1. Reference problem#

1.1. Geometry#

We consider a beam of length \(L=\mathrm{7,62}m\), of rectangular cross section (\(\mathit{Hy}=\mathrm{0,0508}m\) and \(\mathit{Hz}=\mathrm{0,0254}m\)). It is oriented along the \(\mathit{Ox}\) axis.

1.2. Material properties#

The material is isotropic elastic whose properties are:

  • Young’s modulus: \(E=\mathrm{206,8}{10}^{9}\mathrm{Pa}\)

  • Poisson’s ratio: \(\nu =\mathrm{0,3}\)

  • density: \(\rho =\mathrm{7780,0}\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

The beam is embedded at each of its ends.

The load is a seismic excitation perpendicular to the direction of the beam, expressed in the form of an accelerogram. It is taken from a recording of the so-called El Centro earthquake (). The direction of the earthquake is axis \(\mathit{Oy}\). The sample is \(\mathrm{0,01}s\).

_images/100000000000034A00000253F4218E05A6F5E129.png

Illustration 1: Accelerogram called « El Centro » taken over 2 s.

For modeling A, single-pressed excitation is considered: the same accelerogram is imposed at both ends of the beam.

For modeling B, a multi-press excitation is considered: the accelerogram imposed at both ends is the same as in mono-press but, in this case, at the opposite end it is applied with a delay of \(\mathrm{0,25}s\) compared to the origin.

1.4. Initial conditions#

The beam is considered to be at rest before the earthquake arrives.