Anton Kutsenko

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Consider the discrete 1D Schrödinger operator on Z with an odd 2k periodic potential q. For small potentials we show that the mapping: q → heights of vertical slits on the quasi-momentum domain (similar to the Marchenko-Ostrovski maping for the Hill operator) is a local isomorphism and the isospectral set consists of 2 k distinct potentials. Finally, the(More)
One-dimensional propagation of a longitudinal wave through an infinite piezoelectric periodically layered structure is considered. The unit cell consists, in general, of piezoelectric multilayers separated by thin electrodes which are connected through a capacitor with capacity Cj that plays the role of the external electric control providing tunability of(More)
A scheme for evaluating the effective quasistatic speed of sound c in two- and three-dimensional periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for c has a more closed form than previous formulas. It(More)
Effective anti-plane quasistatic moduli for 2D piezoelectric phononic crystals of arbitrary anisotropy are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in one dimension with direct numerical integration along the other direction. As a(More)
The existence of shear horizontal (SH) surface waves in two-dimensional periodic phononic crystals with an asymmetric depth-dependent profile is theoretically reported. Examples of dispersion spectra with bandgaps for subsonic and supersonic SH surface waves are demonstrated. The link between the effective (quasistatic) speeds of the SH bulk and surface(More)
A theoretical study is performed of the bulk acoustic wave propagation in periodic piezoelectric structures with metallized interperiod boundaries. A crucial specific feature of such structures is that the bounded acoustic beam incident perpendicular to an interface can generate scattered (i.e. reflected and transmitted) waves over the whole area of the(More)
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