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1

Rayleigh wave propagation in isotropic sandy layer sliding over isotropic sandy semi-infinite medium with sliding contact

Madan Dinesh Kumar, Kumar Naveen, Rani Annu

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 1

58--70

EN

The present study aims to investigate Rayleigh wave propagation in an isotropic sandy layer overlying an isotropic sandy semi-infinite medium, with interface considered to be imperfect (slide contact and dislocation like model). Expressions for displacement components are obtained using the variable separation method. The dispersion frequency equation for the Rayleigh wave propagating in sandy media is derived using suitable boundary conditions. Particular cases, such as when the interface is in smooth contact and when sandy media are replaced by elastic media, are also discussed. Using MATLAB software, the effects of the imperfectness parameter (slide contact and dislocation like model) and sandy parameter on the Rayleigh waves’ phase velocity are investigated and compared with the already obtained results of the dislocation like model. The present study may find useful applications in geophysics, civil engineering and soil mechanics.

2

Magneto-thermo-piezo-elastic wave in an initially stressed rotating monoclinic crystal in a two-temperature theory

Yadav Anand Kumar

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 3

127--158

EN

This research problem is an investigation of wave propagation in a rotating initially stressed monoclinic piezoelectric thermo-elastic medium under with the effect of a magnetic field. A two-temperature generalized theory of thermo-elasticity in the context of Lord-Shulman’s theory is applied to study the waves under the magnetic field. The governing equations of a rotating initially stressed monoclinic piezoelectric thermo-elastic medium with a magnetic field are formulated. This research problem is solved analytically, for a two-dimensional model of the piezo-electric monoclinic solid, and concluded that there must be four piezo-thermoelastic waves, three coupled quasi waves (qP (quasi-P), qT (quasi-thermal), and qSV (quasi-SV)) and one piezoelectric potential (PE) wave propagating at different speeds. It is found that at least one of these waves is evanescent (an evanescent wave is a non-propagating wave that exists) and that there are therefore no more than three bulk waves. The speeds of different waves are calculated and the influence of the piezoelectric effect, two-temperature parameter, frequency, rotation, and magnetic field on phase velocity, attenuation coefficient, and specific loss is shown graphically. This model may be used in various fields, e.g. wireless communications, signal processing, and military defense equipment are all pertinent to this study.

3

New Surface-Plasmon-Polariton-Like Acoustic Surface Waves at the Interface Between Two Semi-Infinite Media

Kiełczyński Piotr

Archives of Acoustics

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2022

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Vol. 47, No. 3

363--371

EN

This paper presents theory of new shear horizontal (SH) acoustic surface waves that propagate along the interface of two semi-infinite elastic half-spaces, one of which is a conventional elastic medium and a second one an elastic metamaterial with a negative and frequency dependent shear elastic compliance. This new surface waves have only one transverse component of mechanical displacement, which has a maximum at the interface and decays exponentially with distance from the interface. Similar features are also shown by the acoustic shear horizontal Maerfeld-Tournois surface waves propagating at the interface of two semi-infinite elastic media due to the piezoelectric effect that should occur in at least one semi-space. The proposed new shear horizontal acoustic surface waves exhibit also strong formal similarities with the electromagnetic surface waves of the surface plasmon polariton (SPP) type, propagating along a metal-dielectric planar interface. In fact, the new shear horizontal elastic surface waves possess a large number of properties that are inherent for the SPP electromagnetic surface waves, such as strong subwavelength concentration of the wave field in the proximity of the guiding interface, low phase and group velocity etc. As a result, the new shear horizontal acoustic surface waves can find applications in sensors with extremely high sensitivity, employed in measurements of various physical parameters, such as viscosity of liquids, as well as in biosensors, chemosensors, or a near field acoustic microscopy (subwavelength imaging) and miniaturized devices of microwave acoustics.

