Tính toán xác định hệ số động của dầm cầu dưới tác động của tải di động : Luận án PTS. Cơ học: 2 02 02

MUC LUC Trang Muc luc L6i cam on M6 DAU Chuong PHUONG TRINH DAO DONG CUA DAM DAN HOI DU6l TAC DUNG CUA VAT THE DI DONG 1.1 Phirang trinh tong quat dao dong uon cua dam dan hoi 1.2 Phuong trinh dao dong cua dam voi tai h^ng so di dong 1.3 Phuong trinh dao dong cua dam v6i vat the di dong 1.3.1 Phuong trinh dao dong cua vat vdi nen dao dong 1.3.2 Phuong trinh dao dong cua dim du6i tac dung cua vat di dong 1.3.3 He phuong trinh dao dong cua dSm voi vat the di dong 1.4 Phirong phap Bup nov-Galerkin ly thuyet dao dong cac he lien luc Chuong KHAI NIEM VA TINH CHAT CUA HE SO DONG 12 LUC CUA DAM CAU 2.1 Khai niem 12 2.2 Xac dinh he so dong lire hoc cua dam cau v6i tai 13 h4ng so di dong 2.3 Xac djnh he so dong lire hoc ciia dam cau co vat the di 22 dong Chuong XAC DINH HE SO DONG LUC HOC TlTSO LIEU 38 DO DAO DONG 3.1 Thilr nghiem dong voi cau 38 L1 Cac phuong phap kich dong 38 3.1.2 Cac duns cu ihicl hi "hi 41 3.1.3 Cac yeu cdu doi v6i thu nghiem dong 3.2 Cac dai lirong dac diroc 41 42 3.2.1 Tdnsorieng 43 3.2.2 He so can 43 3.3 Tinh he so dong cua dam cau tir so lieu KET LUAN TAI LIEU THAM KHAO 44 45 L d l CAM ON Tac gia xin bay to long biet cm ch^n va sau s4c doi voi thay giao hudng dSn Pho giao su Tien sy khoa hoc Nguyin Tien Khiem, nguai da het sue tan tinh huong dSn, giiip da, tao dieu kien thu£ln Icri va c6 cac chi dSn khoa hoc cho noi dung nghien cuxi cua lu|in van Tac gia chan cam on su giiip dong vien cua cac thay c6 giao cua Trung t^m Hop tac dao tao va b6i duong co hoc Vien Co hoc Nhan day, tac gia cung xin ch^n cam on su quan tarn, dong vien va tao dieu kien thuan Id cua Ban giam doc Trung t^m cong nghe thong tin Dien luc Viet nam, noi tac gia dang c6ng tac MO DAU Cong tac ki^m dinh, chan doan va danh gia cau giao thong Viet nam dang la mot va'n de duoc nhi^u ngudi quan tarn he thong cau giao thong la he thong co so tang quan co gia tri 16n, dam bao hoat dong cua ca nen kinh te quoc dan nhung lai da dang phu'c tap vi k^'t c^'u va co nhieu nguyen nhan khac dSn den su xudng c^'p va hu hong Doi voi cau giao thong, truoc dua vao khai thac dat cong tac kiim tra, danh gia, xem xet viec thi cong co dam bao diing thiet ke va cac thong so yeu cSu hay khong Doi v6i cau cu, viec chuan doan danh gia cau phai dua duoc cac danh gia v6 kha nang lam viec tiep theo v^ bin, cung, on dinh, d6 an toan va tu6i tho lai ciia cau Ket luan dua la can cu vao mot loat cac so lieu ihu Ihap duoc tir Ho so cong trinh, lir kiem tra thuc nghiem va thu tai w M6t nhung thong so quan can phai xac dinh ki^m tra, danh gia c^u la he so dong luc hoc He so dong luc hoc la mot dac trung mo ta anh huong cua cac tai dong len cau so v6i tai tinh duoc tinh b^ng ty so giua chuyen vi dong tren chuyen vi tinh Trong thiet ke, nguoi ta chu yeu dua vao so lieu phan tich tinh, phan ung dong dudi