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1

Modeling of the Acoustic Properties of Foamed Polypropylene Panels

Świrk Patrycja, Leniowska Lucyna

Engineering Transactions

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2025

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Vol. 73, iss. 1

89--101

EN

This article presents research on modelling baffles with the desired properties of the sound absorption coefficient (SAC). The purpose of the study was to model and compare the SAC values based on selected theoretical models with the results obtained from measurements of this coefficient in panels made of foamed polypropylene. The assessment of sound absorption properties was carried out using two theoretical models: the Johnson–Champoux–Allard (JCA) model and the Sgard model. The accuracy of the calculated SAC was verified based on laboratory measurements of this parameter for selected material configurations, using the technique of two microphones in an impedance tube. Both theoretical and experimental studies were conducted on porous materials in the form of granules. The application of the Sgard model yielded the best results, with the smallest discrepancies in relation to the experimental tests. The results can be used to improve the SAC and efficiency of acoustic panels whose basic material is foamed polypropylene.

2

The Theory of Thermoelasticity with Double Porosity and Microtemperatures

Kansal Tarun

Computational Methods in Science and Technology

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2022

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Vol. 28, No. 3

87--107

EN

The aim of the paper is to establish the basic governing equations for anisotropic thermoelastic medium with double porosity and microtemperatures and to construct the fundamental solution of a system of equations in cases of steady, pseudo-, quasi-static oscillations and equilibrium.

3

Response of thermoelastic microbeam with double porosity structure due to pulsed laser heating

Kumar Rajneesh, Vohra Richa

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

76--85

EN

The present investigation is concerned with vibration phenomenon of a homogeneous, isotropic thermoelastic microbeam with double porosity (TDP) structure induced by pulsed laser heating, in the context of Lord-Shulman theory of thermoelasticity with one relaxation time. Laplace transform technique has been applied to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field, and temperature distribution. The resulting quantities are recovered in the physical domain by a numerical inversion technique. Variations of axial displacement, axial stress, lateral deflection, volume fraction field, and temperature distribution with axial distance are depicted graphically to show the effect of porosity and laser intensity parameter. Some particular cases are also deduced.

4

Forced vibrations of a thermoelastic double porous microbeam subjected to a moving load

Kumar Rajneesh, Vohra Richa

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 1

155--166

EN

The present paper deals with forced vibrations of a homogeneous, isotropic thermoelastic double porous microbeam subjected to moving load, in context of Lord-Shulman theory of thermoelasticity with one relaxation time. The Laplace transform has been applied to obtain expressions for the axial displacement, lateral deflection, volume fraction field and temperature distribution. A numerical inversion technique has been used to recover the resulting quantities in the physical domain. Effects of velocity and time parameters are shown graphically by plotting axial displacement, lateral deflection, volume fraction field and temperature distribution against distance. Some particular cases are also deduced.

5

Elastodynamic problem for an infinite body having a spherical cavity in the theory of thermoelasticity with double porosity

Kumar M. R., Vohra R.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

267--289

EN

The present investigation is concerned with homogeneous, isotropic infinite double porous thermoelastic body with a spherical cavity subjected to ramp type mechanical/thermal source in the context of Lord-Shulman theory of thermoelasticity [1] with one relaxation time. Laplace transform technique has been used to obtain the expressions for radial stress, hoop stress, equilibrated stresses and temperature distribution. A numerical inversion technique has been applied to recover the resulting quantities in the physical domain. The components of stress and temperature distribution are depicted graphically to show the effect of porosity and relaxation time parameters. Some particular cases are also deduced from the present investigation.

6

Effect of Hall current in thermoelastic materials with double porosity structure

Kumar R., Vohra R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 2

303--319

EN

The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity structure in the presence of Hall currents subjected to thermomechanical sources. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. A numerical simulation is prepared for these quantities. The effect of the Hartmann number is depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.

7

Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with a double porosity structure

Svanadze M.

