Page 504 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

474 SLENDER STRUCTURES AND AXIAL FLOW

D.3 FLEXURAL RIGIDITY AND DAMPING CONSTANTS

A very important thing to know is that boxes or drums of a given type of silicone rubber
(e.g. Silastic E) have virtually the same physical properties, only so long as they have the
same ‘Zot number’; otherwise, the properties of items cast from different boxes vary a
great deal.
For pipes and cylinders, the two essential quantities to know are (i) the flexural rigidity,
EZ, and (b) the damping constants: a! for viscoelastic Kelvin-Voigt damping and/or p for
hysteretic damping (Sections 3.3.2 and 3.3.5). In some cases, and for shells in all cases,
the Poisson ratio, u, is also needed.
The most convenient method for determining EZ and the damping constants is from
planar free-vibration tests on empty cantilevered vertical pipes - vertical because of
inevitable sagging otherwiset - in which, typically, the first-mode natural frequency,

10
8

5 14

3 12

2 10

8
1 .o

0.8 6

0.5 4

2
0.3

0.2 0
Y
Figure D.3 Real and imaginary components of the first-mode frequency, wl , and the correspon-
ding logarithmic decrement, 61 : -, ‘exact’ Galerkin solution; - - -, approximate Rayleigh method
solution (Pai’doussis & Des Trois Maisons 1971).

+If using very short horizontal pipes to avoid sagging, they may not fulfil the slenderness requirements for
Euler-Bernoulli theory to apply.