Two-dimensional elastodynamic wave propagation in graded structures

A two-dimensional simulation of elastodynamic waves propagating in a continuum with graded elastic properties in one dimension is presented and the refraction/reflection properties are discussed.

Graded materials or functionally graded materials (FGM) are defined as materials featuring gradual spatial transitions in microstructure and/or composition thus having gradually varying mechanical properties like Youngs moduli, shear moduli, and/or densities.

In engineering applications the development of such material systems is motivated so far by the demand to produce objects which are hard and wear resistant at the surface while having a ductile tough body like cutting tools to give an example. Ceramically coated turbine blades might be mentioned as another application where FGMs are used in order to reduce thermally induced mechanical stress concentrations along the ceramic metal interface.

The dynamic response to local disturbances of the equilibria in particular the elastodynamic wave propagation in graded continua is a rarely treated topic. It is of particular interest since the reflection, refraction, and transmission of elastodynamic waves is frequency dependent provided that the spatial area in which the material properties vary is in the order of the elastic wavelengths to be distinguished, a fact which opens a wide field of engineering applications like frequency filters, spectrum analyzers, or acoustic isolation layers.

A finite difference method is implemented to solve the time-boundary problem numerically. The frequency dependent refraction of a plane wave front hitting a graded zone under an arbitrary angle as well as the behavior of a longitudinal wave hitting the ’soft’ acoustic interface perpendicularly are discussed. Aspects of accuracies of the numerical simulation are discussed as well.

Future directions of the on-going research project are presented.