1. Reference problem#

1.1. Geometry#

The characteristics of the straight pipe with a hollow circular cross section are as follows:

outside diameter of the tube:

\(\mathrm{19,05}\mathrm{mm}\),

inner tube diameter:

\(\mathrm{16,87}\mathrm{mm}\).

The total length of the tube is \(\mathrm{1,00 }m\), with:

the length of part \(\mathrm{AB}\):

\(\mathrm{0,4975}m\),

the length of part \(\mathrm{CD}\):

\(\mathrm{0,4975}m\).
_images/Object_1.svg

Note:

Flow velocities are given to the nodes and not to the elements. Two adjacent areas of excitement must be separated by an element ( \(\mathrm{BC}\) in this case). However, the flow speed is well defined at all nodes and it is the stretch \([\mathrm{AD}]\) as a whole that is excited.

1.2. Material properties#

The values of the physical quantities characteristic of each of the elements of the structure are:

Brass tube:

\(E=\mathrm{1,22}{10}^{11}N/{m}^{2}\)

\(\nu =\mathrm{0,3}\)

\(\rho =8320\mathrm{kg}/{m}^{3}\)

Internal fluid:

water

\({\rho }_{i}=1000\mathrm{kg}/{m}^{3}\)

External fluid:

tube immersed in water over the whole length \(\mathrm{AD}\), transverse flow of water over the whole length \(\mathrm{AD}\), \({\rho }_{e}=1000\mathrm{kg}/{m}^{3}\).

An added mass coefficient for calculating the equivalent density of the structure to be studied is taken into account. The structure consists of a beam, an internal fluid, and an external fluid.

1.3. Boundary conditions and loads#

The beam is simply supported at nodes \(A\) and \(D\).

A random load is distributed over the excited length (section \([\mathrm{AD}]\) or sections \([\mathrm{AB}]\) and \([\mathrm{CD}]\)) of the beam. Turbulent excitation is thus achieved by a flow transverse to the tube. Excitations are defined using a speed profile along the beam and a dimensionless excitation spectrum. Each fluid excitation zone is implicitly defined by the portion of the tube over which the flow speed is not zero. In the case of multiple excitations, the areas of excitation must be disjunct.

1.4. Initial conditions#

Since the calculation is frequent, no initial conditions are imposed.