Archives of Mechanics

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2017

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Vol. 69, nr 4-5

347--370

EN

The purpose of the present paper is to develop the classical potential method in the linear theory of thermoelasticity for materials with a double porosity structure based on the mechanics of materials with voids. The fundamental solution of the system of equations of steady vibrations is constructed explicitly by means of elementary functions and its basic properties are established. The Sommerfeld-Kupradze type radiation conditions are established. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method and the theory of singular integral equations.

8

Effect of Hall Current and Thermal Relaxation Time on Thermoelastic Materials with Double Porosity Structure by Using State Space Approach

Kumar R. M., Vohra R.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 4

425--449

EN

The present investigation is concerned with one dimensional problem in a homogeneous, isotropic thermoelastic medium with double porosity in the presence of Hall current subjected to thermomechanical sources. Thermoelastic theory with one relaxation time developed by Lord-Shulman [2] has been used to solve the problem. A state space approach has been applied to investigate the problem. As an application of the approach, normal force and thermal source have been taken to illustrate the utility of the approach. The expressions for the components of normal stress, equilibrated stress and the temperature change are obtained in the frequency domain and computed numerically. Numerical simulation is prepared for these quantities. The effect of Hall current and thermal relaxation time are depicted graphically on the resulting quantities for a specific model. Some particular cases of interest are also deduced from the present investigation.

9

Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity

Kumar R., Vohra R., Gorla M. G.

Archives of Mechanics

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2016

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Vol. 68, nr 4

263--284

EN

This paper is concerned with micropolar thermoelastic materials which have a double porosity structure. The system of the equations of the assumed model is based on the equations of motion, equilibrated stress equations of motion and heat conduction equation for material with double porosity. The explicit expressions for the fundamental solution of the system of equations in the case of steady vibrations are presented. The desired solutions are obtained by the use of elementary functions. Some basic properties are also established.

10

Plane waves and problems of steady vibrations in the theory of viscoelasticity for Kelvin-Voigt materials with double porosity

Svanadze M. M.

Archives of Mechanics

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2016

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Vol. 68, nr 6

441--458

EN

In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic properties of plane harmonic waves are established and the boundary value problems (BVPs) of steady vibrations are investigated. Indeed on the basis of this theory three longitudinal and two transverse plane harmonic waves propagate through a Kelvin–Voigt material with double porosity and these waves are attenuated. The basic properties of the singular integral operators and potentials (surface and volume) are presented. The uniqueness and existence theorems for regular (classical) solutions of the BVPs of steady vibrations are proved by using the potential method (boundary integral equations method) and the theory of singular integral equations.

11

Collapse settlement of dump soils revealed by studies on soil samples of modelled lithology and lump-size distribution

Woźniak H.

Geological Quarterly

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2015

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Vol. 59, No. 2

391--399

EN

The paper deals with the collapse settlement of dump soils i.e., made grounds composed of the overburden soils of mineral deposits, which were worked out with the open-pit method, transported and deposited as a dumped fill. The principal aim of the studies was the analysis of factors controlling the collapse settlement process, mostly the structural model of dump soil and external determinants: initial compaction, initial water content and history of its changes in time as well as the history of loading of studied soil before saturation. In order to reflect the natural structure of dump soils, experiments were carried out on samples of specially modelled lithology and structure. Hence, the samples represented three basic structural models of such soils: non-cohesive, cohesive and transitional, partly cohesive/partly non-cohesive. Attention was paid to diversified dynamics of collapse settlement, which results from two clearly different processes: rebuilding of soil structure and additional consolidation settlement. It was found that from the physical point of view the collapse settlement results from the release of elastic energy delivered to the sample by loading before inundation and accumulated at the contact surfaces of soil lumps.

12

Experimental evidence of the double-porosity effects in geomaterials

Ngoc T.D, Lewandowska J., Bertin H.

