Re-routing of elastodynamic waves by means of transformation optics in planar, cylindrical, and spherical geometries
Seminar Room 1, Newton Institute
Transformation optics has proven a powerful tool to achieve cloaking from electromagnetic and acoustic waves. There are still technical issues with applications of transformation optics to elastodynamics, due to the fact that the elastodynamic wave equation does not in general possess suitable invariances under the required transformations. However, for a few types of materials, invariances of the appropriate kind have been shown to exist.
In the present talk we consider a few canonical scattering and reflection problems, and show that by coating the planar, cylindrical or spherical reflecting or scattering bodies with a fiber-reinforced layer of a metamaterial with a suitable gradient in material properties, the reflection or scattering of shear waves from the body can be significantly reduced.
It has been suggested that constructions inspired by transformation optics could potentially provide protection for infrastructure from seismic waves. Even if waves from earthquakes may have wavelengths making some such suggestions implausible, passive protection from shorter elastic bulk waves from other sources may be achieved by a scheme based on transformation optics. Other suggested applications are in the car and aeronautics industries.
The problems considered here, albeit rather special model problems, hopefully may provide some additional insight into protection against mechanical waves by means of transformation elastodynamics.
A result of the analysis in the case of a spherical case is, that to maximize number of modes to which the coated spherical body is “invisible,” rigid body rotations of the innermost part of the coating should be allowed. (However, this is only essential in the low frequency range.) It is also worth noting that since the transition matrices of scatterers described here have, as it were, quite well-populated null-spaces, they provide simple examples of cases where complete knowledge of the scatterer and of the scattered field does not even remotely suffice to reconstruct the incident field.