Numerical simulation of the dynamic behaviour of poroelastic plates due to acoustical excitation

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.