Complete vibrational bandgap in thin elastic metamaterial plates with periodically slot-embedded local resonators

This paper presents a metamaterial plate (metaplate) consisting of a periodic array of holes on a homogeneous thin plate with slot-embedded resonators. The study numerically proves that the proposed model can generate a complete vibrational bandgap in the low-frequency range. A simplified analytical model was proposed for feasibly and accurately capturing the dispersion behavior and first bandgap characteristics in the low-frequency range, which can be used for initial design and bandgap study of the metaplate. A realistic and practical unit metaplate was subsequently designed to verify the analytical model through finite element simulations. The metaplate not only generated a complete vibrational bandgap but also exhibited excellent agreement in both analytical and finite element models for predicting the bandgap characteristics. This study facilitates the design of opening and tuning bandgaps for potential applications such as low-frequency vibration isolation and stress wave mitigation.