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Number of results: 24
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Abstract

We present the results of investigations of Pb(Fe1/2Nb1/2)O3 (PFN) ceramic samples obtained using two-step synthesis (i.e. columbite method). For obtained samples complex investigations of microstructure, magnetic and electrophysical properties have been performed at low and at high temperatures. Microstructure is characterized by small grains with high homogeneity and high density (low porosity). Impedance of samples and the phase shift angle have been measured using LCR Meter. Next the AC electric conductivity, dielectric permittivity and loss tangent have been calculated. AC conductivity at frequency 3 Hz was measured in similar way using Quantum Design PPMS System in magnetic fields 1000 Oe and 10000 Oe. At temperature range 240K-260K the anomalies of conductivity are observed. These anomalies depend on measuring cycle (heating, cooling) and magnetic field.

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Authors and Affiliations

D. Bochenek
R. Skulski
P. Niemiec
D. Brzezińska
K. Rogacki
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Abstract

Bragg scattering of waves propagating in a periodically disturbed substrate is widely applied in optics and micro-acoustic systems. Here, it is studied for Rayleigh waves propagating on a periodically grooved elastic substrate. Practically applied groove depth in the Bragg grating reflectors does not exceed a few percent of the Rayleigh wavelength. Here, the analysis is carried out for periodic grooves of larger depth by applying the elastic plate model for the groove walls. The computed results show that the surface wave existence and reflection depends strongly on both the groove depth and period, and that there are limited domains of both for practical applications, primarily in comb transducers of surface waves.

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Authors and Affiliations

Eugeniusz Danicki
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Abstract

Comb transducers are applied in ultrasonic testing for generation of Rayleigh or Lamb waves by scattering of the incident bulk waves onto surface waves at the periodic comb-substrate interface. Hence the transduction efficiency, although rarely discussed in literature, is an important factor for applications determining the quality of the measured ultrasonic signals. This paper presents the full-wave theory of comb transducers concluded by evaluation of their efficiency for a couple of examples of standard and certain novel configurations.

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Authors and Affiliations

Eugeniusz Danicki
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Abstract

One major problem in the design of ultrasonic transducers results from a huge impedance mismatch between piezoelectric ceramics and the loading medium (e.g. gaseous, liquid, and biological media). Solving this problem requires the use of a matching layer (or layers). Optimal selection of materials functioning as matching layers for piezoelectric transducers used in transmitting and receiving ultrasound waves strictly depends on the type of the medium receiving the ultrasound energy. Several methods allow optimal selection of materials used as matching layers. When using a single matching layer, its impedance can be calculated on the basis of the Chebyshev, DeSilets or Souquet criteria. In the general case, the typically applied methods use an analogy to a transmission line in order to calculate the transmission coefficient T. This paper presents an extension of transmission coefficient calculations with additional regard to the attenuation coefficients of particular layers. The transmission coefficient T is optimised on the basis of a genetic algorithm method. The obtained results indicate a significant divergence between the classical calculation methods and the genetic algorithm method.

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Authors and Affiliations

Tadeusz Gudra
Dariusz Banasiak
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Abstract

In a television, obtaining a good acoustic response is a challenging issue because of slim mechanical structures. The area dedicated for speaker’s placement is limited and inadequate space inside the cabinet of a TV prevents possible solutions to increase the sound performance. In addition, frame of the TV’s is getting narrower as the customers searching for the highest screen to body ratio. These designing aspects restrain optimal speaker positioning to achieve good sound performance. In this paper, an analysis related to speaker’s placement and mounting angle is proposed. A rotation setup compatible with a TV was prepared to measure different facing position of the speaker. This paper proposes the analysis of speaker’s rotation and facing direction in a flat panel television and its effects on sound pressure level together with deviation of the acoustic response. Measurement results are analyzed with an audio analyzer together with a statistics tool to achieve precise results.
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Authors and Affiliations

Ibrahim Demirel
1

  1. Arçelik AS., Electronics HW Design, Turkey
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Abstract

Recently a new technology of piezoelectric transducers based on PZT thick film has been developed as a response to a call for devices working at higher frequencies suitable for production in large numbers at low cost. Eight PZT thick film based focused transducers with resonant frequency close to 40 MHz were fabricated and experimentally investigated. The PZT thick films were deposited on acoustically engineered ceramic substrates by pad printing. Considering high frequency and non-linear propagation it has been decided to evaluate the axial pressure field emitted (and reflected by thick metal plate) by each of concave transducer differing in radius of curvature - 11 mm, 12 mm, 15 mm, 16 mm.

