Design sensitivity analysis of the acoustic dispersion relations

In general, the design approach using the response (e.g., S-parameters) is widely used, in order to design the acoustic metamaterial (AMM). On the other hand, this approach is very sensitive to the response. Also, the acoustic energy loss due to resonance characteristic of the sonic crystal always exists. Thus, we propose the acoustic dispersion relation-based design approach in order to complement the limitations of this conventional approach. As the first step towards this goal, this paper proposes the design sensitivity analysis methodology for the acoustic dispersion relation. The representative dynamic characteristics of acoustic dispersion relation are natural frequency and group velocity. Any type of the acoustic dispersion relation can be described by these two dynamic characteristics. In other words, this means that the AMM satisfying the specified acoustic dispersion relation can be designed by adjusting these dynamic characteristics. The proposed design sensitivity analysis methodology is verified through the design of the sonic crystal tracking the target natural and group velocity at a single wavevector. This proposed method will be used for design optimization of the acoustic zero-index metamaterial (AZIM) in the future.