The Kirchhoff approximation (KA) for elastic wave scattering from two-dimensional (2D) and three-dimensional (3D) rough surfaces is critically examined using finite-element (FE) simulations capable of extracting highly accurate data while retaining a fine-scale rough surface. The FE approach efficiently couples a time domain FE solver with a boundary integration method to compute the scattered signals from specific realizations of rough surfaces. Multiple random rough surfaces whose profiles have Gaussian statistics are studied by both Kirchhoff and FE models and the results are compared; Monte Carlo simulations are used to assess the comparison statistically. The comparison focuses on the averaged peak amplitude of the scattered signals, as it is an important characteristic measured in experiments. Comparisons, in both two dimensions and three dimensions, determine the accuracy of Kirchhoff theory in terms of an empirically estimated parameter σ 2 /λ 0 ( σ is the RMS value, and λ 0 is the correlation length, of the roughness), being considered accurate when this is less than some upper bound c , ( σ 2 /λ 0 < c ). The incidence and scattering angles also play important roles in the validity of the Kirchhoff theory and it is found that for modest incidence angles of less than 30°, the accuracy of the KA is improved even when σ 2 /λ 0 > c . In addition, the evaluation results are compared using 3D isotropic rough surfaces and 2D surfaces with the same surface parameters.
We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.An active area of research in metasurfaces [25] focuses upon graded resonator metasurfaces, where the general concept is that for a graded surface, or waveguide, different wavelengths are trapped at different spatial positions. Sub-wavelength microstructures are commonly employed in two ways: the first approach is to create effective macroscopic wavespeeds that vary spatially, thus achieving the required control of wave propagation. The second approach involves using deep sub-wavelength resonances to obtain the desired effects. Whilst the latter approach is significantly more difficult to create, it is far more powerful; hence our aim in the present paper is to extend this latter concept to fluid-loaded compliant structures. These ideas are being widely adopted in photonics and phononics due to their excellent abilities to control, manipulate and filter waves in compact devices. Graded and chirped designs include: trapping in rainbow devices [26][27][28][29], flat focussing mirrors and lenses in optics, plasmonics and acoustics [30][31][32][33][34][35], gradient index lens for acoustic and flexural waves focussing [36,37], acoustic absorbers [38][39][40] and sound enhancement [41,42].In the absence of the fluid-loading, it is only very recently that graded sub-wavelength structures for thin elastic plates has been considered as a chirped graded array [43], thin beams [44] or in the context of gradient index (GRIN) lenses created by graded structuration to control elastic symmetric (S 0 ) and antisymmetric (A 0 ) waves [45] and to obtain deeply sub-wavelength focussing [46], cloaking [47] and GRIN lenses (e.g. Luneburg, Maxwell-fisheye and Eaton lenses [44, 48]) using resonator arrays [37]. There is also an active community in so-called platonics [49] studying the generalisations of phononic crystals to elastic plates in-vacuo with considerable progress in pulling out features associated with Dirac cones [50], dynamic anisotropy and lensing /shielding effects [51]. Much of this is concerned with mass-loaded or constrained plates, but recent work on resonator arrays on plates [52] has moved this into contemporary areas of physics...
Practical ultrasonic inspection requires modeling tools that enable rapid and accurate visualisation; due to the increasing sophistication of practical inspection it is becoming increasingly difficult to use a single modelling method to represent an entire inspection process. Hybrid models that utilize different or interacting numerical schemes in different regions, to use their relative advantages to maximal effect, are attractive in this context, but are usually custommade for bespoke applications or sets of modelling methods. The limitation of hybrid schemes to particular modelling techniques is shown here to be related to their fundamental formulation. As a result it becomes clear that a formalism to generalize hybrid schemes can be developed: an example of how such a generic hybrid modelling interface is constructed is illustrated for the abstraction of bulk ultrasonic wave phenomena, common in practical inspection problems. This interface is then adapted to work within a prototype hybrid model consisting of two smaller Finite Element model-domains, and explicitly demonstrated for bulk ultrasonic wave propagation and scattering examples.Sources of error and ways of improving the accuracy of the interface are also discussed.
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