Wave propagation in acoustic metamaterials with intermittent four-bar mechanisms

Abstract

In this paper, we investigate wave propagation in discrete and continuum acoustic metamaterials having lateral local resonators. We aim to achieve dispersion curves depending not only on the mechanical properties of the system but also on its geometry to have more control over the positions and widths of bandgaps. For this purpose, we consider an intermittent four-bar mechanism with lateral local resonators as the proposed phononic chain. Then, we obtain the analytical governing equation of the systems using Hamilton’s principle and Lagrange equations. Finally, we apply Bloch’s theory to analyze wave propagation through both discrete and continuum systems. Our results demonstrate that we can obtain bandgaps dependent on the geometric properties of the systems, besides their mechanical properties. In the discrete phononic crystal, based on the system’s geometry, one or two bandgaps can exist and their widths can vary over 300%. The continuum system is also able to increase its bandgap up to 366% over 1–5 MHz and notably, there is the credibility of manipulating waves at frequencies lower than 1000 Hz. Furthermore, it is observed that different symmetries in each chain can be chosen to pass waves with higher frequencies, and the corresponding dispersion for each symmetry is plotted. The results provide promising means to design waveguides, wave filters, and vibration isolators, more deliberately.