Design of quasi-zero-stiffness elastic diodes for low-frequency nonreciprocity through machine learning

Elastic diodes with nonreciprocity have the potential to enable unidirectional modulation of elastic waves. However, it is a challenge to achieve nonreciprocity at low frequencies (<100 Hz) using existing elastic diodes. This paper proposes a quasi-zero-stiffness (QZS) elastic diode to resolve such a tough issue and fulfill high-quality low-frequency nonreciprocity. The proposed elastic diode is invented by combining a QZS locally resonant metamaterial with a linear one, where the beneficial nonlinearity of the QZS metamaterial facilitates opening an amplitude-dependent band gap at very low frequencies. Firstly, the dispersion relation of the QZS metamaterial is derived theoretically based on the harmonic balance method (HBM). Then, the transmissibility of the QZS elastic diode in both the forward and backward directions is calculated through theoretical analyses and numerical simulations. Additionally, the influences of system parameters on the low-frequency nonreciprocal effect are discussed. The results indicate that considerable nonreciprocity is observed at a quite low frequency (e.g., 9 Hz), which is achieved by amplitude-dependent local resonance combined with interface reflection. Finally, a machine learning-based design optimization is introduced to evaluate and enhance the nonreciprocal effect of the QZS elastic diode. With the aid of machine learning (ML), the computational cost of predicting nonreciprocal effects during design optimization can be significantly reduced. Through design optimization, the nonreciprocal frequency bandwidth can be broadened while maintaining considerable isolation quality at low frequencies.