1. Reference problem#

1.1. Geometry#

_images/100002000000032B0000023B45BC70DBDBD242CB.png

Dimensions of pad \((m)\):

length (according to \(x\)): \(0.35\)

width (according to \(y\)): \(0.25\)

thickness (according to \(z\)): \(0.01\)

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 proportional to the stiffness and to the mass \([C]=\alpha [K]+\beta [M]\).

1.3. Boundary conditions and loads#

    • Embedding the side faces

      • Harmonic pressure of amplitude \(p={10}^{5}\mathrm{Pa}\) at a frequency \(f=1500\mathrm{Hz}\) on the upper side