Page 542 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

512 SLENDER STRUCTURES AND AXIAL FLOW

TrigSimpRules = {
Sin[x-+y-l : > Sin[xl Cos [yl + Sintyl Cos [XI,
Cos[x-+y,l :> CosCxl Cos[yl - Sinixl Sin[yl3

Trigsimpsign = {
(* Sin is an odd function *)
Sintn-?Negative x-.I :> -Sin[-n XI,
Sin[n-?Negative x- + y-I :> -Sin[-n x - yl /;
OrderIx, y1 == 1 && Number~tnl,

(* Cos is an even function *)
Cos[n-?Negative x-.I :> Cos[-n XI,
Cos[n-?Negative x- + y-I :> Cos[-n x - yl /;
Order Ex, y1 == 1 && MrmberQ[nl3

kap = l/2;

rdavIt-I = Integrate[rd,tl /. Trigsimpsign
rdavf = Expand[rBav[2 Pi] - rdav[Oll /. TrigSimpRules
rdavf= Simplify[l/Z?/Pi/nu rdavf];

(Local B) ln[lI7]: =
rthlt-I = Integrate[rtheta,tl ;
rthf = Expand[rth[3 Pi1 - rth[Oll /. TrigSimpRUle8
rthf = Chop [Simplify[
l/nu*(l/2/Pi*rthf - r w0 (1-eps sig))1,0.00011
(Lacal B) In[l221:=
(* ..................................................... *)
(* This corresponds to the equation (43) of the article
by Paidoussis and Semler; as can be Been, the nonlinear
terms are not the same, but the relative magnitude is
exactly the same
(* ..................................................... *I
*)
Simplify [rdavf nul

Simplifyfrthf nul