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International Institute of Zakharenko Waves - IIZWs

IIZWs Пустой

Contact E-mail:, Professor Dr. Aleksey Anatolievich Zakharenko, Diploma Engineer-physicist, Diploma Programmer, Diploma manager, the IIZWs creator and researcher.

Several hot MS/PhD-projects are available here.



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International Institute of Zakharenko waves

Possession of the Internationsl Institute of Zakharenko Waves (IIZWs).

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Studying subjects:  Different dispersive waves such as Rayleigh, Lamb, and Love type waves.



·   It is thought that the non-dispersive Zakharenko type waves representing extreme points of the phase velocity Vph(kd), where k is the wavenumber and d is the plate thickness, can be found in the lowest-order modes of Lamb type waves, when the waves are studied in commonly used [100] and [110] propagation directions in crystals, for instance, non-piezoelectric cubic crystals (metals). It is also thought that the non-dispersive Zakharenko type waves cannot exist in the modes of Lamb waves propagating in isotropic plates that must be verified in experiments.

·   It was numerically discovered new dispersive shear-horizontal surface waves called ultrasonic surface Zakharenko waves (USZW), which can exist in some suitable propagation directions of piezoelectric coated crystals satisfying the condition of perpendicularity between the wave propagation direction and an odd order symmetry axis, in which the dispersive surface Bleustein-Gulyaev waves cannot exist, for example, in layered structures consisting of cubic crystals ([101]-propagation direction for both media). Also, unusual modes of Love type waves were found in the layered structures consisting of two piezoelectric cubic crystals. Concerning piezoelectric cubic crystals, interesting solutions were analytically found studying [101]-propagation direction in the crystals. The solutions correspond to the phase velocity Vph0 = Vt4aK with aK = 2[K(1 + K2)1/2K2]1/2 being less than the speed Vt = Vt4(1 + K2)1/2 of the bulk shear-horizontal (SH) wave (Vt4 = (C66/ρ)1/2). A strong dependence Vph0(K2) on the so-called static coefficient of electromechanical coupling (CEMC) K2 was found. It was also found that for the phase velocity Vph < Vph0 there are all complex roots for any K2 including the special case of K2 = 1/3 where Vph0 = Vt. And for Vph0 < Vph < Vt the roots depend on K2: the roots are pure imaginary in monocrystals with K2 < 1/3, but real for strong piezoelectric cubic crystals with K2 > 1/3. The interesting feature is a very slow velocity Vph0 in weak piezoelectrics with K2 < 1% (even K2 << 1%). The Vph0 calculation can be useful for finding new shear-horizontal (SH) surface waves. The non-dispersive USZW-waves were discovered in my work: A.A. Zakharenko, JZUSA, 2007.

·   It was analytically shown the possibility to find in crystals the other type of surface waves, representing a new supersonic surface wave, polarized in the sagittal plane, like the surface Rayleigh waves are polarized, with the phase velocity, which is greater than the speed Vl of the bulk longitudinal wave. Also, the anisotropy coefficient C2 = [(C11C55)(C33C55) – (C13 + C55)2]/(C33C55) (see A.A. Zakharenko, NonDTE, 2006, and A.A. Zakharenko, ActaAA, 2005) was introduced representing an universal characteristics for Rayleigh-polarized waves propagating in monocrystals and layered systems of all anisotropy classes. I have found that the surface Rayleigh type waves can exist, if there is the following condition for negative C2 > – 1 – C11/C33 – 2(C11/C33)1/2.

·   It was numerically discovered the existence possibility of a new type of dispersive leaky waves in layered systems with polarization, like the Love-wave (shear-horizontal) polarization. These new leaky type waves are called the dispersive leaky Zakharenko type waves (see A.A. Zakharenko, JSV, 2005). It is noted that dispersive leaky Sezawa type waves possessing the Rayleigh-wave polarization, as well as dispersive surface Rayleigh type waves, are readily observed with the same experimental technique.

·   It was found that supersonic surface Love type waves can exist in layered systems owing to the anisotropy factor af = (C44C66C462)1/2/C44, in which such substrates as Muscovite, Phlogopite and Biotite (common micas) are used. Such shear-horizontal supersonic surface LTW-waves can propagate with phase velocity which is greater than the speed Vl of the bulk longitudinal wave for Diamond, Vl ~ 17500 [m/s] representing the fastest known velocity in Acoustoelectronics. (See A.A. Zakharenko, NonDTE, 2005). Also, the paper (A.A. Zakharenko, NonDTE, 2005) offers a method for all-round automation of filter and sensor characterization, as well as production.

·   It was also discovered two new types of surface waves (slow surface Zakharenko modes possessing slow speeds, single modes and the LTW-polarization with the phase velocity less than the LTW phase velocity). One new type of surface waves can also exist when the LTW-waves can not propagate. (See A.A. Zakharenko, NonDTE, 2005). The slow surface Zakharenko waves can be used for sensor and filter applications, like asymmetric Lamb waves (flexural plate waves) with the Rayleigh-polarization are used generally operating in the 1-10 MHz frequency range. In general, technical devices are based on waves with a velocity lower than that of sound in liquids. Currently, there is a great interest to Capacitive Micromachined Ultrasonic Transducers (CMUTs) of microelectromechanical system (MEMS) structures on the Lamb waves in integrated circuit (IC) technology. The CMUTs can be also done on the slow surface Zakharenko waves that could be even technologically preferable resulting in device prize reduction.

·   It was also studied the non-dispersive Zakharenko waves (see A.A. Zakharenko, ActaAA, 2005), including quantum systems, such as both the bulk and surface elementary excitations in the liquid helium-II (see also A.A. Zakharenko, Forum Acusticum, Budapest, Hungary, 2005; A.A. Zakharenko, JZUS A, 2007; A.A. Zakharenko, WRCM, 2007; A.A. Zakharenko, PRAMANA, 2007).