There is a paper by M. Farhat, S. Guenneau and S. Enoch, which has nothing to do with flexural waves. The paper shows that the design works for only 10 rings with 6 different elastic materials.
M. Farhat, S. Enoch, S. Guenneau and A.B. Movchan, Controlling surface waves through artificial transversely isotropic fluid, Physical Review Letters, vol. 101, 1345011, 2008. This research is for protecting against Tsunamis.
There is another paper by M. Brun, S. Guenneau and A.B. Movchan.
This rewritten article was mostly referring to the Brun, Guenneau and Movchan article but had mixed in some references to the Farhat, Guenneau and Enoch article.
Sebastien Guenneau has about 35 research papers from 2007 - 2009.
A New Scientist article discusses what one of the papers. It borrows from the physics of invisibility cloaks could make it possible to hide buildings from the devastating effects of earthquakes.
For a ten meter building, you need a one meter thick foundation with a diameter of 20 meters.
This is something that would only make economic sense for nuclear power plants and high value military or other complexes or if as a society we decided to make key
infrastructure robust. (Like hospitals).
From the American Physical Society and Arxiv a paper by Brun, Guenneau and Movchan. Theoretical work on creating an earthquake cloak (pdf, 9 page)
A derivation of the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with 16 spatially varying entries which are deduced from a geometric transform.
The seismic waves of an earthquake fall into two main groups: body waves that propagate through the Earth, and surface waves that travel only across the surface.
The research team [Michele Brun, Sebastien Guenneau and Sasha Movchan] have calculated that controlling body waves would be too complex, controlling surface waves is within the ability of conventional engineering, they say. Fortunately, it is surface waves that are more destructive, says team member Sebastien Guenneau at the University of Liverpool in the UK.
The new theoretical cloak comprises a number of large, concentric rings made of plastic fixed to the Earth's surface. The stiffness and elasticity of the rings must be precisely controlled to ensure that any surface waves pass smoothly into the material, rather than reflecting or scattering at the material's surface.
When waves travel through the cloak they are compressed into tiny fluctuations in pressure and density that travel along the fastest path available. By tuning the cloak's properties, that path can be made to be an arc that directs surface waves away from an area inside the cloak. When the waves exit the cloak, they return to their previous, larger size.
Unlike some of the optical invisibility cloaks that have been studied in physics labs in recent years, the new cloak is "broadband", meaning that it can divert waves across a range of frequencies.
Achieving control of in-plane elastic waves: Applied Physics Letters
We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity of our approach is confirmed by comparison of the analytic Green's function in homogeneous isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic elastic region surrounded by perfectly matched layers
Cloaking bending waves propagating in thin elastic plates by Mohamed Farhat, Sebastien Guenneau, Stefan Enoch, and Alexander B. Movchan
We introduce a cylindrical cloak to control the bending waves propagating in thin plates. This is achieved through radially dependent isotropic mass density and radially dependent and orthotropic flexural rigidity deduced from a coordinate transformation for the biharmonic propagation equation in the spirit of the paper of Pendry et al. [Science 312, 1780 (2006)]. We analyze the response of the cloak surrounding a clamped obstacle in the presence of a cylindrical excitation. We note that whereas the studied bending waves are of different physical and mathematical nature, they are cloaked in many ways as their electromagnetic and acoustic counterparts; e.g., when the source lies inside the coating, it seems to radiate from a shifted location (mirage effect).