Page 556 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

526 SLENDER STRUCTURES AND AXIAL FLOW

Figure 5.2 Forces in Figure J.l(b) projected onto the Zo and YO axes.

1y2j + lF3k, ey0 = l;,i + 1;2j + 1z3k, e,, = l;,i + 1T2j + 13*3k, we also have (b) ae,,/as =
(aZ;,/as)i + (aly,/as)j + (i31f3/i3s)k, etc. Then, combining the two different forms (a) and
(b) of the expressions for the derivatives in each case, one can obtain the derivatives of
l;j, as follows:

The (XO, YO, ZO) frame is now set to coincide with (XO, yo, ZO), so that 17j = 6ij; also,
li = L3i, i = 1, 2, 3, in (5.12) become the direction cosines of the z-axis referred to the
(xo, yo, LO) frame as given by
au av & I
=
= - - tov + K~W, L32 = - - K,W + sou, ~33 - - K,U + K,W + 1.
as as as
(J. 14)
Then, substituting relations (5.13) into equations (5.10) and (J.l l), the equations of motion
of the pipe along the xo-, yo- and Lo-axes may be written as

(J. 15)