1. Reference problem#
1.1. Geometry#
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Straight pipe with a hollow circular cross section:Outer tube diameter: \(\mathrm{15,90 }\mathrm{mm}\) Inner tube diameter: 1 \(\mathrm{2,72 }\mathrm{mm}\) |
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Total Tube Length: \(\mathrm{1,350 }m\) Part Length \(\mathrm{AB}\): \(\mathrm{0,305 }m\) Part Length \(\mathrm{BC}\): Part Length: \(\mathrm{0,300}m\) Part Length \(\mathrm{CD}\): \(\mathrm{0,305 }m\) Part Length \(\mathrm{DE}\): \(\mathrm{0,440}m\) |
1.2. Material properties#
The values of the physical quantities characteristic of the elements of the structure are:
Brass tube:
\(E=\mathrm{1,1}{10}^{11}N/{m}^{2}\) |
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Internal fluid: air
\({\rho }_{i}=\mathrm{1,3}\mathrm{kg}/{m}^{3}\)
External fluid: |
tube immersed in water over the part of its length between the two supports, tube immersed in air over the cantilever part of its length, transverse flow incident on part \(\mathrm{BC}\) of the tube. |
\({\rho }_{e}=\mathrm{1000,0}\mathrm{kg}/{m}^{3}\) or \(\mathrm{1,3}\mathrm{kg}/{m}^{3}\) depending on the external zone
An equivalent density is attributed to the structure when calculating its modal fluid base at rest; this equivalent density includes the density of the internal fluid, that of the structure and that of the external fluid; the inertial effect of the latter is evaluated by means of an added mass coefficient.
1.3. Boundary conditions and loads#
The beam is simply supported at points \(A\) and \(D\). A distributed random load, transverse to the tube, is imposed on section \(\mathrm{BC}\). This loading is defined, on the one hand using a speed profile along the excited zone, and on the other hand using a dimensionless excitation spectrum.