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1

Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

Kiełczyński P., Szalewski M., Balcerzak A., Wieja K.

Archives of Acoustics

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2015

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Vol. 40, No. 2

273--281

EN

This paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2 type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

2

Thermodynamic Method for Measuring the B/A Nonlinear Parameter Under High Pressure

Kiełczyński P., Szalewski M., Balcerzak A., Wieja K., Rostocki A., Siegoczyński R.

Engineering Transactions

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2014

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Vol. 62, iss. 1

5--15

EN

The nonlinearity parameter B/A is a measure of the nonlinearity of the equation of state for a fluid. The nonlinearity parameter B/A is a physical parameter often used in acoustics, from underwater acoustics to biology and medicine. It can provide information about structural properties of the medium, internal pressure and inter-molecular spacing. The thermodynamic method has been applied for determination of B/A parameter in diacylglycerol (DAG) oil as a function of pressure at various temperatures. Isotherms of the density and phase velocity of longitudinal ultrasonic wave as a function of pressure have been measured. Using the thermodynamic method along with measured isotherms of sound speed and density, the nonlinearity parameter B/A (for DAG oil) was evaluated as a function of pressure (up to 220 MPa) at various temperatures ranging from 20 to 50◦C.

3

Transistor Effect in the Cochlear Amplifier

Kiełczyński P., Szalewski M.

Archives of Acoustics

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2014

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Vol. 39, No. 1

117--124

EN

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.

4

Computer-based simulation of plasma concentration time-proﬁles of drug in nonlinear two-compartment model

Piekarski S., Kiełczyński P., Szalewski M., Rewekant M.

Computer Assisted Methods in Engineering and Science

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2013

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Vol. 20, no. 4

279--288

EN

The main interest of pharmacokinetics is the study of the fate of drugs in the living organism. This work proposes the system of the conservation laws that describes time-dependent concentrations of a drug, after a single intravenous administration. Compared with others, the proposed model considers both free and protein-bound drug concentrations at the same time. Plasma protein binding captured in the model enters the nonlinearity arising from the Guldberg-Waage law. According to our best knowledge, the analytical solution for our system does not exist. Our model allows the calculation of the free and bound-drug protein concentrations at any time point and at any dose after single intravenous bolus dose administration. In order to compare the empirical with simulated data, a numerical approach has been proposed. On the basis of published experimental data the model validation has been carried out. The goodness of ﬁt was satisfactory (R 2 = 0.99) and the experimental and simulated AUC (area under the curve) values, as the measure of the bioavailability of drug, were similar (150 M/hxh−1). The preliminary assessment of the model credibility was positive and encouraged further studies.

5

Power Amplification and Selectivity in the Cochlear Amplifier

Kiełczyński P.

Archives of Acoustics

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2013

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Vol. 38, No. 1

83--92

EN

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.

6

Metody ultradźwiękowe identyfikacji własności sprężystych materiałów gradientowych

Kiełczyński P.

Inżynieria Materiałowa

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2008

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Vol. 29, nr 3

157-164

PL

W pracy przedstawiono wykorzystanie uogólnionych poprzecznych fal powierzchniowych do określenia rozkładów parametrów sprężystych w niejednorodnych materiałach gradientowych na przykładzie próbek stalowych poddanych procesowi hartowania laserowego. W artykule omówiono zastosowanie ultradźwiękowych fal objętościowych i powierzchniowych (rys. 1, 2) do wyznaczania parametrów mechanicznych materiałów. Fale ultradźwiękowe są falami mechanicznymi. Ich własności zależą od własności mechanicznych i mikrostruktury ośrodka, w którym się rozchodzą. Zaletą metod ultradźwiękowych w stosunku do metod mechanicznych badania materiałów jest to, że są one nieniszczące i dają się skomputeryzować, dzięki temu można je stosować bezpośrednio na linii produkcyjnej (in situ) do pomiaru parametrów mechanicznych materiałów. Szczególną uwagę zwrócono na znaczenie poprzecznych fal powierzchniowych, tzn. fal Love'a (rys. 2a, b) i uogólnionych poprzecznych fal powierzchniowych (UPFP) (rys. 3), w badaniach parametrów sprężystych w materiałach gradientowych (Functionally Graded Materials - FGM). Zaletą tych fal w stosunku do powierzchniowych fal Rayleigha jest to, że mają one tylko jedną składową przemieszczenia mechanicznego w przeciwieństwie do fal Rayleigha, które mają dwie składowe. Z tego powodu znacznie upraszcza się opis matematyczny rozchodzenia się poprzecznych fal powierzchniowych w ośrodkach gradientowych. Energia tych poprzecznych fal powierzchniowych (w przeciwieństwie do innych typów fal, np. płytowych fal Lamba) skupiona jest w warstwie powierzchniowej. Głębokość wnikania poprzecznych fal powierzchniowych zależy od częstotliwości. Dlatego nadają się one szczególnie do badania profili własności mechanicznych w niejednorodnych materiałach gradientowych. Zmierzono krzywe dyspersji (rys. 7, 8) poprzecznych powierzchniowych fal typu UPFP rozchodzących się w falowodach powstałych w próbkach stalowych na skutek działania promienia laserowego (rys. 6). Pomiaru krzywych dyspersji (zależności prędkości fali od częstotliwości) dokonano w skomputeryzowanym laboratoryjnym układzie badawczo-pomiarowym, (rys. 4, 5). Prędkość fali UPFP wyznaczono mierząc czas przelotu pomiędzy kolejnymi echami fali ultradźwiękowej. Sformułowano i rozwiązano problem prosty (proste zagadnienie Sturma-Liouville'a) opisujący rozchodzenie się fal UPFP w niejednorodnych ośrodkach gradientowych. Stosując metodę wariacyjną (iloraz Rayleigha), przedstawiono postępowanie odwrotne (odwrotne zagadnienie Sturma-Liouville'a), pozwalające określić rozkład własności sprężystych w funkcji głębokości w badanym materiale niejednorodnym. Korzystając ze zmierzonych krzywych dyspersji fal UPFP oraz ze sformułowanego postępowania odwrotnego wyznaczono rozkłady współczynnika podatności sprężystej ścinania w funkcji odległości od powierzchni (rys. 9, 10), oraz głębokości hartowania w próbkach stalowych (stal 45) poddanych procesowi hartowania laserowego.