4

Propagation of the torsional wave in an irregular self-reinforced composite material bounded between two half-spaces

Gupta Shishir, Das Sandip Kumar

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 4

971--982

EN

This research article is concerned with the analytical assessment and mathematical modelling to unveil the characteristic of a torsional wave in the irregular Earth’s crustal stratum. This investigation has been performed to clarify of possible occurrence of the torsional wave in an irregular self-reinforced composite layer bonded between dry sandy media and an isotropic elastic half-space. Rectangular and parabolic irregularities have been assumed at the interface of the intermediate layer and the lower half-space. In order to acquire the required dispersion equation, the appropriate boundary conditions with the assistance of displacement and stress components have been well satisfied. The effects of different affecting parameters such as reinforcement, sandiness, initial stress and irregularity parameters have been explored and explained by suitable graphs. Moreover, a comparative study has also been accomplished graphically for rectangular, parabolic, and no irregularities.

5

Mathematical study of Rayleigh waves in piezoelectric microstretch thermoelastic medium

Kumar Arvind, Abo-Dahab S. M., Ailawalia Praveen

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

86--93

EN

This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic piezo-electric microstretch-thermoelastic solid half-space. The medium is subjected to stress-free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases have also been derived from the present investigation.

6

Response of corrugated interface on incident qSV-wave in monoclinic elastic half-spaces

Singh S. S., Lalvohbika J.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

727--750

EN

This paper is concerned with the problem of reflection and transmission of elastic waves due to an incident plane qSV-wave at a corrugated interface between two dissimilar monoclinic elastic half-spaces. Due to the corrugated nature of the interface, there exist regularly and irregularly reflected and transmitted elastic waves. Using Rayleigh’s method of approximation, the reflection and transmission coefficients of regular and irregular waves are obtained for the first order of approximation. We have found that these coefficients are functions of the angle of incidence, elastic constants, corrugation and the frequency parameter. These coefficients are obtained for a special type of interface, z =dcos py. We have computed these coefficients for a particular model and discussed the effects of corrugation and frequency parameter.

7

Seismic crust structure beneath the Aegean region in southwest Turkey from radial anisotropic inversion of Rayleigh and Love surface waves

Çakır Ö.

Acta Geophysica

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2018

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Vol. 66, no. 6

1303--1340

EN

The Turkish plate is covered by hundreds of accelerometer and broadband seismic stations with less than 50 km inter-station distance providing high-quality earthquake recordings within the last decade. We utilize part of these stations to extract the fundamental mode Rayleigh and Love surface wave phase and group velocity data in the period range 5–20 s to determine the crust structure beneath the Aegean region in southwest Turkey. The observed surface wave signals are interpreted using both single-station and two-station techniques. A tomographic inversion technique is employed to obtain the two-dimensional group velocity maps from the single-station group velocities. One-dimensional velocity–depth profiles under each twodimensional mesh point, which are jointly interpreted to acquire the three-dimensional image of the shear-wave velocities underneath the study area, are attained by utilizing the least-squares inversion technique, which is repeated for both Rayleigh and Love surface waves. The isotropic crust structure cannot jointly invert the observed Rayleigh and Love surface waves where the radial anisotropic crust better describes the observed surface wave data. The intrusive magmatic activity related to the northward subducting African plate under the Turkish plate results the crust structure deformations, which we think, causing the observed radial anisotropy throughout complex pattern of dykes and sills. The magma flow resulting in the mineral alignment within dykes and sills contributes to the observed anisotropy. Due to the existence of dykes, the radial anisotropy in the upper crust is generally negative, i.e., vertically polarized S-waves (Vsv) are faster than horizontally polarized S-waves (Vsh). Due to the existence of sills, the radial anisotropy in the middle-to-lower crust is generally positive, i.e., horizontally polarized S-waves (Vsh) are faster than vertically polarized S-waves (Vsv). Similar radial anisotropic results to those of the single-station analyses are obtained by the two-station analyses utilizing the cross-correlograms. The widespread volcanic and plutonic rocks in the region are consistent with the current seismic interpretations of the crustal deformations.

