Quasistatic stopband and other unusual features of the spectrum of a one-dimensional piezoelectric phononic crystal controlled by negative capacitance

Normal propagation of the longitudinal wave through the piezoelectric medium with periodically embedded electrodes is considered. Each pair of electrodes is connected via a circuit with capacitance C  . The paper analyzes in detail the unusual features of the dispersion spectrum ω(KT)ω(KT) (K is the Floquet–Bloch wavenumber, T is the period) arising in the special case of a negative value of C  . The solution of the dispersion equation shows explicitly the evolution of the passbands and stopbands tunable by varying C<0C<0. One of the striking features is the existence of the poles of ImKT (infinite attenuation) and of the corresponding jumps of the phase ReKT from 0 to π   in the stopbands for a certain range (C0,C1)(C0,C1) of negative C  . Besides, for C∈(C0,C∞)C∈(C0,C∞) where C∞