All transducers were activated using AVTEC AVG-3A-PS transmitter and Ritec diplexer connected directly to Agilent 54641D oscilloscope. As anticipated, in all cases the focal distance was up to 10% closer to the transducer face than the one related to the curvature radius. Axial pressure distributions were also compared to the calculated ones (with the experimentally determined boundary conditions) using the angular spectrum method including nonlinear propagation in water. The computed results are in a very good agreement with the experimental ones. The transducers were excited with Golay coded sequences at 35-40 MHz. Introducing the coded excitation allowed replacing the short-burst transmission at 20 MHz with the same peak amplitude pressure, but with almost double center frequency, resulting in considerably better axial resolution. The thick films exhibited at least 30% bandwidth broadening comparing to the standard PZ 27 transducer, resulting in an increase in matching filtering output by a factor of 1.4-1.5 and finally resulting in a SNR gain of the same order.

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Authors and Affiliations

Marcin Lewandowski
Andrzej Nowicki
Janusz Wójcik
Ryszard Tymkiewicz
Rasmus Lou-Moller
Wanda Wolny
Tomasz Zawada
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Abstract

This paper presents a new model that describes the physical phenomena occurring in an individual Outer Hair Cell (OHC) in the human hearing organ (Cochlea). The new model employs the concept of parametric amplification and piezoelectricity. As a consequence, the proposed model may explain in a natural way many as yet unresolved problems about the mechanisms of: 1) power amplification, 2) non- linearity, 3) fine tuning, or 4) high sensitivity that take place in the human hearing organ. Mathematical analysis of the model is performed. The equivalent electrical circuits of an individual OHC are established. The high selectivity of the OHC parametric amplifier is analyzed by solving the resulting Mathieu and Ince differential equations. An analytical formula for the power gain in the OHC’s parametric amplifier has been developed. The proposed model has direct physical interpretation and all its elements have their physical counterparts in the actual structure of the cochlea. The numerical values of the individual elements of the electrical equivalent circuits are consistent with the experimental physiological data. It is anticipated that the proposed new model may contribute in future improvements of human cochlear implants as well as in development of new digital audio standards.
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Authors and Affiliations

Piotr Kiełczyński
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Abstract

The paper deals with the issue of constructing delay lines on the basis of surface acoustic waves and their application to single-mode oscillators. As a result of a theoretical analysis concrete delay lines are proposed.

In the contribution, there is presented a theory of designing a symmetrical mismatched and matched delay line for a single-mode oscillator of electrical signals on the basis of which there were designed and fabricated acoustic-electronic components for sensors of non-electrical quantities.

From the experimental results it can be stated that all of six designed and fabricated delay lines can be effectively used in the construction of single-mode oscillators.

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Authors and Affiliations

Milan Šimko
Miroslav Gutten
Milan Chupáč
Daniel Korenčiak
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Abstract

Based on the electromechanical equivalent circuit theory, equations related to the resonance frequency and the magnifying coefficient of a quarter-wave vibrator and a quarter-wave taper transition horn were deduced, respectively. A series of 3D models of ultrasonic composite transducers with various conical section length was also established. To reveal the influences of the conical section length and the prestressed bolt on the dynamic characteristics (resonance frequency, amplitude, displacement node, and the maximum equivalent stress) of the models and the design accuracy, finite element (FE) analyses were carried out. The results show that the addition of prestressed bolt increases the resonance frequency and causes the displacement node on the center axis to move towards the small cylindrical section. As the conical section length rises, the increment of resonance frequency reduces and tends to a stable value of 360 Hz while the displacement of the node on the center axis becomes lager and gradually approaches 1.5 mm. Furthermore, the amplitude of the output terminal is stable at 16.18 μm under 220 V peak-topeak (77.8 VRMS) sinusoidal potential excitation. After that, a prototype was fabricated and validated experiments were conducted. The experimental results are consistent with that of theory and simulations. It provides theoretical basis for the design and optimization of small-size, large-amplitude, and high-power composite transducers.

