This paper is concerned with application of piezoelements with a step change of material properties occurring in the element's plane. Each part of an element may be controlled independently. Analytical models for different shape and location of the inner part of a two-part piezoactuator are developed. Finally, results of numerical simulations concerning effectiveness in vibration reduction of piezoactuators constructed this way are presented.
This paper is concerned with mathematical aspects and numerical modeling of vibration of a circular plate with piezoelectric actuators. Particularly, a thin Kirchhoff-Love plate with arbitrary shaped actuators (e.g. pie-shaped, trapezoid, disc, and rectangular) is considered. In the theoretical model, the moments that act upon a structure and are induced by piezoelectric actuators are described by the generalized tensor product of a distribution and distribution-valued function. Numerical computations utilize the FEM approach supported by Ansys software.
This paper is concerned with mathematical aspects of modelling vibration of a plate with piezoelectric actuators. Particularly, a thin Kirchhoff-Love plate with arbitrary shaped actuators (e.g. triangles, parallelograms, discs) is considered. The moments that act upon a structure and are induced by piezoelectric actuators, are described by the generalized tensor product of a distribution and distribution-valued function. Finally, the formula for the solution of the Cauchy problem in the class of absolutely continuous tempered distribution-valued functions is derived.
The subject matter of this paper refers to the diagnostics of a transformer core, based on measurements and analysis of vibroacoustic signals registered during their normal operation. The paper presents results of the research aimed to evaluate the repeatability of vibration measurements for power transformer core. Recording of vibroacoustic signals was performed under laboratory conditions on dry-insulated transformers. The study concerned evaluation of changes in vibroacoustic indicators of the transformer core during operation with a turned and loosened core. Conclusions from the measurement results were drawn on the basis of the parametric test of significance derived from the variance analysis for many means of single classification basing on the Fisher-Snedecor F-distribution.
The subject matter of this paper refers to the assessment of the technical condition of a power transformer core and windings based on vibroacoustic measurements taken during a transient operation state of the appliance diagnosed - at a transformer unit switch on. The paper presents preliminary results of the research work carried out, which aims at elaborating a new diagnostic and assessment method of the degree of the transformer core and winding pressing using the so-called modified vibroacoustic method. The paper characterizes the measurement path and the assessment method of the core and winding pressing degree based on the selected analyses of the vibroacoustic signal registered. The original research results presented in the paper were obtained at a real 400 kV A power transformer switch on in laboratory conditions - for a regular operation condition and for modeled core damage.
The paper deals with mathematical modeling of acoustic emission signals which are generated in on load tap changers. In power engineering area acoustic emission method is commonly used for diagnosis purposes. Authors in their research works apply it for detection of defects occurring in on load tap changers, which are important elements of power transformers. The acoustic emission method is based on measurements performed by use of wideband piezoelectric transducers that are mounted on transformer tank surface. The registered signal is then analyzed in the time, frequency, and time-frequency domains or is evaluated with computer expert systems for diagnosis purposes. Depending on indicators device technical condition can be determined. The contribution given by the authors in this paper is proposal of a mathematical model, which describes envelope of the measured acoustic emission signal.
The subject matter of this article concerns the diagnostic test results of transformer cores by measuring and analysing vibroacoustic signals registered during their normal operation. The main objective of this research study conducted by the authors, the results of which are published in this paper, is a critical analysis of vibroacoustic criteria, which are adopted in Poland nowadays, and based on which, the assessment of the core technical condition is performed. This article presents exemplary results that were obtained on two twin units of type TET 8509 with a power of 40 MVA. The paper specifies diagnosed structures, the measurement system applied, and the currently used methodology to assess the degree of core loosening. To determine the efficacy and assessment accuracy of the applied vibroacoustic criteria, correlation between mechanical vibration measurements of the tested transformer tanks and results obtained by gas chromatography was performed.
This paper presents the preliminary results of the performed experiment, based on common phenomenon of partial discharges. A simple Geiger-Muller counter (DP-66M) was used for measurement of a dose of ionizing radiation, which is accompanied by partial discharges. Values from which the radiation intensity was dependent could be controlled individually: the distance between measurer and source, as well as the voltage generating partial discharges. The obtained results indicate that in the examined phenomenon, significant dose of X-ray radiation is present. According to the Kramers-Kulenkampff theory, it depends also on the atomic number of elements involved. Using MATLAB software, the obtained data were compiled to develop suitable theory for further research study. There was also implemented fuzzification for the fuzzy logic, and the effect was the capability of forecasting radiation doses according to the fixed variables for a given material, where partial discharges were generated.
The paper presents research results referring to the development of a non-invasive method of assessment of the power transformer core technical condition based on the analysis of the mechanical vibrations registered. It characterizes the power object under study, the measuring system used and the developed methodology of assessment of the core pressing degree using the vibroacoustic method. The original results of the time-frequency analysis of the vibroacoustic signals presented in the paper were obtained during switching on a real 800 kVA dry type power transformer in laboratory conditions. The analysis of the signals registered was carried out for three states of its operation: the core pressed by the manufacturer, the core with loose screws fixing the upper yoke and the core with separated upper yoke beams.
The article presents the results of attempts made to develop a non-invasive diagnostic method of a technical state of a transformer's core based on an analysis of mechanical vibrations registered during the start-up of the transformer analyzed. The paper presents a characteristic of the transformer under study, the measuring systems applied and the method developed for assessing the degree of the core loosening. The original results presented in the paper have been obtained under laboratory conditions during tests conducted on an oil transformer of 200 kVA. The analysis of recorded virboacoustic signals was performed by means of discrete wavelet transform for three different operating cases: the transformer with no core defect, the transformer with loose screws of the magnetic circuit of the upper yoke, and the transformer with completely loosen screws of the beam of the upper yoke and the lower core. The signals have been recorded on two perpendicular measuring axes: 0X and 0Y and their measured values were subject to the wavelet analysis.
