# Project Details

### Description

### Research Area

In many fields of engineering combinations of several materials has to be used

to achieve the required behavior. In particular, the sound insulation of a

structure is normally obtained by attaching some porous layers to the solid

structure which carries the load. Examples are walls of buildings, the engine

hood in a car, or the side wall of an aircraft. The latter will serve in this

project as model problem because it essentially covers all aspects of such a

construction.

Different to a composite plate, here, clearly identifiable

layers are considered where the connection between them vary from tight to

loose or it is simply an air gap. Hence, not only the plate itself also the

coupling has to be considered. Additionally, to describe the sound damping

effect of the porous structure, it has to be coupled to the surrounding fluid.

The aim is to simulate the acoustic behavior of a layered plate

like structure.

### State of the Art

All the classical plate theories, which are widely used in technical

applications, like the Kirchhoff, Mindlin or Reissner plate theories, have in

common, that they all need some a priori assumptions regarding the

distribution of either displacements or stresses in thickness direction.

A theory which does not need such a priori assumptions has been proposed by

Kienzler [4]. Starting from the general formulation of

threedimensional linear elasticity, all the above mentioned unknown

distribitions are approximated over the plate thickness using a series

expansion. Depending on where the series is truncated, the Kirchhoff theory or

a theory very similar to the one of Reissner can be

derived. Due to the series expansion the order of derivable theories has no

limit.

For the development of poroelastic plate theories the threedimensional

poroelasticity of M.A.Biot can be used [3]. So did

D.D.Theodorakopoulos und D.E.Beskos, who proposed a poroelastic Kirchhoff

plate [1]. Poroelastic theories of higher order can also be

found in the literature.

A first step in developing 'consistent poroelastic plate theories' using

Kienzlers ansatz has been taken by A. Busse and M. Schanz [2].

### Project Topics

The aim is to develop a poroelastic plate theory of higher order using

Kienzlers ansatz. The other structural elements can be modeled with

known techniques. The coupling between the single layers and the

coupling of the structure to the surrounding fluid has to be

rigorously analyzed.

Finally, the numerical simulation tool will be validated

by experiments in cooperation with Prof. O. v. Estorff, Hamburg University of

Technology (TU HH).

#### References

[1]

Theodorakopoulos D.D.; Beskos D.E.

Flexural vibrations of poroelastic plates.

*Acta Mechanica*, 103:191-203, 1994.

[2]

Busse A.; Schanz M.

A consistent theory for poroelastic plates.

In

*Proceedings in applied mathematics and mechanics*, volume

5(1), pages 381-382, 2005.

[3]

Biot M.A.

Theory of propagation of elastic waves in a fluid-saturated porous

solid.I/II. Lower/Higher frequency range.

*Journal Acoustic Society of America*, 28(2):168-191, 1956.

[4]

Kienzler R.

On consistent plate theories.

*Archive of Applied Mechanics*, 72:229-247, 2002.

Status | Finished |
---|---|

Effective start/end date | 1/02/07 → 1/05/12 |