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Authors and Affiliations

Tao Chen
Hongbo Lil
Qihan Wang
Junpeng Ye
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Abstract

The paper presents results of numerical calculations and experimental data on the directional pattern of two 38-element parametric arrays composed of ultrasound sources. Two types of antenna arrays are considered, namely with parallel and coaxial connections of ultrasonic transducers (elements). The results of selecting and functional testing of unit elements are described in this paper. It is found that in the coaxial element connection of the antenna array, the level of side lobes is higher than that in the parallel element connection.

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Authors and Affiliations

Denis S. Rakov
Aleksandr S. Rakov
Andrey N. Kudryavtsev
Nikolay P. Krasnenko
Yury A. Chursin
Maksim A. Murin
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Abstract

The aim of this publication is to design a procedure for the synthesis of an IDT (interdigital transducer) with diluted electrodes. The paper deals with the surface acoustic waves (SAW) and the theory of synthesis of the asymmetrical delay line with the interdigital transducer with diluted electrodes. The authors developed a theory, design, and implementation of the proposed design. They also measured signals. The authors analysed acoustoelectronic components with SAW: PLF 13, PLR 40, delay line with PAV 44 PLO. The presented applications have a potential practical use.

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Authors and Affiliations

Milan Šimko
Miroslav Gutten
ORCID: ORCID
Milan Chupáč
Matej Kučera
Adam Glowacz
ORCID: ORCID
Eliasz Kantoch
Hui Liu
Frantisek Brumercik
ORCID: ORCID
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Abstract

The paper presents the description and results of ultrasonic pulse velocity tests performed on heated beams. The studies aimed to verify the suitability of the UPV method for the assessment of the damaged external layer in the cross-section of RC members after a fire. Four beams heated in a planned way from the bottom (a one-way heat transfer) for 60, 120, 180 and 240 minutes and one unheated beam were examined. The tests were performed using an indirect UPV method (linear measurement on the heated surface). Reference tests were conducted using a direct UPV method (measurement across the member section, parallel to the isotherm layout). Exponential transducers were used for testing concrete surface, which was degraded in high temperature and not grinded. The estimated thicknesses of the destroyed external concrete layer corresponded to the location of the isotherm not exceeding 230oC. Therefore, this test can be used to determine at which depth in the member crosssection the concrete was practically undamaged by high temperature.
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Bibliography


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Authors and Affiliations

Julia Wróblewska
1
ORCID: ORCID
Robert Kowalski
1
ORCID: ORCID
Michał Głowacki
1
ORCID: ORCID
Bogumiła Juchnowicz-Bierbasz
1
ORCID: ORCID

  1. Warsaw University of Technology, Faculty of Civil Engineering, Al. Armii Ludowej 16, 00-637 Warsaw, Poland
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Abstract