8

Phase and group velocities of surface waves in left-handed material waveguide structures

Taya S. A., Elwasife K. Y., Qadoura I. M.

Optica Applicata

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2017

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Vol. 47, nr 2

307--318

EN

We assume a three-layer waveguide structure consisting of a dielectric core layer embedded between two left-handed material claddings. The phase and group velocities of surface waves supported by the waveguide structure are investigated. Many interesting features were observed such as normal dispersion behavior in which the effective index increases with the increase in the propagating wave frequency. The phase velocity shows a strong dependence on the wave frequency and decreases with increasing the frequency. It can be enhanced with the increase in the guiding layer thickness. The group velocity peaks at some value of the normalized frequency and then decays.

9

Simultaneous velocity measurement of phases in a liquid-gas system

Musoski R., Stelmach J.

Chemical and Process Engineering

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2017

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Vol. 38, nr 4

577--585

EN

Results of velocity measurements of liquid and gas bubbles in a tank with a self-aspirating disk impeller are analysed. Studies were carried out using a fluorescent dye tracer in the measuring system with two cameras (simultaneous phase velocity measurement) and with one camera (sequential measurement of phase velocity). Based on a comparative analysis of the acquired data it was found that when differences in the phase velocities were small the simultaneous velocity measurement gave good results. However, sequential measurement gives greater possibilities for setting the measuring system and if the analysis of instantaneous velocities is not necessary, it seems to be a better solution.

10

Propagation of Love waves in a void medium over a sandy half space under gravity

Patra P., Gupta A. K., Kundu S.

Acta Geophysica

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2017

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Vol. 65, no. 2

269--274

EN

The present study investigates the propagation of Love wave in a void layer resting over a sandy half space under the effect of gravitational force. The equations of motion have been gathered separately for different layers, and the boundary conditions have been introduced for two different layers at their interface. The mathematical analysis of the problem has been dealt with the help of Whittaker’s function by expanding it asymptotically up to linear terms. The study reveals that in such a situation there exist two different wave fronts for the two abovementioned layers: one is for the effects of gravity and sandy parameters, whereas other is for the effect of void parameter.

11

Dispersion relations for composite structures. Pt. 2, Methods of determining dispersion curves

Barski M., Stawiarski A., Chwał M.

Composites Theory and Practice

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2016

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R. 16, nr 3

147--153

EN

In the first part of the current review, the fundamental assumptions of the theoretical model of elastic waves propagation in multilayered composite material are presented. Next, the equations which describe elastic wave motion in the case of single orthotropic lamina are derived. In the second part of this work, the most commonly used method of determining dispersion curves for multilayered composite material are discussed, namely: the transfer matrix method (TMM), global matrix method (GMM), stiffness matrix method (SMM) and finally the semi-analytical finite element method (SAFE). The first three methods are based on the relationships which are derived in the first part of this review. Moreover, TMM and GMM should be considered numerically unstable in the case of a relatively large product value of wave frequency and the total thickness of the composite plate. However, SMM seems to be unconditionally stable. The last method is based on the finite element approach and it can be used in order to confirm the results obtained using the analytical method. Finally, exemplary dispersion curves are presented. The dispersion curves are determined for the 8-th layer of the composite material, which is made of carbon fiber and epoxy resin. It is assumed that the wave front travels in an arbitrary direction.

