Theoretical and experimental evidence of level repulsion states and evanescent modes in sonic crystal stubbed waveguides

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 \omega(\vec{k}) 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 the 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 necessary for the design of new acoustic and electromagnetic applications based on periodicity

Level repulsion and evanescent waves in sonic crystals

This work theoretically and experimentally reports the evanescent connections between propagating bands in periodic acoustic materials. The complex band structures obtained by solving for the k(¿) problem reveal a complete interpretation of the propagation properties of these systems. The prediction of evanescent modes, nonpredicted by classical ¿(k - ) methods, is of interest for the understanding of these propagation properties. Complex band structures provide an interpretation of the evanescent coupling and the level repulsion states showing the possibility of controlling evanescent waves in periodic materials. © 2011 American Physical Society.V.R.G. and L.M.G.R. would like to thank the facilities provided by the IEMN UMR CNRS 8520. L.M.G.R. would like to thank the UPV for Grant No. PAID-00-11. V.R.G. is grateful for the support contracts of the UPV CEI-01-11. This work was supported by MCI Secretaria de Estado de Investigacion (Spanish government) and the FEDER funds, under Grant No. MAT2009-09438.Romero García, V.; Vasseur, J.; Hladky Hennion, AC.; García Raffi, LM.; Sánchez Pérez, JV. (2011). Level repulsion and evanescent waves in sonic crystals. Physical Review B. 84:2123021-2123024. https://doi.org/10.1103/PhysRevB.84.212302S212302121230248

Etude de la propagation des ondes acoustiques dans les dièdres avec l'aide de la méthode des éléments finis

Un modèle mathématique bidimensionnel a été développé pour étudier la propagation des ondes acoustiques dans les guides d'onde. Ce papier décrit d'abord l'approche théorique proposée puis présente l'application à un dièdre rectiligne élastique dont l'angle au sommet est variable. La comparaison à des résultats empiriques ou à des mesures permet la validation du modèle. Ensuite, la méthode est étendue au cas des guides d'onde courbes.A bidimensional mathematical model has been developed to study the propagation of acoustic waves in waveguides. This paper presents the theoretical formulation and its application to a rectilinear elastic wedge, which top angle is variable. Comparison between finite element results and empirical or experimental results demonstrates the accuracy of the model. Then, the method is extended to curved waveguides

Unified model for the electromechanical coupling factor of orthorhombic piezoelectric rectangular bar with arbitrary aspect ratio

Piezoelectric Single Crystals (PSC) are increasingly used in the manufacture of ultrasonic transducers and in particular for linear arrays or single element transducers. Among these PSCs, according to their microstructure and poled direction, some exhibit a mm2 symmetry. The analytical expression of the electromechanical coupling coefficient for a vibration mode along the poling direction for piezoelectric rectangular bar resonator is established. It is based on the mode coupling theory and fundamental energy ratio definition of electromechanical coupling coefficients. This unified formula for mm2 symmetry class material is obtained as a function of an aspect ratio (G) where the two extreme cases correspond to a thin plate (with a vibration mode characterized by the thickness coupling factor, kt) and a thin bar (characterized by k33′). To optimize the k33′ value related to the thin bar design, a rotation of the crystallogaphic axis in the plane orthogonal to the poling direction is done to choose the highest value for PIN-PMN-PT single crystal. Finally, finite element calculations are performed to deduce resonance frequencies and coupling coefficients in a large range of G value to confirm developed analytical relations

Homogénéisation de matériaux périodiques à l'aide de la méthode des éléments finis, dans la limite des grandes longueurs d'onde

Un modèle numérique a été développé pour étudier la propagation d'ondes planes harmoniques dans un matériau périodique dans une, deux ou trois directions de l'espace. Les propriétés homogénéisées de matériaux poreux sont déterminées sur un modèle anisotrope, dans la limite des grandes longueurs d'onde. Une validation a été faite sur des plaques perforées périodiquement par la mesure des fréquences de résonance.A numerical model has been developed to study the propagation of plane harmonic waves in single, doubly or triply periodic materials. The homogenized properties of porous materials are determined with the help of an anisotropic model, in the limit of large wavelengths. A validation has been carried out with periodically perforated plates, the resonance frequencies of which have been measured

Negative refraction of longitudinal waves in an elastic phononic crystal

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Theoretical and experimental analysis of a piezoelectric plate connected to a negative capacitance at MHz frequencies

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