao ddng vd bidn dp dao ddng ciia chdt die'm thd i Gid thidt mdi bdt ddu dao ddng, cac chat diem deu d vi tri khdi ddu cua bien dp ciia chiing, van tdc ban ddu Id vd cdc chdt diem ddu thac hidn dao ddng didu hda vdi tdn sd thi phaong trinh dao ddng va van tdc ciia khdi lapng thd i cd the bieu thi nha sau:
Xi(Mj=XiCOS0)t 'i(M) = HoXiSin (ot
Can cd cdc bi§u thdc (23), (24) ta cd ddng nang
cue dai ciia chdt diem thd i la —m, (cxc,) , thd nang
cue dai Id ~\tn^g)x^ Odng nang cue dai U^^vk thd nang cue dai U^^ phan biet la tdng ciia dpng nang cue dai vd thd nang cue dai ciia chdt diem, tdc la:
(27)
(28)
Cho hai bi^u thdc trSn bang nhau, ta thu dapc tdn
s6 dao dpng ri§ng cua hd Id:
CO = IgYjn^
I.m,x^
hoac CO = (29)
Chu ky dao ddng ridng co b^n Id:
T = In, (30a)
Day chinh la cdng thdc tinh tan sd dao ddng ridng thd nhat hoac chu ky dao ddng ridng ca ban ciia he nhieu bac ta do; dd, Wj la lapng ciia chdt die'm thd i Khi dung phaong i , phdp nang lapng de tinh chu ky dao I T ddng rieng, ta can phai cd bien dp
ciia cac diem, tdc la phai cd dadng cong dang dao ddng ciia he mdi cd the' sd dung cdng thdc (30a) Oieu dd ddi hdi phdi trade tien gia dinh dacbng cong dao ddng rdi mdi tinh toan Kinh nghiem thac tien chi rang: tinh chu ky CO ban ciia dao ddng rieng CLia he, chi cdn dadng cong dang dao ddng gid dinh cd the thda man dieu kien rang budc ciia diem mut thi hinh dang ciia nd dai the gan xdp xi vdi dang dao ddng thap nhdt ciia he, dp chinh xac ciia chu ky dao ddng ridng tinh dapc bang phaong phap nang lapng kha cao, hoan toan cd the thda man nhu cau thiet ke ddi vdi cdc cdng trinh thac te Khi dd, ta thadng lay dadng cong chuyd'n vi ngang ciia cac chat die'm dadi tdc dpng nam ngang ciia trpng lacpng de' Idm dUdng cong ciia dang dao dpng Nha vay, bieu thdc (30a) cd the vidt thanh:
Hinh 17
V w,A'; (Zw A'
gSw,.A, Zw,A_ (30b) Trong dd:
V\/|: La trpng lapng cua chat diem thd i
A,: Chuyd'n vi ngang ciia chat diem thd i gia thiet cdc lac nam ngang ciia nhdng W, tac dpng len cdc chat diem tac?ng dng
(2) Phuang phap khdi luqng quy ddi
Dimg phaong phdp khdi lapng quy doi de tinh chu ky CO ban ciia ket cdu Id mdt phaong phap tinh toan gan diing hay dapc dp dung khac Khdi niem co ban ciia nd la: tinh toan chu ky co ban ciia dao ddng rieng ciia mdt he nhieu bac ta do, ta dung mpt he cd bac ta don de thay thd, lam cho chu ky dao ddng rieng cua he cd bac ta don bang hoac xap xi nhdt vdi chu ky co ban ciia dao ddng ridng ciia he ban ddu Khdi lapng ciia he cd bac ta dem ndy dapc gpi la khdi lacpng quy ddi (hoac khdi lapng laong daong, khdi lapng thay the') dimg M^,;; bieu thi He cd bac ta don ndy vd he ban dau gidng hoan toan vd hinh thdc ket cdu, didu kien rang budc va dd cdng chi cd mdt didu Id khdng trpng lapng Nd Id mdt he chat diem don cd khdi lapng quy ddi
