Page 189 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

PIPES CONVEYING FLUID: LINEAR DYNAMICS I 171

‘,oPklI
divergence
flutter

0.0 0 1 rU = Wr 2
(b)

Figure 3.71 (a) The system of a cantilevered thin-plate structure with two pairs of flexible pipes
attached, conveying fluid. (b) Stability diagram of 2u2/rr2 - 1 versus (Y = h/r for Zr2/Cw = 1.5;
the solid lines are obtained with B = 0 (Henmann & Nemat-Nasser 1967).

4 is the angle of twist about the x-axis, EC, is the warping rigidity and GJ the torsional
rigidity, E and G being Young’s and the shearing modulus of elasticity, respectively, r
is the polar radius of gyration of a section of the system, M is as just defined and rn the
mass of the structure per unit length. Here it should be recognized that an open section
subjected to torsion also warps (Timoshenko & Gere 1961); e.g. an I-section, if subjected
to torsion, will also sustain bending of the top and bottom flanges.+

‘For example, for an I-section of height h, flange width b, flange thickness tf and stem thickness fw,,
C,v = rfh2b3/24 and J = (2br: + ht:)/3 (Timoshenko & Gere 1961; appendix).