Periodic homogenization of locally resonant uni-directionally ribbed plates

This work deals with the dynamic behavior of periodic ribbed plates. The governing equations of the e ective mechanical behavior is derived through multiscale asymptotic homogenization method. The study focuses on situations of inner resonance that correspond to specific mechanical contrasts between the beam and plate parameters. The asymptotic homogenization process enables to upscale the local dynamics at global scale, and yields a synthetic and analytic macroscopic representation that encompasses the flexural and torsional mechanisms, as well as the unconventional dispersion features associated with inner resonance. The relevancy of homogenized models accounting for inner resonance is demonstrated using numerical computations and experimental measurements. This approach can be used to describe the motion of sti ened panels of industrial interest, design structures having specific features in a given frequency range, such as unconventional radiation e ciency and sound transmission loss.