Abstract
The dynamic behavior of a periodic ribbed plate with local resonance is investigated. The behavior of the cell made of a beam clamped along a plate edge analyzed through multi-scale asymptotic method enables to derive the governing equations of the effective mechanical behavior. This approach allows obtaining a full homogenized analytical model that provides a relevant representation of the flexural and torsional mechanisms at both global and local scales. The complex dynamic behavior is shown to encompass several mechanisms associated with enriched kinematics. Two types of flexural and torsional waves are evidenced and governed by two distinct differential equations that describes (i) waves where both beam and plate moves, and (ii) guided waves where the plate only is set in motion. The inner resonance of the plate induces unconventional dispersion features, with singularities associated either with the symmetric eigenmodes for the bending waves or the antisymmetric modes for the torsional waves. The guided waves are alternatively related to the symmetric and antisymmetric modes of the bended plate and are propagative above the corresponding eigenfrequencies. The predictions of the homogenized model are successfully compared to numerical calculations conducted using Wave Finite Element based methods, for two realistic examples of ribbed plates. The study provides design rules to tailor ribbed plate panels having specific atypical features in a given frequency range.
Highlights
Composite panels with optimized vibroacoustic features practically lead to highly heterogeneous structures made of different components, often periodically distributed e.g. honeycombs, sandwich panels, ribbed plates, beam truss/slats
The present paper focuses on this specific situation in dynamic regime, in which the beam/plate contrasts induce inner resonance phenomena
Asymptotic homogenization applied to periodically ribbed plates allowed predicting their macroscopic behavior accounting for inner resonance resulting from contrasted geometrical parameters and/or mechanical properties
Summary
Composite panels with optimized vibroacoustic features practically lead to highly heterogeneous structures made of different components, often periodically distributed e.g. honeycombs, sandwich panels, ribbed plates, beam truss/slats. A reference study on significantly heterogeneous uni-directionally ribbed panels has been conducted by Fahy and Lindqvist (1976) following the assumption that a pure flexural motion exists in the plates and pure flexural/torsional motion exist in the ribs (Ungar, 1961) This approach does not provides a plate model but yields the dispersion equations analytically, that can be solved numerically, and it has been validated experimentally that this method predicts reliably the dispersion properties of waves in uni-directionally ribbed plate (Ichchou et al, 2008b). Numerical approaches based on the Floquet–Bloch theory has been developed to obtain the propagation features of periodic ribbed plates This method called WFEM (Mead, 1973; Waki et al, 2009), has been used by Ichchou et al (2008b) to recover (i) the results of the Fahy’s approach (Fahy and Lindqvist, 1976), and (ii) experimental dispersion curves. It is stressed that the study yields design rules to tailor ribbed plate panels having atypical features in a given frequency range
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