tac dung cua cac loai tai khac chua duoc nghien cuu mot each day du Khi kiem dinh, danh gia cau he so dong duoc xac dinh b4ng phuong phap thuc nghiem dua tren so lieu Tuy nhien, nuoc ta viec xac dinh he so dong b^ng thuc nghiem lai chua co mot phuong phap thong nhat va hieu qua Truoc thuc te do, tinh toan, nghien cuu tinh chat va d6 xuat phuong phap xac djnh he so dong dua vao dong thoi ca ly thuyet va thuc nghiem, chii den phuong phap xac dinh b^ng thuc nghiem thong qua phan tich dao dong ciia dam dudi tac dung cua vat the di dong la mot viec lam can thiet Tir yeu cau dat va muc di'ch nghien cuu, luan van co nhiem vu giai quyet nhung van de sau: • De nghien cuu tac dung cua vat the' di dong so voi tai tinh va tai h^ng so di dong len dam cau Ian luoi viet cac phuong trinh dao dong cua dam cau dudi dang tong qual, phuong trinh dao dong cua dam Ciiu dudi lac dung ciia lai irong hang so di dong va phucmg irinh dao dong cua dam Citu dudi tac dung cua vai the di dong Tinh toan xac dinh he so dong cua dam cau ducri tac dong ciia tai di dong • Tinh toan va nghien cuu tinh chat cua he so dong luc hoc trudng hop tai h^ng so di dong va vat the di dong de co ket luan \6 anh huong cua v$t th^ di dong den he so dong luc hoc • Tim hieu v6 cong tac thu nghiem dong vdi cau, cac dai lugng dac duoc tir viec thu nghiem dong va phuong phap xac dinh he so dong luc hoc dim ciu dang lam viec tir so lieu dac thuc nghiem Phuong phap nghien cuu duoc ap dung luan van la; phuong phap giai tich d^' giai cac phuong trinh vi phan dao dong cua dam cau va phuong phap thu nghiem dOng d^ xac dinh cac dac trung dong luc hoc cua dam cau phuc vu viec tinh toan he so dong lire hoc tir so lieu Noi dung luan van bao gom: Chuong 1: Phuong trinh dao dong ciia dam dan h6i dudi tac dung cua vat th^ di dong Trong chuong trinh bay \6 cac phuong trinh dao dong t6ng quat cua dim dan hoi, phuong trinh dao dong ciia dam cau dudi tac dung ciia tai h^ng so di dong va phuong trinh dao dong cua dim ciu dudi tac dung cua vat the di dong Chuong 2: Khai niem va tinh chat cua he so dong luc hoc dam cau Chuong dua khai niem ciia he so dong luc hoc dam cau, he so dong luc hoc dam cau duoc giai tir cac phuong trinh dao dong Tinh chat cQa he so dong cung duoc nghien cuu Chuong 3: Xac dinh he so dong lire hoc dam cau tir so lieu dao dong Cong lac thu nghiem dong cau, cac dai luong duoc can cho viec tinh toan he so dong luc hoc va phuong phap xac dinh he so dong luc hoc dua vao so lieu duoc irinh bay day Ket luan chung dua nhimg ket qua chinh va phuong hudng nghien cuu phat tri^n ciia luan van Tinh todn xac dinh he so dong ciia dam edit ducn tdc dong ctia lai di dong CHUONG1 PHUONG TRINH DAO DONG CUA DAM DAN HOI DUOl TAC DUNG CUA VAT THE DI D O N G l.l.Phuong trinh tong quat dao dong uon cua dam dan hoi Noi dung cua phin la thiet lap phuong trinh dao dong uon cua dam dan hoi vdi tai phan bo bat ky Gia thiet r^ng: - dam dong chat vdi dai / - mat khoi luong p - dien tich tiet dien F - pF: khoi luong don vi dai - mo dun dan hoi E - mo dun quan tinh J - EJ: cung chong uon p(xj} Hucftig dao dong Hinh I.