Sensitivity and energy-based optimization of robust aperiodic metamaterials

Abstract

The design of acoustic metamaterials (AMMs) has predominantly relied on periodic configurations to create local resonance bandgaps for vibration control and noise mitigation. However, periodic structures are highly sensitive to manufacturing variability, leading to inconsistent bandgap performance and reduced reliability in practical applications. Aperiodic AMMs have recently emerged as alternatives, offering enhanced robustness and greater design flexibility. Despite their promise, optimizing such structures remains computationally expensive, especially when incorporating robustness considerations through Monte Carlo-based uncertainty quantification. This presents a fundamental challenge in the efficient and scalable design of robust aperiodic AMMs.

This work introduces a novel sensitivity-based measure of robustness, providing a computationally efficient alternative to Monte Carlo simulations. Using local sensitivity analysis, the proposed approach captures the impact of small parameter variations on bandgap robustness, significantly reducing computational costs without compromising accuracy. The robustness measure is integrated into a multi-objective optimization framework that simultaneously maximizes bandgap width and robustness using genetic algorithm. To further enhance the performance, a novel energy-based formulation is developed, which avoids explicitly imposing attenuation constraints. The vibrational energy of LRs is utilized to obtain wider bandgaps, allowing for higher design flexibility.

The methodology is demonstrated on a locally resonant AMM plate or metaplate featuring aperiodically arranged double-cantilever-like resonators. The results reveal that optimized aperiodic designs achieve significantly wider and more robust bandgaps compared to periodic counterparts, validating the effectiveness of the proposed framework. The bandgap performance of optimized aperiodic designs are validated through physical experiments on a metaplate. The resulting computational acceleration provides a step forward in the development of next-generation metamaterials tailored for real-world applications.