1. Reference problem#

_images/Shape1.gif

1.1. Geometry#

Coordinates of points expressed in meters:

\(A:(0.0,0.0)\)

\(B:(0.35,0.0)\)

\(C:(0.35,0.6)\)

\(D:(0.0,0.6)\)

1.2. Elastic properties of the material#

  • \(E=1.8\times {10}^{11}\mathrm{Pa}\) Young’s module

  • \(\nu =0.3\) Poisson’s Ratio

  • \(\rho =7800.0{\mathrm{kg.m}}^{-3}\) Density

  • \(\alpha =3\times {10}^{-5}s\)

  • \(\beta =0.001{s}^{-1}\)

The coefficients \(\alpha\) and \(\beta\) make it possible to build a viscous damping matrix that is proportional to the stiffness and to the mass \([C]=\alpha [K]+\beta [M]\).

1.3. Boundary conditions and loads#

    • Embedding on the \(\mathit{AD}\) side

\(\mathrm{DX}=0.0m\), \(\mathrm{DY}=0.0m\)

      • The \(\mathit{BC}\) side is subject to a harmonic pressure of amplitude \(p\mathrm{=}{10}^{5}\mathit{Pa}\) at a frequency \(f=1500\mathrm{Hz}\)