.


, , , :

. 1.


Ji - i- ;

Ci,j - ;

Di,j - . i j

;

K -

.


(Ji,Ci,j,Di,j) , Ji,Ci,j,Di,j.

:


Ji×xi''+Di-1,i×(xi'-xi-1')-Di,i+1×(xi+1'-xi')+Ci-1,i× (xi-xi-1)-Ci,i+1×(xi+1 - xi) = i (1)


堠 i - i- ;

xi,xi', xi''- , i-

.


(1) , :


J1×x1''+D01×(x1'-x0')-D12×(x2'-x1')+C01×(x1-x0)-C12×(x2-x1)= 1

J2×x2''+D12×(x2'-x1')-D23×(x3'-x2')+C12×(x2-x1)-C23×(x3-x2)= 2

J3×x3''+D23×(x3'-x2')-D34×(x4'-x3')+C23×(x3-x2)-C34×(x4-x3)= 3 (2)

J4×x4''+D34×(x4'-x3')-D45×(x5'-x4')+C34×(x4-x3)-C45× (x5-x4)= 4

J5×x5''+D45×(x5'-x4')-D56×(x6'-x5')+C45×(x5-x4)-C56×(x6-x5)= 5


(2) .


-D01×x0'-C01×x0+J1×x1''+(D01+D12)×x1'+(C01+C12)×x1-D34×x2'-

-C12×x2= 1

-D12×x1'-C12×x1+J2×x2''+(D23+D12)×x2'+(C12+C23)×x2-D23×x3'-

-C23×x3= 2

-D23×x2'-C23×x2+J3×x3''+(D23+D34)×x3'+(C23+C34)×x3-D34×x4'-

-C34×x4=3 (3)

-D34×x3'-C34×x3+J4×x4''+(D34+D45)×x4'+(C34+C45)×x4-D45×x5'-

-C45×x5= 4

-D45×x4'-C45×x4+J5×x5''+(D45+D56)×x5'+(C45+C56)×x5-D56×x6'-

-C56×x6= 5


(3) .


-(D01×s+C01)×x0+(J1×s2+(D01+D12)×s+(C01+C12))×x1 -

-(D12×s+C12)×x2= 1

-(D12×s+C12)×x1+(J2×s2+(D12+D23)×s+(C12+C23))×x2-

-(D23×s+C23)×x3= ×x4

-(D23×s+C23)×x2+(J3×s2+(D23+D34)×s+(C23+C34))×x3-

-(D34×s+C34)×x4=-×x4

-(D34×s+C34)×x3+(J4×s2+(D34+D45)×s+(C34+C45))×x4-

-(D45×s+C45)×x5= 4 (4)

-(D45×s+C45)×x4+(J5×s2+(D45+D56)×s+(C45+C56))×x5-

-(D56×s+C56)×x6= 5



Wp(s) : - D, D1, , x0=0; D56=0; C56=0; C23=0.


 


a11 a12 0 0 0

a21 a22 a23 0 0

D= 0 a32 a33 a34 0 (5)

0 0 a43 a44 a45

0 0 0 a54 a55


堠 a11 = J1×s2+(D01+D12)×s+C01+C12

a12 = -D12×s-C12

a21 = a12

a22 = J2×s2+(D12+D23)×s+C12

a23 = -D23×s

a32 = a23

a33 = J3×s2+(D23+D34)×s+C34

a34 = -D34×s-C34

a43 = a34

a44 = J4×s2+(D34+D45)×s+C34+C45

a45 = -D45×s-C45

a54 = a45

a55 = J5×s2+D45×s+C45


a11 a12 0 0 0

a21 a22 a23 -K×x4 0

D1= 0 a32 a33 K×x4 0 (6)

0 0 a43 0 a45

0 0 0 0 a55



:

D1 -K×(b7×s7+....+b1×s+b0)×x4

Wp(s) = = (7)

D×x4 s×(a9×s9+....+a1×s+a0)×x4


ai, bi Wp(s) :

(8)

a9=J1J2J3J4J5


a8=D01J2J3J4J5+D12J3J4J5(J1+J2)+J1(D23J4J5(J2+J3)+J2(D34J5(J3+J4)+D45J3(J4+J5)))


a7=C01J2J3J4J5+C12J3J4J5(J1+J2)+C34J1J2(J3J5+J4J5)+C45J1J2J3(J4+J5)+D01(D12J3J4J5+D23J4J5(J2+J3)+J2(D34J5(J3+J4)+D45J3(J4+J5)))+D12(D23J4J5(J1+J2+J3)+(J1+J2)(D34J5(J3+J4)+D45J3(J4+J5)))+J1(D23(D34J5(J2+J3+J4)+D45(J4+J5)(J2+J3))+D34D45J2(J3+J4+J5))


