Geology Reference
In-Depth Information
C .
C The sequential process described, axial ---> torsional --->
C ---> v bending requires one final step, i.e., the solution
C " ---> w bending" for the second bending mode. This logic
C is listed without comment.
C .
C .
C COUPLED BENDING VIBRATIONS
C W LATERAL MODE
DO 800 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 (-VNM1(I-2)+2.*VNM1(I-1)
2 -2.*VNM1(I+1)+VNM1(I+2))/(2.*DX**3)
3 +GJ*(DTHDX(I+1)-DTHDX(I-1))*(1./(2.*DX))*
4 (VNM1(I-1)-2.*VNM1(I)+VNM1(I+1))/(DX**2)
5 +BEAMB*WNM2(I)/(2.*DT)
6 +2.*RHO*AREA*WNM1(I)/(DT**2)
7 -RHO*AREA*WNM2(I)/(DT**2)
800 CONTINUE
C .
C .
CALL REDUCE(A,B,C,D,E,W,IMAX)
CALL TRIDI(A,B,C,VECTOR,W,IMAX)
DO 850 I=1,IMAX
WBENDN(I) = VECTOR(I)
850 CONTINUE
C .
C At this point, all of the calculations for a time
C step N are completed and command returns to the top
C of the 900 do-loop for the next time integration.
C .
900 CONTINUE
C .
STOP
END
Figure 4.5.3.
Coupled vibrations, Fortran listing (continued).
Next, we proceed to use the algorithm given in Figure 4.5.3, to calculate
realistic drillstring coupled vibrations. Two detailed examples were selected to
demonstrate the range of capabilities behind the algorithm designed in this topic,
to show that events like
bit bounce, forward rate-of-penetration, stick-slip,
torque-reversal, and drillbit precession
can be modeled and simulated
straightforwardly in a stable fashion.
Search WWH ::
Custom Search