Tri sd Mqj cua khdi lapng quy ddi cd quan he vdi vi tri ciia nd Ndu vi tri tren he ciia nd dd daoc xac dinh thi tri sd taong img ciia M^j se dapc xdc dmh theo Theo kinh nghidm, tdt nhdt nen ddt khdi lapng quy ddi
(4)tai diem cd chuyd'n vi cac dai dao ddng thi se thuan Ipi nhdt
Tri sd cua khdi lacing quy ddi M^^ tinh dapc daa theo quan diem ndng lapng khdng ddi; tac Id ddng nang cac dai ciia he cd bde ta don thay the he ban dau dao ddng bdng ddng ndng cue dai ciia he ban ddu
Vi du, tinh chu ky co ban ciia he nhidu bde ta do hinh 17, ta cd the thay thd bdng he cd bac ta do don bid'u thi hinh 16; he ndy cd khdi lacing quy ddi M^^, cdc yeu td khdc gidng hodn todn nha he ban ddu Can cd vdo ddng ndng cac dai ciia hai he [(xem bieu thdc (23) va bieu thdc (27)] bdng nhau, ta cd the thu dapc bieu thdc dadi day:
Vdy: M qd I.m,xf (31)
Trong dd x^,: Chuyen vi cue dai ciia vi tri khdi lapng quy ddi
C6 dapc khfli lapng quy ddi rdi, thi ta c6 t h i tinh chu ky CO ban cua no theo he cd bac ta dan, nghTa la:
T = ITT^JM^ (32)
Vidu 1: Cd mpt cdng son ddng chdt vdi tidt
didn ddu khdng ddi bilu thi hinh 18a Chidu ddi thanh Id I; dd cdng khdng udn Id EJ; trpng lapng tren
mpt don vi chidu dai la q (khdi lapng tren mpt don vi chidu ddi Id —)
g
Tinh chu ky dao dpng rieng T
^f
9
k!
- °
.?5^ •-12 T
(^') (b) (c)
Hinh 18
Giai Phdn deu cdng son doan Td dd,
ta thay thd cd bac ta vd han ban ddu thdnh mdt he cd nhieu bac ta vciri khdi lacpng tap trung nha hinh 18b bieu thi Nay ta Idn lapt tinh chu ky dao ddng ridng ciia nd theo phaong phap ndng lapng vd phaong phdp khdi lapng quy ddi nha sau:
Trpng lapng ciia mdi chat diem Id W^ qt
Ta l^y dutfng cong dfl v5ng cua cflng son chiu tdc ddng ciia trpng lapng ban thdn phdn bo d^u Idm dudng cong dang dao ddng tuc Id:
qi 4 f
8EJ 3t 3e' e
i \
Bi^u thue tr§n Id dadng cong dp vong ciia cdng son dudi tdc ddng ciia trpng lutmg ban thdn phSn b6 d^u - Cd th^ tra cdu mfln Sdc b4n vdt Ii3u ciia chudng trinh dai hpc Ta Idn lutJt mang cdc
1 5/"
tri s6 V = —L — L — , — (.vk —( th6 vdo bigu 10 10 10 10 10
thuc tr§n, thi ta c6 th^ tinh ducc ehuydn vi ciia cdc ch4t diem nha sau:
r i V
^ = qt
8EJ
qt SEJ
qt
ll_Li _l|i
3U0J 3U0^
+ —
" i r ^ y _ r V
loj
-I-SEJ [0,0187]
+ 10
8E/
1 ^
8£y
1 ^
8£/
If
3110
V i O y
4 r 10
SEJ [0,1468]
-I-A <; -I-A +
vlOy
SEJ [0,332]
'\(
31
' ^
loj ' 'i 3I
/ v V
+ : )
UO /
<7>
,10;
3
-1-8EJ [0,532]