a6=C01(D12J3J4J5+D23J4J5(J2+J3)+J2(D34J5(J3+J4)+D45J3(J4+J5)))+C12(D01J3J4J5+D23J4J5(J1+J2+J3)+(J1+J2)(D34J5(J3+J4)+D45J3(J4+J5)))+C34(D01J2(J3J5+J4J5)+D12J5(J3+J4)(J1+J2)+J1(D23J5(J2+J3+J4)+D45J2(J3+J4+J5)))+C45(D01J2J3(J4+J5)+D12J3(J4+J5)(J1+J2)+J1(D23(J4+J5)(J2+J3)+D34J2(J3+J4+J5)))+D01(D12(D23J4J5+D34(J3J5+J4J5)+D45J3(J4+J5))+D23(D34(J2J5+J3J5+J4J5)+D45(J4+J5)(J2+J3))+D34D45J2(J3+J4+J5))+D12(D23(D34(J1J5+J2J5+J3J5+J4J5)+D45(J4+J5)(J1+J2+J3))+D34D45(J3+J4+J5)(J1+J2))+D23D34D45J1(J2+J3+J4+J5)


a5=C01(C12J3J4J5+C34J2(J3J5+J4J5)+C45J2J3(J4+J5)+D12(D23J4J5+D34(J3J5+J4J5)+D45J3(J4+J5))+D23(D34(J2J5+J3J5+J4J5)+D45(J4+J5)(J2+J3))+D34D45J2(J3+J4+J5))+C12(C34J5(J3+J4)(J1+J2)+C45J3(J4+J5)(J1+J2)+D01(D23J4J5+D34(J3J5+J4J5)+D45J3(J4+J5))+D23(D34(J1J5+J2J5+J3J5+J4J5)+D45(J4+J5)(J1+J2+J3))+D34D45(J3+J4+J5)(J1+J2))+C34(C45J1J2(J3+J4+J5)+D01(D12(J3J5+J4J5)+D23(J2J5+J3J5+J4J5)+D45J2(J3+J4+J5))+D12(D23(J1J5+J2J5+J3J5+J4J5)+D45(J3+J4+J5)(J1+J2))+D23D45J1(J2+J3+J4+J5))+C45(D01(D12J3(J4+J5)+D23(J2(J4+J5)+J3(J4+J5))+D34J2(J3+J4+J5))+D12(D23(J1(J4+J5)+J2(J4+J5)+J3(J4+J5))+D34(J3+J4+J5)(J1+J2))+D23D34J1(J2+J3+J4+J5))+D01(D12(D23(D34J5+D45(J4+J5))+D34D45(J3+J4+J5))+D23D34D45(J2+J3+J4+J5))+D12D23D34D45(J1+J2+J3+J4+J5)


a4=C01(C12(D23J4J5+D34(J3J5+J4J5)+D45J3(J4+J5))+C34(D12(J3J5+J4J5)+D23(J2J5+J3J5+J4J5)+D45J2(J3+J4+J5))+C45(D12J3(J4+J5)+D23(J2(J4+J5)+J3(J4+J5))+D34J2(J3+J4+J5))+D12(D23(D34J5+D45(J4+J5))+D34D45(J3+J4+J5))+D23D34D45(J2+J3+J4+J5))+C12(C34(D01(J3J5+J4J5)+D23(J1J5+J2J5+J3J5+J4J5)+D45(J3+J4+J5)(J1+J2))+C45(D01J3(J4+J5)+D23(J1(J4+J5)+J2(J4+J5)+J3(J4+J5))+D34(J3+J4+J5)(J1+J2))+D01(D23(D34J5+D45(J4+J5))+D34D45(J3+J4+J5))+D23D34D45(J1+J2+J3+J4+J5))+C34(C45(D01J2(J3+J4+J5)+D12(J1(J3+J4+J5)+J2(J3+J4+J5))+D23J1(J2+J3+J4+J5))+D01(D12(D23J5+D45(J3+J4+J5))+D23D45(J2+J3+J4+J5))+D12D23D45(J1+J2+J3+J4+J5))+C45(D01(D12(D23(J4+J5)+D34(J3+J4+J5))+D23D34(J2+J3+J4+J5))+D12D23D34(J1+J2+J3+J4+J5))+D01D12D23D34D45