}.1 Dao dong uon cua dam Ta la'y true trung hoa ciia dam d trang thai ban dau chua cd tac dong cua tai la true x\ true r vuong gdc vdi true x Dam duoc xet vdi dao dong uon ve phuong :; bo qua dao dong xodn va dao dong doc true Tai mat cat A ta cd: Do vong u=uf.v./i Gdc xoay (p=(p(xj) Tinh todn xdc dinh he so dong ctia dam can du&i tdc dong ciia tai di dong Mo men uon M-M(x,t) Luc cat Q=Q(x,t) Y>i thiet lap cac phuong trinh vi phan dao dong uon, ta xet mot phan to ciia dzim CO chi6u dai dx nhu mo hinh sau day p(x,t) K4 ^ ^ M + A dx dx ^ R Hinh I.J He Ivtc tdc dung len mot phan to cua dam He lire tac dung len phan to bao gom: p(x,t)dx; luc cat Q va Q-\-~dx; dx mo menM va M + dx; luc quan tinh R = pF—rdx; dx ' df dw phu thuoc vao van tdc R = (3(pF — )dx, (3 = const luc can Theo nguyen ly D'Alembert, tir di^u kien can bang cac luc theo phuong z tacd: dO •Q-^^dx dx hay d' w + Q + p(x,t)dx^pF—rdxdf -f- + pF(—^ ^P'^) dx df dt dw p(pp — )dx = dt (1-1-1) = P(''>0 Mat khac mo men uon M tai mat cat bat ky khong chi phu thuoc vao cong x ma phu thuoc vao van tdc bien thien cua nd M = EJ(x + d'w dx a^) dt :> M = EJ( — r + a — — ) GX exet Tinh todn xdc dinh he so dong ciia dam can dudi tdc dong ciia tdi di dong (1.1.2) Tir di^u kien can bang cac mo men, bo qua cac dai luong bac cao cua dx ta cd: Q= dM dx Thay M tir (1.1.2) vao bieu thiic tren ta duoc: ^ c.,.5V d'w Q = EJ(— ^-a—T— ) ^ dx' dx'dt Thay Q vao (1.1.1) ta nhan duoc phuong trinh: (1.1.3) dx dx dt dt dt Day la phuong trinh mo ta dao dong uon cua dam dan h6i vdi tai phan bd bat ky 1.2.Phirong trinh dao dong cua dam vdi tai h^ng so di dong Xet tai hang so cd gia tri FQ De mo ta tai hang sd P„di dong tren dam ta sir dung ham Delta-Dirac S(x) Theo dinh nghia, ham Delta-Dirac xac dinh bdi he thuc: S(x-a) ox^a coc^x = a cu the: b(x -a) = lim bjx - a) i-*0 I |x-a| € e>0 va cd tinh chat: CO l8(x-a)dx=I —00 \f(x)8(x-a)dx=f(a) -co Cd the' xem tai tap trung P(, di dong lac dong len dam nhu la mot luc phan bd/;(.v.;j cd cudng P„ tren khoang [vf-i:, M+c]inc la tai vi irf lure ihdi cua tai di dong tai thoi diem / Sir dung ham Delta-Dirac ta c6 p(xj)- Tinh todn \ac dinh he so dong ciia dam can diccn tdc dong ciia tdi di dong F„d(x-\t} That vay, theo tinh ch^^t ham Delta-Dirac: P = p(x,t)-2€ = = P.5(x-vt)-2£ = limP,SJx-vt)-2e^PJim^-2E c-*0 £-*0 = P^ 2£ Tir do, phuong trinh dao dong cua dam vdi tai hang sd di dong nhu sau: d^w d^w EJ(^^^(^^P^) dx dx dt d'w dw df dt = P(^'0-PoS(x-vt) (1.2.1) 1.3.Phirong trinh dao dong cua dam vdi vat the di dong U.l.Phuang trinh dao dong ctia vat vol nen dao dong m Y '^ X / / / / / / / / / / / / / / Hinh 1.3.