1. Reference problem#

1.1. Geometry#

Rectangular beam, composed of two layers of different materials:

_images/Cadre1.gif

Image 1.1-1: Geometry of the viscoelastic beam.

Width: 0.01 m

Length: 0.15 m

Thickness: Elastic material (layer No. 1 at the bottom): 0.001 m

Viscoelastic material (top layer no. 2): 0.002 m

1.2. Material properties#

The material of layer No. 1 below is isotropic elastic (steel); its properties are constant:

  • Young’s modulus \(E=210000\mathit{MPa}\)

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

  • density \(\rho =7800\mathit{kg}/{m}^{3}\)

  • hysteretic damping \(\eta =\mathrm{0,001}\)

The material of the top layer No. 2 is viscoelastic (elastomer); some of its properties are frequency-dependent:

Frequency (Hz)

Real part of Young’s modulus \(E\) (MPa)

Loss factor \(\eta\)

1

23.2

1.1

10

58

0.85

50

145

0.7

100

203

0.6

500

348

0.4

1000

435

0.35

1500

464

0.34

Table 1.2-1 : ****Frequency-dependent properties of viscoelastic material. **

The others are constant:

  • Poisson’s ratio \(\nu =\mathrm{0,45}\)

  • density \(\rho =1200\mathit{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

Embedded on a steel edge.

1.4. Initial conditions#

Not applicable (natural mode calculation).