Page 543 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

NONLINEAR DYNAMICS THEORY APPLIED TO A PIPE CONVEYING FLUID 5 13

(LOCd B) Out[121]=
3
2.27738 eps mu r + 0.273127 eps2 mu2 r - 0.312835 r
(Local B) oUt[122]=
-0.90322 eps mu r - 0.0823938 eps2 mu2 r + 0.371685 r3 +
16.1603 eps r sig
(Local B) In[124]:=
epe = 1;
rl2 = Simplify[rdavf /r]
(kd B) Out[124]=
2
0.0704619 mu + 0.00845055 mu2 - 0.00967909 r
(Local B) In[I28]:=
(* .....................................................
*)
(* Compute the limit cycle amplitude *)
(* .....................................................
*)
rlc = Sqrt[- CoefficientIrl2,mul mu / CoefficientCr12,rA211

(Loc~ B) Out[128]=
2.69811 Sqrt [mu]
(Local B) In[130]:=
x[l] = rlc Cos[wO tl;
xl21 = rlc Sin[wO tl;
(Local B) In[134]:=
(* ..................................................... *)
(* Transform back into original coordinates *I
(* .....................................................
*I

disp = Simplify[y[[lll phIl1 + yC[2ll ph[211;
vel0 = SimplifyCy[C311 phlll + yCC411 phC2ll;