PL

W części pierwszej pracy omówiono założenia dotyczące teoretycznego modelu propagacji fal sprężystych w wielowarstwowych materiałach kompozytowych. Następnie wyprowadzono równania opisujące zjawisko propagacji fal sprężystych w pojedynczej warstwie o ortotropowych własnościach mechanicznych. W części drugiej przedstawiono podstawy najczęściej wykorzystywanych metod wyznaczania krzywych dyspersji dla ośrodków wielowarstwowych, a mianowicie: transfer matrix method (TMM), global matrix method (GMM), stiffness matrix method (SMM), a także semi-analytical finite element method (SAFE). Pierwsze trzy podejścia oparte są bezpośrednio na równaniach wyprowadzonych w części pierwszej. Metody TMM oraz GMM uważane są za numerycznie niestabilne w przypadku odpowiednio dużych wartości iloczynu częstotliwości i całkowitej grubości płyty kompozytowej. Natomiast wydaje się, że podejście SMM jest numerycznie bezwarunkowo stabilne. Ostatnia z wymienionych metod oparta jest na metodzie elementów skończonych i można ją efektywnie wykorzystać w celu potwierdzenia wyników otrzymanych przy użyciu poprzednio wymienionych algorytmów. Jako przykład pokazano krzywe dyspersji wyznaczone dla 8-warstwowego materiału kompozytowego wykonanego z włókna węglowego, przy czym założono, że czoło fali porusza się w dowolnie założonym kierunku.

12

Dispersion relations for composite structures. Pt. 1, Basic assumptions and relationships for monoclinic lamina

Barski M., Stawiarski A., Chwał M.

Composites Theory and Practice

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2016

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R. 16, nr 3

125--131

EN

Nowadays, the propagation of elastic waves, particularly Lamb waves, is very often used in detecting damages in different kinds of composite materials. These systems are known as structural health monitoring (SHM). However, the phenomenon of Lamb wave propagation is very complex, especially in the case of thin-walled composite structures. Generally, three types of Lamb waves are observed, namely: longitudinal or pressure waves (L), shear vertical (SV) and shear horizontal (SH). The phase and group velocities of the mentioned waves depend on the thickness of the structure and the frequency of the excited signal. This fact makes proper interpretation of the received dynamic response of the structure difficult or even impossible. Therefore, determining the appropriate dispersion curves for different materials is a very important issue. In the present review, the most commonly used analytical approaches for determining dispersion curves in the case of multilayered composite plates are presented. At the very beginning of this work the solution for single isotropic plates is presented. Next, the fundamental assumptions of the theoretical model, which describe the elastic wave propagation phenomenon in multilayered materials, are discussed. In the first part, the relationships describing the elastic wave propagation for single orthotropic lamina are presented. There are two studied cases: namely when the wave front of the elastic wave travels along the principal directions of the material and when the wave front of the elastic wave travels in any arbitrary direction.

PL

Obecnie zjawisko propagacji fal sprężystszych, a w szczególności fal Lamba jest często wykorzystywane przy projektowaniu różnych systemów wykrywania uszkodzeń w wielowarstwowych materiałach kompozytowych. Systemy te są ogólnie znane pod skrótem SHM (Structural Health Monitoring). Jednakże, zjawisko propagacji fal Lamba w kompozytowych konstrukcjach cienkościennych posiada bardzo skomplikowany charakter. W ogólnym przypadku w zależności od płaszczyzny polaryzacji drgań cząstek rozróżniamy trzy rodzaje fal Lamba, a mianowicie: falę podłużną (L) oraz fale poprzeczne spolaryzowane w kierunku pionowym (SV) oraz poziomym (SH). Dodatkowo, każda z wymienionych fal w zależności od grubości materiału oraz częstotliwości generowanego sygnału posiada odpowiednie mody. Mody te propagują się z różną prędkością zarówno fazową, jak i grupową. Zjawisko to znacznie utrudnia interpretację zarejestrowanej dynamicznej odpowiedzi konstrukcji. W pracy szczegółowo opisano najczęściej wykorzystywane analityczne metody wyznaczania krzywych dyspersji. Na początku przedstawiono rozwiązanie dla jednowarstwowej płyty izotropowej. Następnie omówiono podstawowe założenia teoretycznego modelu propagacji fal sprężystych w materiałach wielowarstwowych. W części pierwszej zaprezentowano równania opisujące zjawisko propagacji fal sprężystych w jednowarstwowych płytach o własnościach ortotropowych. Rozważano dwa przypadki, a mianowicie kiedy czoło fal sprężystych porusza się wzdłuż osi głównych materiału oraz kiedy czoło fali porusza się w dowolnym kierunku.

