Local Resonance Prediction Based on Physics-Informed Machine Learning in Piezoelectric Metamaterials

Under ideal assumptions of infinite lattices where the infinite wave attenuation intensity is achievable, the bandgap estimation considers the bandgap bounds to achieve broadened band width. However, for practical applications in which finite or limited numbers of unit cells are allowed, the induced bandgap region actually includes frequencies with poor wave attenuation intensity. Therefore, for realizing true wave attenuation applications at targeted operating frequencies, it is of critical importance to locate the operating frequency not only within the bandgap region but also at which the wave attenuation intensity is strongest. To address this issue, we explore a tool for estimating the operating frequency with strong wave attenuation intensity from local resonances of scattering unit cells. Since the implicit correlation between the local resonance and the frequency location of strong wave attenuation intensity is determined by multiple parameters and cannot be analytically expressed by the complicated modeling, we suggest a physics-informed machine leaning approach. By introducing analytical modeling physics into the machine learning models, both the operating frequency and the corresponding achievable strongest wave attenuation intensity can be predicted, which could provide insight into the future design and optimization in the piezoelectrical local resonance metamaterials field.