, . , [email protected] 1 1. . , . : ; ; . (. 1.1):, (); , - (
); , ( ).. 1.1. , , , , , - (). . - , , , , . : . , , ,. . . , . ,
- , . - , . (), -. . (. . 1.1): L; , : L ; L, , [ ()] [ ()]; , ; D,
- ; d, - . D d F. , , . , , . :1, . , [email protected] L/B, ; B/d,
, ; L/D, ; D/d, . , . : - S L :=S/(LB);(1.1) -- - d: = /(Bd);(1.2)
- , , V L, d:Cb = V/(LBd);(1.3) - V , - L: = V/(L);(1.4)- V, S d: =
V/(Sd).(1.5), b , - , =Cb/; =b/.(1.6) . . , , Oxyz, , - - , Oz - -
(. 1.2).. 1.3. ,, , d- Oz; - --(); - ( ). = 0, , ; = 0, , . , - , ,
, = 0, - = 0. : - , , - , . , . ( = 0), d ( ):D = d + L/2 tg ~ d +
L/2 (1.7)D = d - L/2 tg ~ d - L/2 (1.8) dH- dK . 2, . ,
[email protected] :d - d = L tg L.(1.9) . : , . (. 1.3), , , ; . ,
, : , - . ", " ". , . , , ; , -, - ; , , -. , - . , " " ". , " , "
- ; , - . " " ., , . . . ( ). , . , , 21, . . 20 , . 2. . . = V. -
. . 1.4. , . , , (. 1.4):- , - = g, () G (xg, yg, zg);- , ; , - V(-
), ()- (, , zc). , , , , . , , . , , ., , , , ( ) :3, . ,
[email protected] = V ; = V(1.10) (1.10) . , , , . - - ; , - - , .
. . x tg + y tg - z + d = 0.(1.11) , , G , , (1.11), , :(xg-x) +
(zg-zc)tg = 0;(yg-yc) + (zg-zc)tg = 0.(1.12)(1.12)aae. (1.10)
(1.12) . ( = = 0), (1.12) xg=xc; yg=yc.(1.13) . . ( ) , , , , . (.
1.1), () mi, () xizi, mixi mizi . ( , , .). 1.1. mi, zi, Mz = mizi,
xi, x = mixi, 1 2 3 4 5 6 ( , )m0 z0 m0 z0 x0 m0x0 (, , )m3 z3 m3
z3 x3 m3x3 1ml z1 m1 z1 x1 m1x1 2m2 z2 m2 z2 x2 m2x2.. m6 z6 m6 z6
x6 m6x6 mi mizi mixi 2, 4 6 = mi ; xg = mixi / mi ; zg = mizi / mi
(1.14) , yg , . , . . , , , , , ( ). , , , , . ( ) , , ( ) . , (.
1.5), - . , , . . ( ) . , , 4}, . , [email protected] , : V; zc; S;
xf; Cb; - ; 1xIyf;zmZM; r R, M, 1 .. 1.5. , , , (. 1.6). . 1.6. xf,
- , - , , . ; - . . , V , . ( = 1,025 /3), =f(d), (. 1.7).. 1.7. (.
1.8), V .5, . , [email protected]. 1.8. . , S d, (. 1.9). :- , , ;-
zc ;- . . 1.9. . , , , , , , . , , , . . 1.10. , , (. 1.10). , 21 ,
. . ( ) 20 . . 1.10 (0-, 2-, 4- . .). , 1 : 100 , 1 : 25 . , . 6, .
, [email protected] d. d. , l l. . 0,5 . . , , . , . 1.108-. :+2 /2
/;LLdx V +2 /2 /1LLcxdxVx (1.15) . 1.2. 1.2. V i(i `i) i `i010 0
0-1nn-1n`n-1`n(n-1)( n-1- `n-1)n(n- `n) `1 `2 (n- `n)/2 n(n- `n)/2
1 2V = l 1 Xc = l(2/ 1). l = L/20 . , , 0,2- 0,3. A (. . 1.10, , ).
, () -, LBf V ) 2 )( 2 / 2 (2 (1.16) f- () . . 1.10, - :f = D + t -
F m - dcp.(1.17) D - ; tn - ; F - ; m - -; dcp - ( ), t d d d dl l
Ll ld 1]1
+ + + ) ( ) () (21. . . .(1.18) t - . , ( ) ( xc) .., , . , , -
, , (. 1.11). :- , , ;- ;- . . , (. 1.12) = mg : ., , () d. V 11 V,
., , ,. V , 7, . , [email protected] S, - dV = Sd.(1.19). 1.11. .
1.12. d , p = .(1.20) (1.20) (1.19) d, d = p/(S) = m/(S).(1.21) ,
(1.21) ; , , . . d. . 1.12 , p V , . , . V . , e , () . , , . 1.12
. (1.21) . , 15-20 % .q- 1. q, d = m/q. (1.22) (1.21) (1.22), , q S
q = S/100. (1.23)() 1,025/3, q=f(d). , - q. . 15-20% , (1.21)
(1.22) . , =f(d). ( ) 0, -d0(.1.13). 0 . , d , , d. , , 0.. 1.13. .
