Diffusion-based design of locally resonant sub-systems using a reduced wave finite element framework
Résumé
This paper presents a diffusion formulation for the Wave Finite Element (WFE) Framework, applied to the design of micro-resonators for low-frequency vibration control. First, the information resulting from diffusion analysis is compared with the one provided by a direct application of Bloch theory, in the case of periodically distributed resonators. Main advantages of diffusion methods are that the spacing between the resonators can be modified without resuming unit-cell analysis and that scattering effects, inherently produced by the host structure, can be distinguished from the sole resonator's influence. Then, the method is combined with an existing wave-based state vector reduction scheme to further reduce the computational efforts. Formulation is introduced and applied to a rectangular host structure with 3D-modeled resonators bonded on its surface. Eventually, damping-related transmission, reflection and diffusion effects produced by the resonators are studied around their harmonic frequency.
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