Effects of negative capacitance circuits on the vibration attenuation performance of a nonlinear piezoelectric metastructure

Nonlinear metamaterials present wideband and multimode vibration attenuation features leveraged by mechanisms such as internal resonances, bifurcations, and chaos. Nonlinearities can be provided to a metamaterial through periodic modulation of nonlinear constitutive material laws, by inducing periodic geometry asymmetries, or by including nonlinear local forces. This paper investigates the effects of nonlinear electrical attachments on the vibration attenuation performance of a onedimensional piezoelectric metamaterial. We investigate the effects of negative capacitance circuits on the restoring function of the nonlinear piezoelectric unit cell, whose linear term (controlled by the negative capacitance) can be rendered either positive or negative, paving the way towards the realization of monostable or bistable electromechanical attachments. We show that a piezoelectric metamaterial with nonlinear attachments attains enhanced broadband capabilities brought by the negative capacitance circuits. Numerical time- and frequency-domain analyses elucidate the effects of the nonlinear electrical attachments on the vibration attenuation of an one-dimensional electroelastic metastructure, revealing multimode attenuation features and attenuation bands substantially wider than the ones provided by a linear electroelastic counterpart.

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