The 8 reference contexts in paper R. Vasiliauskas, K. Ragulskis, L. Patašien, A. Fedaravičius, Р Василяускас , К. Рагульскис , Л. Паташене , А. Федаравичус (2015) “ГОЛОГРАФИЧЕСКАЯ ВИЗУАЛИЗАЦИЯ ВИБРАЦИЙ ПЬЕЗОКЕРАМИЧЕСКИХ ЦИЛИНДРИЧЕСКИХ ПРЕОБРАЗОВАТЕЛЕЙ // HOLOGRAPHIC VISUALIZATION OF CYLINDRICAL PIEZOCERAMIC TRANSDUCERS VIBRATIONS” / spz:neicon:pimi:y:2013:i:2:p:88-94

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    Theoretical investigation of cylindrical piezoceramic transducers′ vibrations (we suggested the principles for the development of precision piezoelectric motors with several degrees of freedom, thus realizing high precision in space and in plane positioning systems)
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    and dynamic analysis of their components have indicated that an increase in the loading force and initial tension decreases the harmonic components of fluctuations. This article analyzes the working cylindrical piezoceramics transducers (Figure 1), when a control signal is sent only to one active control cylindrical transducer of the mechatronic system [3–5].
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    systems) [1, 2] and dynamic analysis of their components have indicated that an increase in the loading force and initial tension decreases the harmonic components of fluctuations. This article analyzes the working cylindrical piezoceramics transducers (Figure 1), when a control signal is sent only to one active control cylindrical transducer of the mechatronic system
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    . In this case, even deformation of the working part surface in the operation area of the active cylindrical piezoceramics transducers′ vibrations is observed. Slight surface deformation in the operation area of other active piezostack emerges due to conditions of their fixing onto the surface of the working part of the mechatronic system.
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    Upon having illuminated the hologram after two exposures with a copy of the cylindrical piezoceramic transducers vibrations, both transducers reflected by the object surface before and after the deformation, are restored at the same time
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    . The results of their interference – the system of interferential fringes is observed against the background of the surface of the object image, which provides information about changes in the object’s status having occurred in the period between showings.
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    The ineffective electrical energy is stored as electrostatic energy in the piezoceramics material and reverts it to the power supply in the final process of an operating cycle. The analyzed criteria have made possible to choose the piezomaterial for an optimal construction having a maximum displacement
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    . The experimental investigation of precision vibrosystems by means of holographic interferometry enables one to obtain appreciably larger amounts of information about the vibrating surface in comparison with traditional methods.
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    The paper deals with the consideration of methods for the determination of the vibrational characteristics of precision mechanical systems from the holographic interferograms of linked analysis of these characteristics by using numerical techniques based on the theories of mechanical system vibration and holographic interferometry
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    . Method of holographic visualization of cylindrical piezoceramic transducers vibrations When wave properties are defined by a travelling wave, quantitative analysis of interferograms shall be performed in the following method.
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    The characteristic function of the distribution of interference bands on the surface of the piezoceramic cylinder, when holographic interferogram is fixed at time-average and harmonic vibration is present, is defined as
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    : .exp 1 0 kdt T Miix   (9) Inserting expressions (7) into the equation (6) we get the value of Ωi that should be inserted into the characteristic function of band distribution (9).
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    We obtain the following  sin), (cos 2 exp 1 2 0 1 dt i T Mix          (10) where  ()cos, cos()cos 0 100 i i r i i i t i i i z i WK UKVK   (11)  i i r i i i t i i i z i VKWK UK   ()sin()sin sin 00 20 . (12) After the use of equation
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    equation (10) will look like: ,2 1 2 2 2 01     MxiinJ (13) where J0 – Bessel function of the first kind of order zero. Using (7), (11), (12) and (13) values of point i located on the surface of piezoceramic cylinder, we will obtain the following equation of the distribution of the interference bands on the surface of the vibrating piezoceramic cy
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    FWij , FVij , FUij are calculated using analytical expressions of self-excited vibration types related to the geometrical shapes of transducers and the conditions of their fixing in various structures. Aiming to calculate coefficients AjW, AjV, AjU and angles αi, βi, γi we need to minimize the equation formed on a basis of the equation (14) in a method described
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    : 222 11 1 2 1 11 4 sinsin cossin coscos                                                             i i i z n u ij u ij i t n v ij v j i i r n w ij w ij i z n u ij u j i i t n v ij v ij i r n w ij w ij AFKAFK AFKAFK FAFKAFK .(16) Function Fi shall be differentiated with respect to each unknown component o
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