Metamaterials and periodic structures are widely utilized for their ability to attenuate vibrations across specific frequency ranges, known as bandgaps. However, traditional materials in linear time-invariant systems typically exhibit fixed bandgap properties, limiting their effectiveness when subjected to varying disturbances. To address this challenge, it is essential to develop systems with tunable frequencies to enhance vibration attenuation. This can be achieved by exploiting smart structures and nonlinearities in resonator design. This paper introduces a novel nonlinear resonator embedded with Shape Memory Alloy (SMA), leveraging the concept of bi-stability. By adjusting the current applied to the SMA and exploiting the inherent resonator nonlinearity, our design enables the formation of different or broader bandgaps. Different or wider bandgaps are obtained when acting upon the SMA, by adjusting the applied electric current, which affects the intrinsic nonlinearity of the bistable resonator, leading to distinct performance according to different input excitation levels. To demonstrate the effectiveness of this approach on a smart metamaterial, we present a beam equipped with multiple smart resonators, showcasing its ability to attenuate specific frequency ranges or extend existing bandgaps. This work represents a significant advancement in the field, offering a versatile solution for dynamic vibration control in variable environments.
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