Page 138 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)
P. 138
120 SLENDER STRUCTURES AND AXIAL FLOW
12
10
8
b
6
4
2
1
Figure 3.35 The effect of material damping, modelled by the hysteretic model, and of external
viscous damping on stability of a cantilevered pipe conveying fluid (y = k = 0): -, undamped
system; - - - , with hysteretic damping, p = 0.065; ---, with viscous damping, (T = 1.42;
-.- , with viscous damping, o = 0.23 (Gregory & PaYdoussis 1966b). The black dots mark the
threshold values of B beyond which, for each of these three cases, the system is destabilized by
damping.
due to dissipation in the material of the pipe. In this respect, it is useful to adapt the
relationships of Section 2.2.3 to the work at hand. For unconfined fluid, the damping
force is given by
(3.105)
from (2.153) and (2.157), respectively, where S= DR?/u, R, being the outer radius of
the pipe. In terms of the dimensionless parameters used here,
(3.106)
