Thermal tuning of vibration band gaps in homogenous metamaterial plate

Abstract

The acoustic metamaterial is a class of artificial structures designed to transmit, prohibit, or trap and amplify vibration waves at certain frequencies by periodically manipulating the physical parameters such as modulus, density and chirality. Compared to the traditional phononic crystals with the fixed configuration of periodic multi-materials or geometric structures, a novel design with homogenous temperature-sensitive material will probably embody the advantages in both fabricability and tunability. To concrete and validate this design concept, a thin plate merely adopting homogenous thermo-sensitive epoxy resin is presented as an illustration in this research. By periodically distributing the heating source in a particular shape, a periodic thermal field can be induced and further naturally elicits a periodic distribution of Young's modulus. The thermal diffusion effect and nearly power-law-decreasing modulus-temperature relation give rise to a concentric circular distribution of Young's modulus, which transforms the homogenous plate into a novel gradient metamaterial plate. The transmitting and prohibiting effect in wave propagation is validated for both longitudinal and bending vibration waves by theoretical modeling and finite element analysis (FEA). Further research shows that the vibration band gaps can be significantly tuned in both frequency and bandwidth by the power density and configuration of the heat source. The longitudinal vibration band gaps indicate attenuation with the larger high-temperature region; nevertheless, the widest bending vibration band gaps are not monotonically changing. Additionally, the frequencies in both vibration modes decrease with the increasing thermal field. This research explores a novel construction concept for the periodic metamaterial plate by homogenous smart material, which may present more possibilities with the development of multi stimulus responsive smart materials and the physical field application technologies in the future.