Abstract
The complex band structures calculated using the extended plane wave expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical methods, providing novel interpretations of several phenomena as well as a complete picture of the system. In this work, we theoretically and experimentally observe that in the ranges of frequencies where a deaf band is traditionally predicted, an evanescent mode with excitable symmetry appears, changing drastically the interpretation of the transmission properties. On the other hand, the simplicity of the sonic crystals in which only the longitudinal polarization can be excited is used to interpret, without loss of generality, the level repulsion between symmetric and antisymmetric bands in sonic crystals as the presence of an evanescent mode connecting both repelled bands. These evanescent modes, obtained using EPWE, explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other in good agreement with both experimental results and multiple scattering predictions. Thus, the evanescent properties of the periodic system have been revealed to be necessary for the design of new acoustic and electromagnetic applications based on periodicity.
Highlights
Theoretical techniques and the experimental setupThe propagation properties of periodic materials can be analyzed solving for both the eigenvalue and the scattering problems
The complex band structures calculated using the extended plane wave expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical ω(k) methods, providing novel interpretations of several phenomena as well as a complete picture of the system
These evanescent modes explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other
Summary
The propagation properties of periodic materials can be analyzed solving for both the eigenvalue and the scattering problems The former can be used to obtain the dispersion relation of a system, whereas the latter can be used to obtain the scattering of waves in finite structures. We built a finite SC hanging the rigid scatterers on a periodic frame (figure 1) and the SCW is generated removing the central row of the complete structure. We note that this system avoids the excess attenuation effect [33]. A 3D computer-controlled automatic positioning system together with an automatized acquisition system, called the 3D robotized e-acoustic measurement system (3DReAMS), has been used to obtain the pressure field inside the waveguide. We analyzed the acoustic field inside the guide of both the complete SCW and the stubbed SCW by moving the microphone in steps of 1 cm
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