Page 466 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

438 SLENDER STRUCTURES AND AXIAL FLOW

are wholly real so long as the system remains stable, unless dissipation is taken into
account (or the fluid conveyed is viscous).
The dynamics of the system as predicted by inextensible, extensible and modified
inextensible theory will be discussed in this section; the same is done in Sections 6.5
and 6.6 for other boundary conditions. It is recalled that in the conventional inextensible
theory not only is extensibility of the centreline neglected, but also the effect of the steady
forces arising from the centrifugal and pressure forces generated by the internal fluid as it
moves along the pipe; i.e. no which comprises the axial force Q, and the pressure force
is
nP neglected. In the modiJed inextensible theory these forces are taken into account.
In the extensible theory, the extension of the centreline is also taken into account.

6.4.1 Conventional inextensible theory

Typical results for in-plane motion of a clamped-clamped semi-circular pipe conveying
fluid are presented in Figure 6.5, showing the evolution of the lowest eigenfrequencies of

Figure 6.5 Dimensionless eigenfrequencies W* by conventional inextensible theory for in-plane
motion of a clamped- clamped semicircular pipe conveying fluid as functions of the dimensionless
flow velocity E*, for I7 = 0 and (a) B = 0; (b) B = 0.5. --- Chen (1972a); -, Misra et al.
(1988a).