EN

In the paper the application of the generalized shear surface waves for the determination of the elastic parameters of non-uniform graded materials, based on the example of steel samples subjected to the laser hardening was presented. In the article, the use of the bulk and surface ultrasonic waves (Fig. 1, 2) for evaluation of the mechanical parameters of materials is discussed. Ultrasonic waves are mechanical waves and their parameters depend on the mechanical and microstructural properties of materials where these waves propagate. Ultrasonic methods for investigation of the material properties are non-destructive methods. This is a main advantage of the ultrasonic methods in relation to the mechanical methods used for investigation of the mechanical properties of materials. Moreover, ultrasonic methods can be computerized. Due to this reason, ultrasonic methods can be employed directly on the production line for measuring the mechanical parameters of materials. The importance of the shear surface waves (i.e., Love waves, Fig. 2a, b) and generalized shear surface waves (Fig. 3) in the investigations of elastic parameters of graded materials (Functionally Graded Materials - FGM) was stressed. Rayleigh surface waves posses two components of the mechanical displacement. The shear surface waves posses only one component of the mechanical displacement what is an advantage. Due to this reason, the mathematical description of the propagation of the shear surface waves is simpler than that using the Rayleigh waves. Energy of the shear surface waves (in contrast to the other types of waves, e.g., plate Lamb waves) is concentrated in the surface layer. The penetration depth of the shear surface waves depends on frequency. Therefore, they are very useful to determine the profiles of the mechanical properties of non-homogeneous graded materials. The dispersion curves of the generalized shear surface waves propagating in waveguides produced in steel samples (Fig. 6) subjected to laser hardening were measured (Fig. 7, 8). The dispersion curves (dependence of wave velocity on frequency) were measured in the computerized laboratory measuring set-up (Fig. 4, 5). Velocity of the shear surface wave was evaluated by measuring time-of-flight between two subsequent echoes of an ultrasonic surface wave. The direct problem (direct Sturm-Liouville problem) for propagating generalized shear surface waves was formulated and solved. Employing the variational method (Rayleigh quotient), the inverse method (inverse Sturm-Liouville problem) was presented which enabled the determination of the profiles of elastic properties as a function of depth in the investigated non-homogeneous material. By using the measured dispersion curves of the generalized shear surface waves and developed inverse procedure, the distributions of the elastic compliance versus depth (the distance from the surface of steel 45 exposed to laser hardening) were determined (Fig. 9, 10), along with the case depths in the investigated steel samples.

7

Absorption of Ultrasonic Waves in Aqueous Binary Mixtures of alfa-Cyclodextrin and Some Amphiphilic Substances

Balcerzak A., Płowiec R., Kiełczyński P., Juszkiewicz A.

Molecular and Quantum Acoustics

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2002

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Vol. 23

15-25

8

Ultrasonic investigations of aqueus solutions of α-cyclodextrin and amphiphil substances having different "heads" and identic "tails"

Balcerzak A., Płowiec R., Kiełczyński P., Juszkiewicz A.

Archives of Acoustics

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2002

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Vol. 27, no. 4

361-371

EN

Velocity and absorption of ultrasonic waves in aqueuos solutions of a-cyclodextrin containing amphiphil substances with different ``heads" and identic ``tails" were carried out. As a result of the mutual interactions between a-cyclodextrin and the amphiphil substance the low frequency ultrasonic relaxation process has been established. Thermodynamic and kinetic parameters related to this process have been calculated. Obtained results have been discussed considering molecular structure of the amphiphil substances.

9

Finite element method (FEM) and impulse response method (IRM) analysis of circular ultrasonic transducers

Kiełczyński P.

Archives of Acoustics

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1998

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Vol. 23, no. 2

291-306

EN

Circular transducers with axially-symmetric vibrational profiles were considered. Vibrational patterns of transducer structures were calculated using the Finite Element Method. Analytical formulas for the impulse response function h(X,t) for circular transducers and vibration velocity profiles, approximated by linear and quadratic polynomials, on the finite element (annulus) were established. These formulas enable accurate calculations of acoustic field distributions in near and far-field, respectively. Calculated profiles of an acoustic field were compared with the experimental data.