Longitudinal wave localization in phononic crystals with negative capacitance

Abstract eng:
A new kind of phononic crystals consisting of elastic rod by piezoelectric shunt with negative capacitance is presented. By the continuity conditions at the interface between different unit cells, the transfer matrix is derived. Based on the Lyapunov exponent of elastic waves in periodic structures and the algorithm presented by Wolf, the localization factor is presented. Numerical calculations are performed for the both the ordered periodic structures and random disorder of the negative capacitance. Results show the influences of the negative capacitance on the stop band properties and localization characteristics of longitudinal elastic waves. It provides a method to tune the band gap properties and control the propagation of elastic waves by the electric circuit method which is different from the traditional mechanical ones.

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