This article deals with the subject matter of improvement of the acoustic emission methods used for location of partial discharges, which may occur inside power transformer insulation systems. Analytical solutions of spherical equations for location of partial discharge generation using the acoustic method were shown in detail. Presented in the article method of solving the assumed equations is based on the analytical method and matrix notation. Theoretical considerations and later the measurement-based verification refer to the use of the triangulation method for location of the occurrence of partial discharges. The results of the scientific and research works that have been presented in this article are the next stage of research aimed at development of on-line diagnosis system for insulation systems of electrical equipment, allowing for detection, measurement and identification of forms and locations of partial discharges using the acoustic emission method.
Subject matter of this article concerns the results of research works on the development and use of the vibroacoustic method to evaluate technical state of transformer cores. The article presents obtained measurement results of transformer mechanical vibration for two cases of its operation: with twisted and loosened core. In order to demonstrate negative effects of operating a transformer with a loosened core, this publication presents thermographic images showing temperature distribution on its magnetic core. The article characterises the examined transformer, employed measurement system and methodology of the completed experiment. The vibroacoustic and thermographic measurements were carried out during idle work of the transformer. Core vibration was registered for three measurement axes: 0X, 0Y and 0Z. Completed tests have proven that loosened screws pressing the core cause evident increase in the value of magnetic core vibration acceleration. At the same time, the temperature rises by more than 25%.
Results of scientific research works considering selection of measuring transducer applied for registration of acoustic emission signals generated by on load tap changers are presented in the paper. During the coupling process acoustic emission signals are generated by: the mechanical setup of tap changer, contacts operation, and other phenomena. For most on load tap changers types, the working medium is insulation oil in which the acoustic wave being formed propagates to the steal tank. There exists a possibility to register acoustic emission signals with a piezoelectric transducer attached to the outer tank surface or with a hydrophone immersed in the oil. Acoustic emission signal obtained in such manner contains information which describes operation of the power tap changer and the selector. A comparative analysis of acoustic emission signals generated by on load tap changers working under laboratory conditions, with applied measuring transducers with different transmittances, is presented in the paper. The comparative analysis was performed in order to determine their suitability for on load tap changers technical condition diagnosis. Based on the results achieved, one transducer which allows the registration of acoustic events generated during on load tap changers operation was selected.
The paper is an analytical and experimental study of a smart structure consisting of steel plate with bonded piezoelectric transducers and porous elastomer layer. Active control of sound radiation from a plate clamped at the edge square is examined. Simulations and numerical computation of the experiment are performed in Ansys environment. Calculations of plate vibration and sound radiation under stepped harmonic force are performed. The experimental setup consists of two rooms with the test opening in between. A variety of test cases were studied for three different configurations: steel plate + piezoelectric transducer, steel plate + elastomer layer, steel plate + piezoelectric transducer + elastomer layer. The aim of the paper is to illustrate the possibilities of using piezoelectric materials as an active control with elastomer layers as passive methods in one structure to improve the transmission loss.
The paper concerns an active vibration protection (p-reduction) of the structure via piezoelectric transducers; p-reduction corresponds to an active vibration reduction (a-reduction). The quantity and effectiveness of the (a- or p-) reduction, among other parameters, depend on the piezoelectric transducers distribution on the structure. The best results are obtained bonding piezoelectric transducers to the structure in the sub-domains with the largest curvatures; it is so-called quasi-optimal distribution of the piezoelectric transducers. Up to now, the quasi-optimal distribution was determined based on heuristic reasons only. The aim of the paper is to confirm quasi-optimal distribution in analytical way. The beam clamped at one end, vibrating with first three modes separately, is chosen as the research object. It is assumed that the piezoelectric transducers are exactly the same. Demanding the vibration amplitude to be equal to zero (i.e. p-reduction condition), the general formula for interacting forces piezoelectric transducers-beam is derived. Next, such an appropriate distribution of piezoelectric transducers is searched analytically, that the minimal forces are achieved; it leads to the best reduction effectiveness. It turned out that the analytical method pointed out quasi-optimal distribution of the piezoelectric transducers. The validation of theoretical considerations is confirmed numerically.
This paper deals with an active vibration protection (p-reduction) of the beam-actuators mechanical system, hence it concerns separate modes. The paper's aim is an effectiveness analysis of the p-reduction assuming different number of actuators. It is assumed a priori that actuators are bonded to the beam in the sub-domain with the largest curvatures and they are exactly the same. The beam clamped at one end is chosen as the research object. Next, as required by the p-reduction condition, the number and distribution of actuators are changed. It turns out that the best reduction effectiveness, measured via any effectiveness coefficient, is obtained for one actuator bonded in the sub-domain with the largest curvature. The validation of theoretical considerations is confirmed numerically.
An analytical solution is obtained, based on linear quadratic problem well-known in the control theory. The problem is formulated for fixed-free beam vibration (fourth order partial differential equation) in Hilbert space and the point control and distributed output is considered. Beam deflection at any point is chosen as a criterion of optimization. In this case it means the linear quadratic problem. Up to now, the linear quadratic problem was formulated many times, but only for the time-dependent equation. The aim of the paper is to obtain the value of the cost functional formulated as the function of distribution of actuators. The minimum of this function leads to the optimal actuators location. The results obtained with this method confirm the results obtained in heuristic way and pure analytical one for separate mode; it is pointed out that the actuators ought to be bonded on the beam sub-regions in which the mode curvatures take their local maximums and the highest value.
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