Evaluation of uncertainty effects to band gap behavior of circuitry-integrated piezoelectric metamaterial using order-reduced analysis

Acoustic metamaterials with unit cells that are integrated with piezoelectric transducer circuitry exhibit interesting band gap behaviors that can be used for wave/vibration manipulation. This research reports the evaluation of uncertainty effects to a typical piezoelectric metamaterial, where uncertainties in geometry/configuration and in circuitry elements are taken into consideration. Monte Carlo–type analysis is performed to assess the band gap features under these uncertainties. In order to facilitate tractable computation in uncertainty analysis, order-reduced modeling of the electro-mechanically integrated system is formulated. The component mode synthesis–based order-reduced modeling increases the computational efficiency significantly while maintaining good accuracy. Results show that the band gap behavior is generally less sensitive to configuration uncertainty but can be greatly affected by circuitry parameter uncertainty. These results can be used to guide the design and synthesis of piezoelectric metamaterials, and the method developed can be applied to the uncertainty quantification of other types of metamaterials.