Page 538 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

508 SLENDER STRUCTURES AND AXIAL FLOW

(Local B) Zn[44]:=
(* NORMAL FORM OF THE HOPF BIFURCATION using Mathematics *)

amode = 2; (* Number of modes *)
ar = 0.005; (* Damping coefficient alpha *)
uhb = 7.093; (* Critical flow velocity *)
beta = 0.2; (* Maas parameter beta *)
gama = 25; (* Gravity parameter *)

u = uhb + eps mu;

rlC11 = 1.875104043341462;
rlC21 = 4.694091054370627;

xb = 1.0;
DO [{
si[il = (Sinh[rl[il l-Sin[rl[iIl)/
(CoshCrl [ill +Cos [rl [ill ) ,
ph[iI = Cosh[rl [il *xbI -Cos [rl [il *&I -
ai [il *(Sinh[rl [il *&I -Sink1 [il *xbI
I, {i,nmodell

DO I Do [(
tauti,jl = (rl[il/rl[jl)A2,
one[i,jl = (-1lA(i+j),
If [j==i,
bb[i,jl = 2.0,
bb[i,jl = Q.O/(tau[i,~l+one[i,~l)l,
If [j==i,
ccIi,jI = rl Ijl *si [jI*(a.O-rl Ijl*si[jl),
cc[i, j1 = 4.0*~r1[j1*si~j1-rl[i1*si[il)/
(one Ii, j 1 -tau [i, j 1 1 1 ,
If j==i,
ee[i,jI = 2.0 - 0.5*cc[i,j],
ee[i, j1 = (4.0*(rl [jI*si[jl -rl[il*si[i]+2.O)*
0- ci , j 1 -
+2.0*(l.0+tau~i,jIA2)*bb[i,jl)/