a3=C01(C12(C34(J3J5+J4J5)+C45J3(J4+J5)+D23(D34J5+D45(J4+J5))+D34D45(J3+J4+J5))+C34(C45J2(J3+J4+J5)+D12(D23J5+D45(J3+J4+J5))+D23D45(J2+J3+J4+J5))+C45(D12(D23(J4+J5)+D34(J3+J4+J5))+D23D34(J2+J3+J4+J5))+D12D23D34D45)+C12(C34(C45(J1(J3+J4+J5)+J2(J3+J4+J5))+D01(D23J5+D45(J3+J4+J5))+D23D45(J1+J2+J3+J4+J5))+C45(D01(D23(J4+J5)+D34(J3+J4+J5))+D23D34(J1+J2+J3+J4+J5))+D01D23D34D45)+C34(C45(D01(D12(J3+J4+J5)+D23(J2+J3+J4+J5))+D12D23(J1+J2+J3+J4+J5))+D01D12D23D45)+C45D01D12D23D34


a2=C01(C12(C34(D23J5+D45(J3+J4+J5))+C45(D23(J4+J5)+D34(J3+J4+J5))+D23D34D45)+C34(C45(D12(J3+J4+J5)+D23(J2+J3+J4+J5))+D12D23D45)+C45D12D23D34)+C12(C34(C45(D01(J3+J4+J5)+D23(J1+J2+J3+J4+J5))+D01D23D45)+C45D01D23D34)+C34C45D01D12D23


a1=C01(C12(C34(C45(J3+J4+J5)+D23D45)+C45D23D34)+C34C45D12D23)+C12C34C45D01D23


a0=C01C12C34C45D23


b7=D34J1J2J5


b6=(C34J1J2J5+D34(D01J2J5+D12J5(J1+J2)+D45J1J2))


b5=(C01D34J2J5+C12D34J5(J1+J2)+C34(D01J2J5+D12J5(J1+J2)+D45J1J2)+C45D34J1J2+D34(D01(D12J5+D45J2)+D12D45(J1+J2)))


b4=(C01(C34J2J5+D12D34J5+D34D45J2)+C12(C34J5(J1+J2)+D01D34J5+D34D45(J1+J2))+C34(C45J1J2+D01(D12J5+D45J2)+D12D45(J1+J2))+C45D34(D01J2+D12(J1+J2))+D01D12D34D45)


b3=(C01(C12D34J5+C34(D12J5+D45J2)+C45D34J2+D12D34D45)+C12(C34(D01J5+D45(J1+J2))+C45D34(J1+J2)+D01D34D45)+C34(C45(D01J2+D12(J1+J2))+D01D12D45)+C45D01D12D34)


b2=(C01(C12(C34J5+D34D45)+C34(C45J2+D12D45)+C45D12D34)+C12(C34(C45(J1+J2)+D01D45)+C45D01D34)+C34C45D01D12)


b1=(C01(C12(C34D45+C45D34)+C34C45D12)+C12C34C45D01)


b0=C01C12C34C45


Wp(s) Wp(s) , .. ai,bi, , , , . , . .

MATHCAD Wp(s), Wp(s) . . Wp(s) lai, lbi . , . lai=0 Wp(s) Wi(s)= 1/s, lbi=0 Wi(s)= s. lai, lbi (Ti×s+1)×(1/Ti), Ti=1/li , Wp(s). li, li* (Ti2 × s2 +2×xi×Ti×s +1)×(1/Ti2), Ti=1 / |li| , xi=Re(li) / |li|. , :


(si)×(Tg×s+1)×( Tn2 × s2 +2×xn×Tn×s +1)

Wp(s) = k × kw × (9)

(sj)×(Tk×s+1)×( Tm2 × s2 +2×xm×Tm×s +1)


(1/Ti) × (1/Ti2)

kw =

(1/Ti) × (1/Ti2)


, :


J1 = 0.25 ×2 C01 = 1×103 ×/. D01=0.001 ××

J2 = 0.03 ×2 C12 = 1×103 ×/. D12=0.001 ××

J3 = 0.01 ×2 C23 = 0 D23=0.1 ××

J4 = 0.15 ×2 C34 =1×104 ×/. D34=0.001 ××

J5 = 1 ×2 C45 =1×103 ×/. D45=0.01 ××

= 1000


:


1) .

:

J1 = 0.25 ×2 C01 = 1×1020 ×/. D01= 0.001 ××

J2 = 0.03 ×2 C12 = 1×1020 ×/. D12= 0.001 ××

J3 = 0.01 ×2 C23 = 0 D23=0.1 ××

J4 = 0.15 ×2 C34 =1×1020 ×/. D34=0.001 ××

J5 = 1 ×2 C45 =1×1020 ×/. D45=0.01 ××

= 1000

D23 = 0.01 ... 1 H××

:


k × kw

Wp(s)= (10)

s × (T×s+1)


, w, kw .1.


.1.

D23

T

w=1/T

kw

0.01

116

0.0086

150

0.1

11.6

0.086

15

1

1.16

0.86

1.5

: 1, 2, 3, 4






           

2009 .