A multi-objective design optimization strategy for acoustic/elastic metamaterials under impact loading

The use of optimization procedures for designing acoustic/elastic metamaterials (A/E MMs) has gained significant interest since they enable the efficient attainment of unique functionalities often contradicting. When it comes to vibration attenuation caused by mechanical stress waves, such as impact loads, the dynamic properties of A/E MMs are optimized so that their wave-control ability is maximized. However, the mechanical performance of A/E MMs during the propagation of such waves is normally not evaluated into the design optimization stages. This may compromise not only the load-bearing capacity of MMs, but also their ability in attenuating vibrations. To prevent such effects, we propose a design strategy that incorporates the stress analysis in the early design phase of A/E MMs subjected to an impact load. The effective mass density approach is applied, from which the vibration attenuation is identified at frequency ranges where the resonator moves out-of-phase in relation to the applied excitation. Regarding to the A/E MM mechanical behavior, maximum von Mises stress is calculated through the transient analysis of a unit cell array subjected to a dynamic load. A Pareto front shows a trade-off behavior between the A/E MM functionalities. With that, we emphasize the importance of incorporating the mechanical performance into the design stage of A/E MMs for vibration attenuation of structures undergoing high impact loads, such as installation of foundations by impact hammering. This brings A/E MMs closer to real applications involving energy filtering at specific frequencies from transient loads, designed in an optimized and efficient way.