Design of Thin-Walled Metastructures for Advanced Elastic Wave Management

The development of advanced methodologies for the control and attenuation of broadband, non-stationary elastic energy propagating through structural systems has been a long standing challenge in many fields of engineering. These capabilities are of particular importance to enable the next generation of high performance aerospace and mechanical systems that will be required to operate under extreme conditions.

The relatively recent discovery of Acoustic Metamaterial(AMM) has open a new direction to manipulate and passively control acoustic wave in bulk materials and structures. Only recently, this concept was extended to the field of elastic waves propagation in structural elements. Nevertheless this class of applications still remains very limited with even fewer examples of experimental validations. Some of the contributing factors are connected to the fabrication complexity of multi-material systems and to their lack of load-bearing capabilities.

This research advances the state-of-the-art for acoustic metameterials by integrating their principles at rather the structural geometric level in order to surpass these limitations. Consequently, this thesis proposes a single-material based thin-walled system with carefully tailored internal geometries while providing the same level of elastic wave control capabilities enabled by multi-material designs, therefore introducing the concept of elastic \ extit{metastructure}. The main element of the proposed design approach leverages on the use of embedded geometric tapers realized by controlling spatially the thickness variation of flat waveguides. This is a key aspect to maintain structural integrity and to be able to transfer metamaterial concepts to structural element design. Particular emphasis is placed on the identification of novel methodologies to design, model and evaluate the performance of thin-walled elastic metastructures.

Similarly to AMMs, metastructures can be classified, as non-resonant and locally-resonant types. This research proposed, for the first time, a non-resonant metastructure design based on the use of Acoustic Black Holes, which is an axial-symmetric taper following power-law thickness profile. Simple yet versatile, the ABH-based design is demonstrated to exhibit the same plethora of high-level wave functionalities, including but not limited to local Zero-Group-Velocity-Point, positive and negative bi-refraction, mode hybridization and anisotropy, and Dirac-Like Cones, than more complex multi-material resonant systems. The ABH-based design finds a direct application to the design of embedded acoustic lenses in thin-walled elastic waveguides enabling acoustic focusing, collimation and bi-refraction over both the short and long wavelength regimes.

The second part of the dissertation extends the concept of a geometric taper to the design of locally-resonant metastructures and explores their novel functionalities. More specifically, this study will present the first experimental observation of a double-zero-index (near zero effective mass density and elastic compliance) material in the elastic structural elements. Using an effective medium description, results confirm the possibilities to map the metastrucuture behavior to a medium having simultaneous zero mass density and elastic compliance in shear. Both the numerical and experimental investigations confirm the remarkable capabilities of this metastructure system including unconventional effects such as cloaking, supercoupling and energy squeezing.

Finally, the last part of the dissertation presents the first design and implementation of an elastic metasurface fully embedded into a thin-walled waveguide. A metasurface is a subwavelength interface capable of producing abrupt phase shift gradient of incoming wave, and hence achieving ``on demand' refraction properties. Also this concept leverages the locally-resonant geometric taper design in order to synthesize a flat metasurface capable of anomalously refraction, focusing and non-paraxial acoustic beam propagation.

Overall, this research provided clear theoretical, numerical and experimental evidence of the potential of geometrically-tailored metastructures to achieve high level wave management functionalities.