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 omega(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 < 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 pi in the stopbands for a certain range (C-0, C-1) of negative C. Besides, for C is an element of (C-0, C-infinity) where C-infinity < C1, the spectrum possesses a low-frequency absolute stopband starting from the quasistatic limit omega = 0 and including the tunable pole of ImKT inside. This stopband is related to the negative value of the quasistatic effective elastic constant in the range (C-0, C-infinity). At C = C-infinity, the effective constant is infinite while the spectrum degenerates to the straight line K = 0 at any omega. For C close to C-infinity, the spectrum consists of the branches with high group velocity and of the quasiflat branches. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.