In many therapeutic applications of a pulsed focused ultrasound with various intensities the finite- amplitude acoustic waves propagate in water before penetrating into tissues and their local heating. Water is used as the matching, cooling and harmonics generating medium. In order to design ultrasonic probes for various therapeutic applications based on the local tissue heating induced in selected organs as well as to plan ultrasonic regimes of treatment a knowledge of pressure variations in pulsed focused nonlinear acoustic beams produced in layered media is necessary. The main objective of this work was to verify experimentally the applicability of the recently developed numerical model based on the Time- Averaged Wave Envelope (TAWE) approach (Wójcik et al., 2006) as an effective research tool for predicting the pulsed focused nonlinear fields produced in two-layer media comprising of water and tested materials (with attenuation arbitrarily dependent on frequency) by clinically relevant axially-symmetric therapeutic sources. First, the model was verified in water as a reference medium with known linear and nonlinear acoustic properties. The measurements in water were carried out at a 25◦C temperature using a 2.25 MHz circular focused (f/3.0) transducer with an effective diameter of 29 mm. The measurement results obtained for 8-cycle tone bursts with three different initial pressure amplitudes varied between 37 kPa and 113 kPa were compared with the numerical predictions obtained for the source boundary condition parameters determined experimentally. The comparison of the experimental results with those simulated numerically has shown that the model based on the TAWE approach predicts well both the spatial-peak and spatial-spectral pressure variations in the pulsed focused nonlinear beams produced by the transducer used in water for all excitation levels complying with the condition corresponding to weak or moderate source-pressure levels. Quantitative analysis of the simulated nonlinear beams from circular transducers with ka ≫ 1 allowed to show that the axial distance at which sudden accretion of the 2nd or higher harmonics amplitude appears is specific for this transducer regardless of the excitation level providing weak to moderate nonlinear fields. For the transducer used, the axial distance at which the 2nd harmonics amplitude suddenly begins to grow was found to be equal to 60 mm. Then, the model was verified experimentally for two-layer parallel media comprising of a 60-mm water layer and a 60-mm layer of 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany). This medium was selected because of its tissue-mimicking acoustic properties and known nonlinearity parameter B/A. The measurements of both, the peak- and harmonic-pressure variations in the pulsed nonlinear acoustic beams produced in two-layer media (water/1.3-butanediol) were performed for the same source boundary conditions as in water. The measurement results were compared with those simulated numerically. The good agreement between the measured data and numerical calculations has shown that the model based on the TAWE approach is well suited to predict both the peak and harmonic pressure variations in the pulsed focused nonlinear sound beams produced in layered media by clinically relevant therapeutic sources. Finally, the pulsed focused nonlinear fields from the transducer used in two-layer media: water/castor oil, water/silicone oil (Dow Corning Ltd., Coventry, UK), water/human brain and water/pig liver were predicted for various values of the nonlinearity parameter of tested media.

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Authors and Affiliations

Tamara Kujawska
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Abstract

The paper presents a new electromechanical amplifying device i.e., an electromechanical biological transistor. This device is located in the outer hair cell (OHC), and constitutes a part of the Cochlear amplifier. The physical principle of operation of this new amplifying device is based on the phenomenon of forward mechanoelectrical transduction that occurs in the OHC's stereocilia. Operation of this device is similar to that of classical electronic Field Effect Transistor (FET). In the considered electromechanical transistor the input signal is a mechanical (acoustic) signal. Whereas the output signal is an electric signal. It has been shown that the proposed electromechanical transistor can play a role of the active electromechanical controlled element that has the ability to amplify the power of input AC signals. The power required to amplify the input signals is extracted from a battery of DC voltage. In the considered electromechanical transistor, that operates in the amplifier circuit, mechanical input signal controls the flow of electric energy in the output circuit, from a battery of DC voltage to the load resistance. Small signal equivalent electrical circuit of the electromechanical transistor is developed. Numerical values of the electrical parameters of the equivalent circuit were evaluated. The range, which covers the levels of input signals (force and velocity) and output signals (voltage, current) was determined. The obtained data are consistent with physiological data. Exemplary numerical values of currents, voltages, forces, vibrational velocities and power gain (for the assumed input power levels below 1 picowatt (10-12 W)), were given. This new electromechanical active device (transistor) can be responsible for power amplification in the cochlear amplifier in the inner ear.

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Authors and Affiliations

Piotr Kiełczyński
Marek Szalewski
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Abstract

Several modelling techniques are currently available to analyse the efficiency of inter-digital transducers (IDTs) fabricated on piezoelectric substrates for producing surface acoustic wave (SAW) devices. Impulse response method, equivalent circuit method, coupling of modes, transmission matrix method, and numerical techniques are some of the popular ones for this. Numerical techniques permit modelling to be carried out with any number of finger electrode pairs with required boundary conditions on any material of interest. In this work, we describe numerical modelling of SAW devices using ANSYS to analyse the effect of mass loading, a major secondary effect of IDTs on the performance of SAW devices. The electrode thickness of the IDT influences the resonance frequency of the SAW delay line. The analysis has been carried out for different electrode materials, aluminium, copper, and gold, for different substrate materials, barium titanate (BaTiO3), X-Y lithium niobate (LiNbO3), lithium tantalate (LiTaO3), and the naturally available quartz. The results are presented and discussed.
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Authors and Affiliations

