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DTHDX(1) = (THETAN(2)-THETAN(1))/DX
TORBIT = GJ*DTHDX(1)
DTHDX(IMAX) = (THETAN(IMAX)-THETAN(IMAXM1))/DX
DO 505 I=2,IMAXM1
DTHDX(I) = (THETAN(I+1)-THETAN(I-1))/(2.*DX)
505 CONTINUE
C COUPLED BENDING VIBRATIONS
C V LATERAL MODE
C This section on coupled vibrations implements Equations
C 4.5.7 and 4.5.8. We annotate the listing for Equation 4.5.7
C describing v(x,t) in detail. The coefficients, D, E, A,
C C, B and W are determined by one-to-one comparison from
C the pentadiagonal form in Equation 4.5.7.
C
DO 600 I=3,IMAXM2
D(I) = EI/DX4
E(I) = EI/DX4
A(I) = -4.*EI/DX4 -AE*DUDX(I)/(DX*DX)
1 +AE*(DUDX(I+1)-DUDX(I-1))/(4.*DX*DX)
C(I) = -4.*EI/DX4 -AE*DUDX(I)/(DX*DX)
1 -AE*(DUDX(I+1)-DUDX(I-1))/(4.*DX*DX)
B(I) = 6.*EI/DX4 +2.*AE*DUDX(I)/(DX*DX)
1 +BEAMK +BEAMB/(2.*DT) +RHO*AREA/(DT**2)
W(I) = Q -GJ*DTHDX(I)*
1 (-WNM1(I-2)+2.*WNM1(I-1)
2 -2.*WNM1(I+1)+WNM1(I+2))/(2.*DX**3)
3 -GJ*(DTHDX(I+1)-DTHDX(I-1))*(1./(2.*DX))*
4 (WNM1(I-1)-2.*WNM1(I)+WNM1(I+1))/(DX**2)
5 +BEAMB*VNM2(I)/(2.*DT)
6 +2.*RHO*AREA*VNM1(I)/(DT**2)
7 -RHO*AREA*VNM2(I)/(DT**2)
600 CONTINUE
C .
C .
C Next, the coefficients for the downhole indexes i = 1 and
C 2, and for the surface indexes i = imax-1 and imax, must
C be given in order to have imax equations in imax unknowns.
C These, not shown for now, are discussed later in the text.
C .
C .
C Once all of the required matrix coefficients are defined,
C the outer-most "bands" of the pentadiagonal matrix can be
C eliminated, to reduce the matrix to tridiagonal form, and
C the result can be solved solved using the TRIDI call.
C
CALL REDUCE(A,B,C,D,E,W,IMAX)
CALL TRIDI(A,B,C,VECTOR,W,IMAX)
C .
C Then, the v(x,t) solution is updated by copying the newly
C obtained solution from the tridiagonal solver.
C
DO 650 I=1,IMAX
VBENDN(I) = VECTOR(I)
650 CONTINUE
Figure 4.5.3.
Coupled vibrations, Fortran listing (to be continued).
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