" i r ^ 3I10;
.2(1
' 4f9^
3I1O;
T
3
+
SEJ [0,933]
- Niu ta dung phuong phap nang luqng de tinh
toan, trade tien phdi tinh ra:
l^.x!=-ql 'ql^^
SEJ
(0,0187)'+(0,1468)'+' + (0,332)'+(0,532)' + + (0,933)'
(5)Y^w,x^=~qi 'qt^
f „D^ \
qi SEJ
\SEJ [1,9625]
0,0187 + 0,1468 + + 0,332 + 0,532 + 0,933
Mang cdc ket qua tren day thd vdo bieu thdc (30a), ta cd:
T^ln In
TW,:
gTW,x, 2n
1,282 l,9625g
^qt_^
ySEJj n952t
3,5 V EJ
So vdi tri s6 chinh xdc
2n 3,515
m
— = 1,7987^'
EJ thi sai sd
Id 0,43%
- Niu ta diing phuang phap khdi luqng quy dd'i de tinh toan, trade tien ta phai tinh khdi lapng quy ddi Mqj Gid sd khdi lapng quy ddi dapc bd tri tai ddu miit tren cua cdu kien nha hinh 18c bid'u thi, chuyen vi tai ddu mut tren Id:
" SEJ Vay ta co:
id
4 > ^
mi q£
SEJ [1,282]
^SEJ J
= 0,256mi = -mi 4
Trong do, m la khdi lapng ciia mpt dtjn vi dai cau kien
1 e' Vay: T = ITTJM.S =
2nJ-m£-= 2;r.j~t 2n
3,47 £' r = i 811^^ —
So sdnh vdi tri sd chinh xdc thi sai sd Id 1,28% Mdt didu quan trpng cdn ghi nhd Id vide tinh todn vi du tren ddy theo phaong phdp khdi lapng quy ddi de giai thich rang: Ddi vdi nhd mpt tdng cd khdi Iddng phdn bd taong ddi ddu theo chidu cao, ndu dd la mdt ngdi nhd trdng ben hoac nhd cdng nghiep mdt tdng thi tinh todn chu ky dao dpng rieng ciia he kdt cdu, ta cd the' mang 1/4 tdng khdi lapng ciia nd dat tai diem mut tren dinh cot vd tinh todn theo he cd chdt diem don Id dapc
' i k
c it
'W//
»l.io
M yi dy Cd m0t cdng son ddi I, khdng trpng lacpng; dp cimg khdng udn cua tidt didn
4
Id EJ Tai didm C cdch ddu mut ngdm Id — ^ , cd mdt 5
khdi lapng tap trung m Tinh khdi lapng quy ddi tai ddu milt A ciia cdng son (Xem hinh 19)
Giai: Dadng cong dan hdi ciia cdng son cd mdt don vi lac ndm ngang tac dpng tai ddu miit cdng son - dapc Idy lam dadng cong dang dao ddng, tdc la gia
thidt: (UJ (1^)
X = W-/)
Hinh 19
6EJ
Thi chuyen vi tai ddu miit tren la:
3EJ
Chuyen vi ciia die'm C la:
X , = • 6EJ
f,
3e -i
\-1/
5 J
6EJ
48 64 25 125 e =
1
- X
6EJ 125
The vao bieu thdc (31), ta thu daoc:
i
^ - Z-,-f
m 1 176
6EJ 125 ^ ^ ^
3EJ 176
250 m = 0,496w « 0,5w
Vi du ndy giai thich rdng: ddm cdu true ciia
nhd cdng nghidp mdt tdng d vi tri gdn - chidu cao
ciia cdt, thi ta cd thd Idy tdp trung - khdi lapng ciia cdu trgc dat tai dinh cdt; rdi lai cdng vdi khdi laong ciia mdi de tinh chu ky dao ddng rieng ciia nd nhu hd cd bac t a d o don,
Tavide phdn tich hai vi du trdn day, ta cd the biet rang: khdi lacpng quy ddi Id khdi lapng ciia he ban ddu nhan vdi mdt he sd mdi thu dapc He sd goi la he sd quy ddi taong daong ddng lac ciia he lan lapt cd gia tri bdng 0,25 vd 0,5.0