Sheeja P. George
1 2
ORCID: ORCID
Johney Issac
2
Jacob Philip
3

  1. Department of Electronics, College of Engineering, Chengannur, Kerala, India
  2. Department of Instrumentation, CUSAT, Kochi, Kerala, India
  3. Amaljyothi College of Engineering, Kanjirappally, Kottayam, Kerala, India
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Abstract

Based on the ray acoustic model, a new relationship between the radiation force and the acoustic power is studied for a rectangular weakly focusing transducer. The effect of pressure reflection coefficient on this model is discussed. For a totally absorbing target, an approximate closed-form expression is also derived and the performance of this model is compared with that of the far-field integration model. The numerical results show that the agreement is excellent with these two models, which can be both used for correction of measured results, but the formula based on the ray acoustic model can be applied more widely in practice because of its simpler expression. The experimental results show further the effectiveness of the relationship between radiation force and acoustic power for rectangular weakly focusing transducer based on the ray acoustic model. The results presented in this paper are important for application of ultrasound transducers in therapy.
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Authors and Affiliations

Lili Yu
1
Shuchang Qiao
1
Wende Shou
2 3
Junhua Li
4

  1. Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China
  2. School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China
  3. Shanghai Institute of Ultrasound in Medicine, Shanghai 200233, China
  4. College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China
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Abstract

Hydroacoustic projectors are useful for generating low frequency sounds in water. Existing works on hydroacoustic projectors require two significant enhancements, especially for designers. First, we need to understand the influence of important projector design parameters on its performance. Such insights can be very useful in developing a compact and efficient projector. Second, there is a need for an integrated model of the projector based on easily available and user-friendly numerical tools which do not require development of complex customised mathematical analogs of projector components. The present work addresses both such needs. Towards these goals, an experimentally validated, easy-to-build projector model was developed and used to conduct design sensitivity studies. We show that reductions in pipe compliance and air content in oil, and an increase in orifice discharge coefficient can yield remarkable improvements in projector’s SPL. We also show that reductions in pipe length and cylinder diameter cause moderate improvements in performance in mass and stiffness controlled regions, respectively. In contrast, the projector performance is insensitive to changes in pistonic mass, cylinder length, and diaphragm stiffness. Finally, we report that while pipe compliance and air content in oil can sharply alter system resonance, the effects of changes in pipe length and pistonic mass on it are moderate in nature.
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Authors and Affiliations

Vattaparambil Sreedharan Sreejith
1
Nachiketa Tiwari
1

  1. Dhwani Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
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Abstract

Featured with a higher velocity, increased power handling capability, and better aging behavior, surface transverse wave (STW) shows more promising prospects than Rayleigh wave nowadays in various sensing applications. The need to design, optimize, and fabricate the related devices motivates the development of modeling and simulation. For this reason, a three-dimensional (3D) finite element (FE) simulation of STW on quartz, considering the crystal cut angle and the electrode effects, is presented in this study. Firstly, we investigated the effects of quartz’s cut angle on the generated waves. Here, the polarized displacements were analyzed to distinguish the wave modes. Secondly, the investigations of the electrode effects on the polarized displacement, phase velocity, and electromechanical coupling factor ( K2) were carried out, for which different material and thickness configurations for the electrodes were considered. Thirdly, to examine the excitation conditions of the generated waves, the admittance responses were inspected. The results showed that not only the crystal cut angle but also the density and the acoustic impedance of the interdigital transducer (IDT) material have a strong influence on the excited waves. This article is the first to analyze STWs considering quartz’s cut angle and electrode effect through a 3D FE model. It could provide a helpful and easy way to design, optimize, and fabricate the related surface acoustic wave devices.
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Authors and Affiliations

Chao Jiang
1 2 3
Xiaoli Cao
1 2
Feng Yang
1 2 3
Zejun Liu
1

  1. School of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing, China
  2. Chongqing Key Laboratory of Intelligent Perception and Blockchain Technology, Chongqing Technology and Business University, Chongqing, China
  3. Chongqing Engineering Laboratory for Detection, Control and Integrated System, Chongqing Technology and Business University, Chongqing, China
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Abstract

The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.

