In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave trapping, mode conversion from surface (Rayleigh) waves to bulk (shear) waves, and spatial frequency selection. Devices built around these concepts allow for precise control of surface waves, often with structures that are subwavelength, and utilise Rainbow trapping that separates the signal spatially by frequency. Rainbow trapping yields large amplifications of displacement at the resonator positions where each frequency component accumulates. We investigate whether this amplification, and the associated control, can be used to create energy harvesting devices; the potential advantages and disadvantages of using graded resonant devices as energy harvesters is considered. We concentrate upon elastic plate models for which the A 0 mode dominates, and take advantage of the large displacement amplitudes in graded resonant arrays of rods, to design innovative metasurfaces that trap waves for enhanced piezoelectric energy harvesting. Numerical simulation allows us to identify the advantages of such graded metasurface devices and quantify its efficiency, we also develop accurate models of the phenomena and extend our analysis to that of an elastic half-space and Rayleigh surface waves.

Important distinctions are made between two related wave control mechanisms that act to spatially separate frequency components; these socalled rainbow mechanisms either slow or reverse guided waves propagating along a graded line array. We demonstrate an important nuance distinguishing rainbow reflection from genuine rainbow trapping and show the implications of this distinction for energy harvesting designs. The difference between these related mechanisms is highlighted using a design methodology, applied to flexural waves on mass loaded thin Kirchhoff-Love elastic plates, and emphasised through simulations for energy harvesting in the setting of elasticity, by elastic metasurfaces of graded line arrays of resonant rods atop a beam. The delineation of these two effects, reflection and trapping, allows us to characterise the behaviour of forced line array systems and predict their capabilities for trapping, conversion and focusing of energy.

We amalgamate two fundamental designs from distinct areas of wave control in physics, and place them in the setting of elasticity. Graded elastic metasurfaces, so-called metawedges, are combined with the now classical Su-Schrieffer-Heeger (SSH) model from the field of topological insulators. The resulting structures form one-dimensional graded-SSH metawedges that support multiple, simultaneous, topologically protected edge states. These robust, enhanced localized modes are leveraged for applications in elastic energy harvesting using the piezoelectric effect. The designs we develop are first motivated by applying the SSH model to mass-loaded Kirchhoff-Love thin elastic plates. We then extend these ideas to using graded resonant rods, and create SSH models, coupled to elastic beams and full elastic half-spaces.

We identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe.

We experimentally demonstrate that a rainbow-based metamaterial, created by a graded array of resonant rods attached to an elastic beam, operates as a mechanical delay-line by slowing down surface elastic waves to take advantage of wave interaction with resonance. Experiments demonstrate that the rainbow effect reduces the amplitude of the propagating wave in the host structure. At the same time, it dramatically increases both the period of interaction between the waves and the resonators and the wavefield amplitude in the rod endowed with the harvester. Increased energy is thus fed into the resonators over time: we show the enhanced energy harvesting capabilities of this system.