Wave propagation in metamaterial plates with periodic local resonances

Vibration characteristics of metamaterial plates manufactured from assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures has been shown to exhibit a unique stop band behavior extending to very low frequency ranges. A finite element model (FEM) is developed to predict the modal and frequency response of different configurations of the metamaterial plates. A Floquet-Bloch approach is exercised to demonstrate the stop band and mechanical filtering capabilities over a broad range of frequencies. The predictions of these theoretical models are validated experimentally when the plates are excited by a mechanical shaker over a frequency range of up to 5 kHz. It is observed that there is a good agreement between the theoretical predictions and the experimental results for different configurations of the metamaterial plate. The obtained results emphasize the potential of such plates to provide significant vibration attenuation and exhibit stop bands extending to low frequencies. Such characteristics indicate that metamaterial plates are more effective in attenuating and filtering low frequency structural vibrations than plain periodic plates of similar size and weight.