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Authors and Affiliations

Jurij Tasinkevych
Ihor Trots
Ryszard Tymkiewicz
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Abstract

Thermo-optic properties enhancement of the bi-stable temperature threshold sensors based on a partially filled photonic crystal fiber was reported. Previously tested transducers filled with a selected group of pure n-alkanes had in most cases differences between switching ON and OFF states. Therefore, the modification of filling material by using additional crystallization centers in the form of gold nanoparticles was applied to minimize this undesirable effect. The evaluation of the thermodynamic properties of pentadecane and its mixtures with 14 nm spherical Au nanoparticles based on the differential scanning calorimetry measurements was presented. Optical properties analysis of sensors prepared with these mixtures has shown that they are bounded with refractive index changes of the filling material. Particular sensor switches ON before melting process begins and switches OFF before crystallization starts. Admixing next group of n-alkanes with these nanoparticles allows to design six sensors transducers which change ON and OFF states at the same temperature. Thus, the transducers with a wider temperature range for fiber-optic multi-threshold temperature sensor tests will be used.

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Authors and Affiliations

N. Przybysz
P. Marć
E. Tomaszewska
J. Grobelny
L.R. Jaroszewicz
ORCID: ORCID
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Abstract

The emergence of high-intensity focused ultrasound applications brings great potential to establish noninvasive therapeutic treatment in place of conventional surgery. However, the development of ultrasonic technology also poses challenges to the design and manufacture of high-power ultrasound transducers with sufficient acoustic pressure. Here, the design of a sector vortex Archimedean spiral phased array transducer that is able to enhance focal acoustic pressure is proposed by maximizing the filling factor of the piezoelectric array. The transducer design was experimentally verified by hydrophone measurements and matched well with acoustic simulation studies. The focal deflection was shown to be feasible up to ±9 mm laterally and up to ±20 mm axially, where the effective focal acoustic pressure can be maintained above 50% and the level of the grating lobe below 30%. Furthermore, a homogeneous pressure distribution without secondary focus was observed in the pre-focal region of the transducer. The rational design of a high-intensity focused ultrasound transducer indicates promising development in the treatment of deep tissue thermal ablation for clinical applications.
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Authors and Affiliations

Xiaodan Lu
1
Deping Zeng
2

  1. State Key Laboratory of Ultrasound in Medicine and Engineering, College of Biomedical Engineering Chongqing Medical University Chongqing, China
  2. National Engineering Research Center of Ultrasound Medicine Chongqing, China
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Abstract

The condition monitoring techniques like acoustic emission, vibration analysis, and infrared thermography, used for the failure diagnosis of bearings, require longer processing time, as they have to perform acoustical measurement followed by signal processing and further analysis using special software. However, for any bearing, its period of usage can be easily determined within an hour, by measuring the bearing sound, using sound level meter (SLM). In this paper the acoustical analysis of the spindle bearing of a radial drilling machine was performed using SLM, by measuring the sound pressure level of the bearing in decibels, for different frequencies, while muting all the other noises. Then using an experimental set up, two database readings were taken, one for new bearing and the other for completely damaged bearing, both are SKF6207, which itself is the spindle bearing. From these three sets of sound pressure level readings, the period of usage of the spindle bearing, was calculated using an interpolation equation, by substituting the life of the bearing from the manufacturer’s catalogue. Therefore, for any machine with a SKF6207 bearing, its usage time can be estimated using the database readings and one measurement on that machine, all with the same speed.

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Authors and Affiliations

S. Charles
Joslin D. Vijaya
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Abstract

Mixed boundary-value problem for periodic baffles in acoustic medium is solved with help of the method developed earlier in electrostatics. The nice feature of the method is that the resulting matrices are relatively easy for computations and that the results satisfy exactly the energy conservation law. Illustrative numerical examples present the wave-beam steering (in the far-field) in a baffle system that may be considered as a model of one-dimensional ultrasonic transducer array.

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Authors and Affiliations

Yuriy Tasinkevych
Eugeniusz Danicki

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