Page 454 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

426 SLENDER STRUCTURES AND AXIAL FLOW

6.2.3 The boundary conditions

The boundary conditions are as follows.
(i) Ifan end is clamped,

au
u = 0, - = 0, w = 0, for in-plane motion; (6.43a)
as
av
2, = 0, - = 0, $ = 0, for out-of-plane motion. (6.43b)
as
(ii) If an end is pinned,

for in-plane motion; (6.44a)

for out-of-plane motion. (6.44b)

(iii) lfan end is free,

0, for in-plane motion; (6.45a)

(6.45b)

6.2.4 Nondimensional equations

It is convenient to analyse the equations of motion in dimensionless form by defining the
following quantities:

U V W S s=t( EI ) ’I2
L’
91 = - 92=-, q3=-, <=-
L L L’ (M + m)L4 ’