Abstract Summary
Periodic systems exhibit frequency bands (pass-bands and stop-bands or bandgaps) which can manipulate propagating waves in certain frequency ranges. Phononic crystals (PCs) can create bandgaps by virtue of Bragg’s scattering, at wavelengths of the order of their unit cell size. However, this poses a restriction on their application in low-frequency ranges, for which a very large unit cell size will be required. On the other hand, acoustic metamaterials (AMMs) can create bandgaps at much lower frequencies than those possible by PCs, by utilizing the concept of local resonance (LR). Many design strategies and architectures have been explored to achieve wide low-frequency bandgaps in AMMs for several applications, which include noise/vibration insulation, energy absorption and harvesting, protection of sensitive machinery and components, and earthquake shielding. There are always some imperfections and uncertainties associated with the manufacturing process of any material or structure. Periodic systems like most AMMs, are sensitive to such manufacturing variabilities, which may considerably affect their performance. There may also be issues like vibration mode localization that arise due to the presence of such imperfections. Very limited literature has explored the role of aperiodicity in the performance of AMMs. Further, the introduction of aperiodicity in the design methodology of AMMs within a probabilistic framework has not been adequately addressed. Systems such as spring-mass models or vibrating beam structures provide a simple framework to explore complex AMM design methodologies. In this study, we try to incorporate aperiodicity in a LR metamaterial beam design to address two issues: (i) increase the width of low-frequency LR bandgap, and (ii) reduce the effect of manufacturing variabilities on the bandgap and make the system more robust. The metamaterial beam comprises a homogeneous host beam with free-free boundary conditions. Fifteen equally spaced double-cantilever-like beams are installed on this host beam, acting as resonators. These resonators create a LR bandgap in the 750-1000 Hz frequency range. A genetic algorithm-based optimization technique is utilized to achieve a novel design of the resonators. This algorithm maximizes the bandgap width (in the same frequency range) and allows for introducing aperiodicity in the system by assigning different properties to some resonators. This design is numerically shown to have a much-enhanced LR bandgap width vis-à-vis the periodic system. Furthermore, manufacturing variabilities in the system parameters (dimensions, Young’s modulus, density) and their effect on bandgap width is considered. Uncertainty quantification using Monte Carlo simulations shows that aperiodicity in design contributes toward robustness with respect to such imperfections or variabilities. Thus, adopting this design philosophy of introducing aperiodicity can improve the overall functionality of AMMs.
