Optimal design of rainbow metamaterials

Nonperiodic metamaterials with appropriately designed resonator distributions can have superior vibration attenuation capabilities compared to periodic metamaterials. In this study, we present an optimization scheme for the resonator distribution in rainbow metamaterials that are constitutive of a Π-shaped beam with parallel plate insertions and spatially varying cantilever-mass resonators. To improve the vibration attenuation of rainbow metamaterials at specific design frequencies, two optimization strategies are proposed, aiming at minimizing the maximum and average receptance values. Objective functions are set up with the frequency response functions predicted by the displacement transfer matrix model. The masses of the two sets of resonators, clamped at different side walls of the Π-shaped beams, constitute the set of design variables. Optimization functions are solved using a genetic algorithm method. Results of case studies showed that the receptance values of the nonperiodic metamaterial is greatly reduced within the optimization frequency range, in comparison to the periodic metamaterial.