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D. Annexe, Modèle analytique d'une poutre tri-couche piézoélectrique avec non-linéarités de von Kármán Ce modèle analytique démontre bien que le terme paramétrique est deux fois plus élevé en actionnement qu'en détection. Ces termes ont été indiqués en rouge dans les équations modales obtenues. La symétrie de la structure par rapport à la surface moyenne permet plusieurs simplifications. En particulier, il n'y a pas de couplage membrane-flexion induit par la stratification. De plus, le mouvement axial statique de la poutre peut aussi faire l'objet d'une condensation dans l'équation du mouvement transverse