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.