Formation of band gaps in thin plate with a periodic array of resonators

L'étude porte sur les caractéristiques vibratoires des plaques en cristaux phononiques constituées d'un réseau périodique bidimensionnel de résonateurs (masse-visse) attachés à une plaque fine homogène. Des simulations numériques basées sur la méthode d'éléments finis ont permis de calculer les diagrammes de bandes des plaques périodiques et d'analyser l'effet des paramètres géométriques sur la variation des bandes d'arrêts. Des calculs de coefficient de transmission d'une onde plane selon la direction OX mettent en évidence la présence des bandes d'arrêts prédites par le diagramme de bande. Ces résultats numériques sont validés expérimentalement par des mesures vibratoires de deux plaques en cristaux phononiques avec périodicités a=40 mm puis 50 mm. La plaque testée est encastrée sur l'un de ses cotés entre deux poutres en aluminium dont le déplacement de translation à basses fréquences est imposé par une table vibrante ce qui permet d'imposer une propagation d'onde unidirectionnelle. Cette étude expérimentale montre une atténuation remarquable de l'onde dans les intervalles correspondants aux bandes d'arrêt totale et bande d'arrêt directionnel de résonance.Vibration characteristics of locally resonant (LR) phononic plates consisting of two-dimensional periodic array of resonators (mass-screws) attached to a thin homogenous plate are investigated. In the numeric simulations, we employ finite-element method to calculate band structures of the proposed periodic plates and to analyze the effect of geometry parameters on the opening mechanism and evolution behavior of band gaps. Further, vibration transmission is calculated for plane wave propagation along the OX direction and the results are in good agreement with the band gap predicted by the band structure in this direction. The predictions of these theoretical examinations are validated experimentally by two experimental measurements of fabricated LR phononic plates with different lattice constant a=40 then 50mm. The tested plate is clamped along one side to a shaking table to generate plane wave propagating along the OX direction. The experimental measurements of the vibration attenuation in this direction are in good agreement with the theoretical frequency of complete band gap and directional resonance gap

Collisions in double string plucked instruments: Physical modelling and sound synthesis of the viola caipira

The viola caipira is a folk guitar widely used in traditional and modern Brazilian music. It consists, in general, of 10 metallic strings arranged in five pairs, tuned in unison or octave, with the thinnest string located in the middle. An experimental study of the viola caipira pluck by means of a high speed camera reveals some specificities of the instrument. It is found that the instrument is characterized by a double pluck excitation since the two strings of a given pair are plucked successively and rapidly. Collisions between strings arranged in the same pair are identified. A hybrid model, based on a modal approach, is carried out for sound synthesis purposes. It includes 10 strings with non-planar motions coupled with the body and collisions between strings. A finite difference scheme is used to compute the coupling forces at each time-step, which permits a set of sound simulations. The effects of string/string collisions on the viola caipira sounds are identified and discussed. It is found that the model reproduces the main vibroacoustic features of the viola caipira, among which the sympathetic string resonances and the string/string collisions observed in the video analysis443178197CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES141214/2013-999999.010073/2014-00Brazilian Coordination for the Improvement of Higher Education Personnel Foundation [99999.010073/2014-00]; National Council for Scientific and Technological Development in Brazil [141214/2013-9]; French National Center for Scientific ResearchCentre National de la Recherche Scientifique (CNRS