1. Reference problem#

1.1. Geometry#

_images/Shape1.gif

Geometry of plate \((m)\):

\(L=1\)

\(e=0.001\) thickness

Coordinates of points \((m)\):

\(O(0.0,0.0)\)

\(E(-0.1,-0.1)\)

Mesh group:

\(\mathrm{CONT}\text{\_}\mathrm{NO}\): \(\mathrm{AB},\mathrm{BC},\mathrm{CD},\mathrm{DA}\) sides

\(\mathrm{COND2}\text{\_}\mathrm{NO}\): Face \(\mathrm{ABCD}\) except point \(E\)

1.2. Elastic properties of the material#

  • \(E=7.1E10\mathrm{Pa}\) Young’s module

  • \(\nu =0.3\) Poisson’s ratio

  • \(\rho =7820.0{\mathrm{kg.m}}^{-3}\) Density

  • \(\mathrm{AMOR}\text{\_}\mathrm{ALPHA}=0.5{\mathrm{N.s.m}}^{-1}\)

  • \(\mathrm{AMOR}\text{\_}\mathrm{BETA}=0.1{\mathrm{N.kg}}^{-1}\)

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

1.3. Boundary conditions and loads#

    • Imposed travel:

        • \(\mathrm{CONT}\text{\_}\mathrm{NO}\): zero movements and rotations

        • \(\mathrm{COND2}\text{\_}\mathrm{NO}\): zero movements and rotations

      • Excitation force \((N)\):

        • Point \(E\): \(\mathrm{Fz}=1\)