A metamaterial beam with inverse nonlinearity for broadband micro-vibration attenuation

Abstract

Strong nonlinearity usually becomes noticeable when nonlinear materials or structures undergo large deformation. However, we present here the inverse nonlinearity, where the nonlinearity is inversely proportional to the deformation. We demonstrate this peculiar behavior in a nonlinear metamaterial beam, which is endowed with an array of piezoelectric patches shunted with nonlinear digital oscillators. The nonlinear digital oscillator is physically suggested by coding digital controllers to form an effective nonlinear capacitor, which is connected to an analog inductor. We also analytically interpret this inverse nonlinearity through the effective bending stiffness of the metamaterial beam. It is found that the vibration attenuation bandwidth of the nonlinear metamaterial beam under small-amplitude excitations is three times larger than that under relatively large-amplitude excitations. Thanks to the programmability of digital circuits, the nonlinear oscillators can be easily tuned with various nonlinearities, making vibration control adaptable in both penetration strength and frequency bands. The nonlinear metamaterial beam enlarges vibration control in both frequency and amplitude domains and sheds lights on broadband low-intensity sound and micro-vibration control.