Flexural waves in structured elastic plates: Mindlin versus bi-harmonic models

The paper presents an analytical approach to modelling of Bloch–Floquet waves in structured Mindlin plates. The emphasis is given to a comparative analysis of two simplified plate models: the classical Kirchhoff theory and the Mindlin theory for dynamic response of periodic structures. It is shown that in the case of a doubly periodic array of cavities with clamped boundaries, the structure develops a low-frequency band gap in its dispersion diagram. In the framework of the Kirchhoff model, this band gap persists, even when the radius of the cavities tends to zero. A clear difference is found between the predictions of Kirchhoff and Mindlin theories. In Mindlin theory, the lowest band goes down to ω = 0 as the radius of the cavities tends to zero, which is linked with the contrasting behaviour of the corresponding Green functions.