} Vat vcri nen di dong Xet vat the cd khdi lugfng m dat tren mot 16 xo cutig k va bo giam cha'n he sd c Ca he dat tren n^n cd dich chuyen thing dung la x„ Lay gdc toa la nen dung yen ban dau va dua vao cac ky hieu sau day: Xi - dai 16 xo khong bi nen (hang sd) X() - khoang each ban dau tir vat den nen (hang sd) A XQ= A'/ - Xo - nen tinh cua 16 xo sau vat da dat vao vi tri ban dau (hang sd) A- khoang each tu'c thdi (tai thdi diem /) tir vat den nen ban dau (ham cua thoi gian) x„ - la djch chuyen tuyel ddi ciia nen (khoang each cua nen tuc thdi den nen ban dau) Nhu vay ta cd the' tinh cac dai luong sau day lai thdi diem / Chuyen dich luyel ddi cua vai, ky hieu la x = xft) - x„ ~x(t) Tinh todn xdc dinh he so dong ciia dam can didri tdc dong ciia tdi di dong 2.Chuy^n dich tuong ddi ciia vat so vdi n^n, ky hieu la z = x-x^ ^x(t)~xjt) = x(t)-x^-xjt) 3.Tai trang thai ban dau can bang tinh cua vat ta cd: kAx,=mg (1.3.1) 4.Luc dan hdi sinh 16 xo bang he sd k nhan vdi chenh lech dai ciia 16 xo so vdi trang thai tu do, tu'c la: P^=k-(x-x^-x,) = k-(x-x^-x,^-AxJ = k(x-xJ-kAx, ^ P^=kz-mg (1.3.2) 5.Luc can nhdt sinh bo giam chan: P^=c-(x-xJ^c-(i-xJ =c-z (1.3.3) Dua vao cac dai luong da duoc tinh toan, ta c6 the thiet lap phuong trinh chuyen dong ciia vat That vay, tir cac luc tac dung len vat sau day: quan tinh ciia vat: - mx(t) luc cua vat: -mg luc dan hoi 16 xo: -kz-\- mg lire can nhdt bp giam chan: -cz Theo nguyen ly D'Alembert ta duoc phuong trinh: - mx(t) - mg -kz -\- mg -cz -0 hay mx(t)-\-kz-hcz = nhung vi: x = z-\-x^ nen phuong trinh dao dong cudi ciing cd dang: m'z + cz-¥kz = -mx^ (1.3.4) L32.Phi(ang trinh dao dong ciia dam ditai tdc dung ciia vat di dong Trong muc 1.1 ta da thiet lap phuong trinh dao dong udn ciia dam vdi lire tac dung phan bd bat ky va d muc 1.2 la phuong trinh dao dong ciia dam vdi tai di dong Nhu vay, de thiet lap phuong trinh dao dong ciia dam dudi tac dung cua vat the di dong, ta chi can tinh luc tac dung vao dam vat the dao dong tai vi tri CLia vat la A=*^=V/ Trong 1.3.1 coi dam la nen dao dong tuc la: x^=w(vtj)==xjt) Tinh todn xdc dinh he so dong cua dam can di(&i tdc dong ciia tai Ji dong (1.3.5) 34 Tir (2.3.26) ta nhan thay ham sin(3v^t -^ ^^,) se dat gia tri cue dai trudc ham sin(v,t-\-cpj,) neu ciing pha ban dau Neu chon v cho (pi, = (pj.-7r thi ca sin(3v^t + cp„ ) va sin(v^t -\- cp^^) ciing dat gia tri cue dai la chu ky dau Do vay fj(x,t) dat gia tri cue dai: Pi ^0 —hsin—- (o, M,A,.v^ ^p ^^^AiW^ ^(oy; -v;y +4h;v^ 2^(co;-9vy'^36h;v/ TDC Sin co; -1 lp,'+p,My,y + ' M,A„y ^ I J + [ , J 4(oj;-v]y^4h;v] Pi MyA„ 2^(co;-9v;y+36h;v^ TDC, -ysin—co; I \p;+P,M,A,y + [''y]({AjMj) -^(o); -vy +4hy; Pi •> , MyA„ 2^(co;-9v; y +36h;v; sin—- I 0); y+P,M,A„v; + V J -j- yl(co; -v; y +4h;v; \si (0 yi MyA„ y +36h;v; 2^(co; -9v; - TD I p P,(co;-vy ^((o; -y- y +4h;v; r«/ - v ; r +4h;v, - Tinh todn xdc dinh he sddpng ciia ddm cdu dudi tdc dong ciia tai di dong 35 , ^ P-My(w;-v^)^ \ ' ^ {p,MyJ P,My ~2[(co;-v;y+4h;^;n^ (co;-v;y+4h;v; 4(co; -v; y +4h;v; Vr