13

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.

14

The forward-wave and backward-wave behaviors of electromagnetic waves in two-dimensional photonic crystals

Jiang P, Yang H., Xie K.

Optica Applicata

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2014

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Vol. 44, nr 1

17--27

EN

The negative refractions are discussed in detail to demonstrate two different two-dimensional photonic crystal structures that undergo negative refractions associated with the backward-wave and forward-wave phenomenon, respectively. The presentation of the left-handed property of effective negative index photonic crystal is followed by a discussion of a backward flowing phase and causality. The forward-wave negative refraction occurs in photonic crystals as a result of anisotropy. This paper is based on the theoretical analysis and is illustrated with the results of finite element method simulations.

15

Elastic properties of some clay minerals

Vyzhva S. A., Prodayvoda G. T., Vyzhva A. S.

Nafta-Gaz

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2014

|

R. 70, nr 11

743--756

EN

A new method for the quantitative estimation of the elastic properties of clay minerals based on the principles of crystal-chemical systematization of clay minerals elastic properties was developed. An accurate mathematical method has been devised to approximate elastic properties of a random symmetry medium to those of a similar transversely isotropic elastic medium. A first successful attempt was made at a quantitative assessment of the elastic constants of all clay mineral constituents in transversely isotropic approximation, which fully agrees with experimental data on these minerals. Extensive research has been carried out into the anisotropy parameters of clay mineral elastic waves and their correlation with the structural features of minerals. This method can be used for approximating the elastic constants of other rock-forming minerals.

PL

Opracowano nową metodę oceny ilościowej sprężystych własności minerałów ilastych w oparciu o zasady krystaliczno-chemicznej systematyzacji tych własności. Nowa, dokładna matematyczna metoda ma na celu przybliżenie własności sprężystych ośrodka o losowej symetrii do tych o podobnym sprężystym ośrodku poprzecznie izotropowym. Pierwszej udanej próby dokonano przy ilościowej ocenie stałych sprężystych wszystkich komponentów minerałów ilastych w poprzecznie izotropowym przybliżeniu, co jest w pełni zgodne z danymi eksperymentalnymi dotyczącymi tych minerałów. Przeprowadzono wszechstronne badanie parametrów anizotropowych fal sprężystych minerałów ilastych i ich korelacji ze strukturalnymi cechami minerałów. Metoda ta może zostać wykorzystana do przybliżenia stałych sprężystych innych minerałów w formacjach skalnych.

16

Phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic cylinders

Ahmed Shah S., Javvad Hussaini S.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 2

337--346

EN

The present paper is devoted to the study of phase velocity and attenuation of longitudinal shear vibrations of hollow poroelastic circular cylinders in the presence of dissipation. The explicit expressions for phase velocity and attenuation of longitudinal shear vibrations are derived. The frequency equation of longitudinal shear vibrations and modes obtained in a previous paper are used to compute the phase velocity and attenuation for different dissipations for thin and thick poroelastic cylindrical shells and poroelastic solid cylinder. The physical parameters of sandstone saturated with kerosene and sandstone saturated with water are used for the purpose of computation. It is found that the phase velocity is linear beyond certain frequency. Phase velocity is smaller for a typical anti-symmetric mode compared to the flexural mode. It is greater for the second mode than that of the first mode. Also the phase velocity is larger for a thin poroelastic cylindrical shell than that of a thick poroelastic cylindrical shell. The same is true for attenuation also. Attenuation is very high for the considered dissipations and it increases with the increase in dissipation.

