Aperiodicity induced robust design of metabeams: Numerical and experimental studies

Abstract

Various design strategies have been explored to achieve wide local resonance (LR) bandgaps in acoustic metamaterials (AMMs), which have applications in vibration absorption and low-frequency noise mitigation. Conventionally, most methodologies model AMMs as periodic systems. Additionally, maintaining a reasonable resonator mass is desirable for many engineering applications. These factors restrict their possible design space and effectiveness. Such periodic structures are also sensitive to imperfections or manufacturing variabilities. To overcome these issues, we propose a novel methodology for optimal design of robust aperiodic AMMs. First, through a detailed parametric study, we establish a relationship among degree of aperiodicity, bandgap width, and its robustness. A robustness measure is defined to quantify the sensitivity of the bandgap with respect to manufacturing defects. We report two key observations: (i) aperiodicity helps in enhancing the bandgap and robustness, and (ii) the bandgap is not monotonically related to the robustness. These observations suggest the need for a multi-objective optimization in the aperiodic regime. Subsequently, all resonators’ mass, stiffness, and position are treated as design variables in a global optimization problem, which is solved using the genetic algorithm. This methodology offers users complete flexibility in imposing various design constraints.

Numerically, an AMM beam or metabeam is considered, comprising equally spaced double-cantilever-like resonators on a homogeneous host beam, producing an LR bandgap spanning 750–1000 Hz. Through multi-objective optimization, aperiodic designs with enhanced performance are achieved, with significantly wider and more robust bandgaps than periodic systems with similar mass. Interestingly, the global optima resides in the vicinity of the periodic configuration, as shown by parametric studies. The optimized aperiodic designs are validated through physical experiments on a vibrating beam. These findings open a new avenue for designing metamaterials.