Deep learning-accelerated inverse design of NURBS shell-based metamaterial with quasi-zero stiffness

Low-frequency vibrations pose significant challenges in engineering applications, necessitating the development of high-performance vibration isolation structures. Traditional isolation systems suffer from a trade-off between load-bearing capacity and vibration isolation performance, limiting their effectiveness in low-frequency applications. This paper proposes a novel non-uniform rational B-splines (NURBS) shell-based metamaterial (NSM) with tunable bandgap characteristics, capable of achieving outstanding low-frequency vibration attenuation. The dispersion relation and transmissibility of the metamaterial are derived based on a diatomic chain model. A deep learning-accelerated inverse design framework is developed, integrating a deep neural network (DNN) surrogate model with an improved real-coded genetic algorithm (IRGA). This approach enables the rapid design of metamaterial unit cells that achieve quasi-zero stiffness (QZS) characteristics using a single structural element. The designed unit cell offers exceptional compactness and high load-bearing capacity while allowing customizable stiffness and load requirements. Theoretical analysis and numerical simulations are conducted to evaluate the vibration isolation performance of the metamaterial. By adjusting the pre-displacement, the dynamic stiffness of the unit cell can be tuned, leading to the modulation of the bandgap frequency range and enhanced low-frequency vibration suppression. Furthermore, quasi-static and dynamic experiments validate the effectiveness of the design methodology and the superior vibration attenuation capability of the metamaterial. Experimental results show that when the unit cell operates in the QZS state, vibration attenuation begins at approximately 16 Hz.