Modelling response of phononic Reissner–Mindlin plates using a spectral decomposition

This paper reviews our very recent research focused on modelling of the phononic structures using homogenization of high contrast elastic media. We consider the Reissner–Mindlin type of the homogenized plate which involves frequency-dependent mass coefficients associated with the plate cross-section rotations and the plate deflections. Frequency intervals called band gaps exist for which these coefficients constituting the effective mass matrix can be negative, such that the propagation of elastic waves is restricted, or even stopped. We propose a spectral decomposition based method which is suitable to compute the structure response to an external harmonic loading by forces with frequencies in range of the band gaps. Numerical illustrations are given.