17

Vibrations in a fluid-loaded poroelastic hollow cylinder surrounded by a fluid in plane-strain form

Shanker B., Nath C. N., Shah S. A., Reddy P. M.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

189--216

EN

Plane-strain vibrations in a fluid-loaded poroelastic hollow cylinder surrounded by a fluid are investigated employing Biot’s theory of wave propagation in poroelastic media. The poroelastic hollow cylinder is homogeneous and isotropic, while the inner and outer fluids are homogeneous, isotropic and inviscid. The frequency equation of the fluid-loaded poroelastic cylinder surrounded by a fluid is obtained along with several particular cases, namely, fluid-loaded poroelastic cylinder, fluid-loaded bore, poroelastic cylinder surrounded by a fluid and poroelastic solid cylinder submerged in a fluid. The frequency equations are obtained for axially symmetric, flexural and anti-symmetric vibrations each for a pervious and an impervious surface. Nondimensional frequency for propagating modes is computed as a function of the ratio of thickness to the inner radius of the core. The results are presented graphically for two types of poroelastic cylinders and then discussed.

18

Stoneley waves at swelling porous elastic media

Kumar R., Taneja D., Kumar K.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1177-1192

EN

A frequency equation for Stoneley waves at a bonded interface between two swelling porous elastic half spaces [SP/SP] is derived. It is found that Stoneley waves in a swelling porous elastic medium are dispersive in nature. Numerical computations are performed to study the variation of phase velocity and attenuation coefficient with respect to the wave number. Amplitude ratios are obtained and also represented graphically. Some particular cases are also discussed.

19

Dispersion of waves in coated poroelastic circular cylinders

Shah S. A., Tajuddin M.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 1

213-231

EN

The phenomenon of crack initiation due to dynamic contact loading is referred to as fretting fatigue. This situation is commonly encountered in mechanical couplings subjected to vibration. Whenever a material has good mechanical properties but poor fretting resistance it is advantageous to provide a layer of material having good fretting resistance instead of changing the entire material. This extra layer of material can be provided by coating or by any other surface treatment methods. Wave propagation in coated poroelastic cylinders of infinite extent is investigated employing Biot's theory. The coated poroelastic cylinder consists of two poroelastic cylinders of different poroelastic materials bonded at the curved surface such that the liquids in the poroelastic materials are immiscible. Frequency equations of coated poroelastic cylinders are derived both for pervious and impervious surfaces. Let the infinite coated poroelastic cylinder be homogeneous and isotropic and the outer boundary is free from stress. At the interface of the core and coating, the stresses and displacements are continuous. For motions having infinite wavelength or when the wavenumber is zero, the axial shear and radial modes of the coated poroelastic cylinder are uncoupled each for a pervious and an impervious surface. The frequency equation of axial shear vibrations is same for pervious and impervious surfaces. Non-dimensional phase velocity for propagating modes is computed as a function of propagation constant in the absence of dissipation. The results are presented graphically for two types of coated poroelastic cylinders and then discussed.

20

Quantitative Ultrasound of Cancellous Bone. Modeling and Experiment

Pakuła M.

Image Processing & Communications

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2012

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Vol. 17, no. 4

23--30

EN

The paper present theoretical and experimental issues related to application of Quantitative Ultrasound (QUS) for assessment of cancellous bone quality and prediction of bone fractures. Commonly used for modeling of ultrasonic wave propagation in cancellous bone, the macroscopic Biot’s theory is discussed in context of its potential applicability for theoretical prediction of wave parameters: phase velocity and attenuation coefficient as functions of frequency. The analysis of the model is focused on the absorption mechanisms responsible for attenuation of ultrasonic waves in cancellous bone, which based on the ultrasonic experiments presumably play a predominant role in the total attenuation. The suitability of the model is discussed and verified by comparison of results of sensitivity analysis of the model with ex vivo experimental ultrasonic data obtained for cancellous bones filled with different fluids.