-, . , . . =1,0/3, , 1,015-1,035/3. , . , , V 8, . ,
[email protected] 1, 2, V. , ,V=2(V+V). (1.24) d ( ), V = Sd, S- .
oao, (1.24) 1V = 2(V + Sd). (1.25), d, d = (V/S)( 1- 2)/ 2.(1.26)
(1.26) () 1=l,025/3 2 = 1,0 /3, S=100q/ (1.23), d = (l/40)/(100q),
(1.27), d ,d = /(40q).(1.28) , , (1.28), . . , , , . , , . , ,
25-30 %, 10-15, 80-100 %. , . , , , . , , , , . - ( , .). , : , , ,
.. 300, -. - (. 1.14). , .. 450 . 300. .., , :- , ;- ;- .. 1.14 , ,
. 230, , 540 ., , , ., 3, , 1/48 . , 100 50 . , . , . ( ) (1.28). ,
1/48. , , 9, . , [email protected] , (1.28). , , , , 24 . , , , , .
, , .. 1.14. . 1.15. , ap, , [ , (. . 1.14)]. . apy, , (. 1.15). .
, , 1 ; 1 (. . 1.15). , -. ll, -l- ( - ). , , , . d.,d.,dM , d d d.
, , , (. 1.16):d = d. + l(d.- d.)/[L (l + l)] - td = d. l(d.-
d.)/[L (l + l)] - t. 1.16. d = dM l(d. - d. )/[L - (lH+l)] -
t(1.30) (+) (1.30) , -.10}(1.29), . , [email protected] 2 3. . . ,
. , , ., , . . , , , . , . , , , . ", 1749. " . . ( ). , , , . , ,
, , . - . , , , , , . , (1.10). , , V . , , , , , . , , , , - (). ,
, , , . . , (. 2.1). , d 11; 1 2. dS, xOz. yddS, 1 2 ,2 1 S SydS d
ydS d (2.1) S1 S2 - , . , (2.1), S1 S2 . , . , : ., . , , , 10-12
(. 2.2). .11, . , [email protected] . 2.1. . 2.2. . - , . . d (. .
2.1) , , 1 mi. ri , mi - . . 2.1 , , - ( mi) . , V, , , , . . . , (
) . - , , 11- d (. . 2.1). , , F (1) . F1 FB1B 1dyc. Vdyc=Vd xOz, ,
. dS, xOz. ( - f) yddS, , ) (2 11]1
S S Sf fydS y dS y d ydS y y d d V (2.2) S. ,, ;2S y ydS I dS
yfSxS (2.3) Ix - . , (2.2) d I d S y I d VrF f x i ) (2(2.4)IF- .
ri=IF/V. (2.5), , R, , - (. 2.3). , , . r = I/V; R=Iy//V. (2.6) rR
, . m .12, . , [email protected]. 2.3. . ,, , , . , , . , , -. , ,
h .. 2.4. . 2.4, , G m, , , :h=zc + r-zg; h=zm-zg; h = r-a,(2.7) a
- . H = zc + R - zg; H = zM-zg; H = R-a. (2.8) . , h > 0, , - (.
2.5). . G (h = 0) (h < 0), . .. 2.5. .. 2.5, , , , (- ). , , :
.........................................................0,51,0
.................................................................
0,31,4..........................................................................
0,10,6...........................................................................
1,03,513, . ,
[email protected].........................................................................
1,04,0 . , . , - - . , , . , , , . . () (. 2.6). , , 1 , , m. , , ,
GK = l - , G . .. 2.6. mGK l = hsin. (2.9) MB=Phsin, (2.10), , ,
sin , MB=Ph. (2.11) . (2.9)- (2.11) . , :M=sin.(2.12) , . 10-12, .
-. , , , , =, . . . (2.11) , = M/(Ph) = M/k0. (2.13) =/() = /0.
(2.14) k0 = Ph, (2.13), , K0 = - . . - - , , . M, (/) , 1. , MMMMd
d '81 . 9 , (2.15)14, . , [email protected] - , (H) g = 9,81 /2. ,
dH - dK =L, (2.14) (2.15), , 0 M, 1 , LHLPHM 81 . 9(2.16), H=R-aR ,
. / L R M (2.17) (2.17) =f(d), M . M m, , 10. ( ) =/ m .(2.18)
(2.13) (2.18), , k=Ph , 10, 3 . 57 / 3 . 57 / Ph k m (2.19)M=f(d),
m=f(d), . 4. , h = zm - zg.(2.20) zm , . zg, . , ". , , . , :h =
M0/(P00)(2.21) 0 - , - ; 0 - ; 0 - , .-(, ) (. 2.7). -- , (2.21),
l. . , ( ).. 2.7. - , ( , ) - . (. 2.8) (). , 4 1,5 . , . ( , , ).
. , -, / k tg (2.22) k - ; - . - 15-20 1,0-1,2 , . ( ). .15, . ,
[email protected] . 2.8. 1 ; 2 ; 3 ; 4 ; 5 , , , (. 2.9). .. 2.9. (
). , . P0 = k. V(2.23)k- , ;- , ; V- . , . 5. , . , . , m , (1 1
z1) (x2, y2, z2) , . 2.10., , . Axyz, (Az), - - ( ).16, . ,
[email protected]. 2.10. Oz(. 2.11) , , , , , . . 2.11. (2.7)
(2.8):h = zm - zg; = z - zg.(2.24) zm = z = 0, h = H= - zg.(2.25)
zg : - , , . zg = (m/)(z2-z1) (2.26) - ; z1 z2 - . (2.26) (2.25), h
= H = -(m/)(z2-z1) (2.27) (2.27) , (z2 0,dM
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