1. Reference problem#

1.1. Geometry#

_images/10000000000002950000015E5995D9654244415A.png

Beam length: \(\mathrm{1.5m}\)

Discreet stiffness: \(\mathrm{kax}\), \(\mathrm{kay}\),, \(\mathrm{kbx}\), \(\mathrm{kby}\)

1.2. Material properties#

Material for the line element: \(E=2.0E+10\), \(\rho =1000.0\)

Mechanical characteristics of the girder: \(\mathrm{section}=\text{'}\mathrm{CERCLE}\text{'}\), \(\mathrm{rayon}=0.1\), \(\mathrm{ep}=0.1\)

The stiffness of the springs:

\(\mathrm{Kxa}\)

\(\mathrm{Kya}\)

\(\mathrm{Kxb}\)

\(\mathrm{Kyb}\)

\(10N/m\)

\(20N/m\)

\(25N/m\)

\(22N/m\)

1.3. Boundary conditions and loads#

At points \(A\) and \(B\): blocking the degrees of freedom: \(\mathrm{DX},\mathrm{DY},\mathrm{DZ}\)

At points \(\mathrm{A1}\) and \(\mathrm{B1}\): blocking the degrees of freedom: \(\mathrm{DZ},\mathrm{DRX},\mathrm{DRY}\)

The springs are modelled by dimensionless discretes. Nodes \(A\) and \(\mathrm{A1}\), \(B\) and \(\mathrm{B1}\) are geometrically confused.

The characteristics of the wind speed field, along axis \(y\):

\(\mathit{Vy}\mathrm{=}\mathrm{20.sin}(\omega \mathrm{.}t)\), with \(\omega =2.\pi \mathrm{.}f\) and \(f=0.2\mathrm{Hz}\)

1.4. Initial conditions#

The beam has an angle of \(30°\) (\({\theta }_{0}=30°\)) with respect to the \(x\) axis.