1. Reference problem#

1.1. Geometry#

_images/Cadre3.gif

Image 1.1-1: Sandwich plate geometry.

Rectangular sandwich plate composed of three layers of different materials:

Side: 0.05m x 0.15m

Thickness: aluminum (top): 0.5 mm

viscoelastic material (center): 1 mm

steel (bottom): 1 mm

1.2. Material properties#

The material of the top layer is aluminum (isotropic elastic); its properties are constant:

  • Young’s modulus \(E=70000\mathit{MPa}\)

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

  • density \(\rho =2700\mathit{kg}/{m}^{3}\)

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

The material in the bottom layer is steel (isotropic elastic); 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 \(\eta =\mathrm{0,002}\)

The core layer material 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 the 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#

Boundary conditions:

  • embedding on one edge of the steel layer.

Loading:

  • nodal force at point A: FZ=1.

1.4. Initial conditions#

Not applicable (harmonic calculation).