Bandgap evolution of metamaterials with continuous solid–liquid phase change

Abstract

Owing to the instinct difference in atomic buildings between solid and liquid, the phase change of material can fundamentally change wave energy propagation. In the present work, a novel elastic metamaterial system called solid–liquid phase change metamaterial (SPCM) is proposed, which allows continuous variation of the vibration isolation bandgap in thermal environments. The metamaterial is carefully designed by inserting phase change material (PCM) into an external framework. To reveal how wave propagation is affected by phase change, we develop a theoretical model based on Lagrange’s equation, which can describe the kinematic relations within the metamaterial during the entire phase change process. The model is verified through numerical calculations after the dynamic effective parameters are obtained, and good agreement can be found in the band structure and vibration transmission calculation at different phase change states. Due to the continuous phase change of PCM, the frequency range of the negative effective parameter shifts to lower frequencies, leading to a thermally tunable bandgap. Nevertheless, the constantly changing bandgap covers a certain range during the entire phase change process, indicating that the SPCM designed in this work can offer stable vibration attenuation in a wide range of thermal environments. The design and theory would be critically useful in the design of adaptive metamaterial bandgap in thermal environments.