Acta Geophysica

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2014

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Vol. 62, no. 3

642--655

EN

Double-porosity is an important characteristic of microstructure in a large range of geomaterials. It designs porous media with connected fissures/fractures or aggregated soils. The origin of double-porosity can be natural or/and it can result from mechanical, chemical or biological damage. The presence of double-porosity can significantly affect the behaviour of geomaterials. In this paper we provide an experimental evidence of the double-porosity effects by performing laboratory experiments. Series of tracer dispersion experiments (in saturated and unsaturated steady-state water flow conditions) in a physical model of double-porosity geomaterial were carried out. For the comparative purposes, experiments of the same type were also performed in a singleporosity model medium. The results clearly showed that the doubleporosity microstructure leads to the non-Fickian behaviour of the tracer (early breakthrough and long tail) in both saturated and unsaturated cases.

13

Fundamental solutions in the full coupled theory of elasticity for solid with double porosity

Svanadze M., De Cicco S.

Archives of Mechanics

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2013

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Vol. 65, nr 5

367--390

EN

This paper discusses the full coupled linear theory of elasticity for solids with double porosity. The system of the governing equations is based on the equations of motion, conservation of fluid mass, the constitutive equations and Darcy’s law for material with double porosity. Four spatial cases of the dynamical equations are considered: equations of steady vibrations, equations in Laplace transform space, equations of quasi-static and equations of equilibrium. The fundamental solutions of the systems of these partial differential equations (PDEs) are constructed by means of elementary functions and finally, the basic properties of these solutions are established.

14

Groundwater flow in fractured aquifers in the Sevier Thrust Belt, Wasatch Mountains, Utah, USA

Matyjasik M., Yonkee W., Barnett D.

Biuletyn Państwowego Instytutu Geologicznego

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2002

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nr 404

85--106

PL

Szczelinowe poziomy wodonośne są coraz częściej eksploatowane w intensywnie rozwijających się zachodnich regionach USA, w tym Emigration Canyon w okolicach Salt Lake City w stanie Utah. Pod względem fizjograficznym obszar badań zlokalizowany jest w górach Wasatch (zachodnia część Gór Skalistych), pod względem strukturalnym – w obrębie pasa płaszczowinowego Idaho–Utah–Wyoming. Obszar badań charakteryzuje się serią uskoków i fałdów płaszczowinowych zbudowanych z miąższych serii skał osadowych, które zostały przesunięte na wschód lub południowy wschód podczas kredowych i wczesnotrzeciorzędowych ruchów górotwórczych. Utwory płaszczowinowe uległy dodatkowym deformacjom tektonicznym w postaci lokalnych spękań, drugorzędnych fałdów i uskoków. Typowe serie osadowe to wapienie, dolomity, piaskowce, mułowce i iłowce deponowane od karbonu do kredy. Lokalnie przykryte są zlepieńcami późnokredowymi. Skały te charakteryzują się stromym upadem. W iłowcach i mułowcach występują lokalne, równoległe do kierunku warstwowania spękania, w skałach gruboławicowych (wapienie, dolomity, piaskowce) występują szczeliny o zmiennej orientacji.Piaskowce i skały węglanowe stanowią warstwę wodonośną, charakteryzują się wysokimi wartościami współczynnika filtracji, natomiast iłowce i mułowce to utwory słabo przepuszczalne i stanowią zazwyczaj warstwy napinające zwierciadło wody. Pompowania badawcze wykazały, że utwory słabo przepuszczalne mogą przewodzić wodę, aczkolwiek proces ten jest nieporównywalnie wolny w stosunku do przepływu w warstwach wodonośnych. System przepływu wód podziemnych jest również silnie uzależniony od morfologii terenu.Na badanym obszarze występują dwa poziomy wodonośne o charakterze szczelinowym: dolnojurajska formacja Nugget oraz środkowojurajska formacja Twin Creek, rozdzielone serią słabo przepuszczalnych iłowców. Formacja Nugget składa się głównie z gruboławicowych piaskowców charakteryzujących się wyraźną porowatością szczelinową i porową, formacja Twin Creek – z cienkoławicowych wapieni i wapieni marglistych charakteryzujących się porowatością szczelinową. Oba poziomy wodonośne wykazują cechy syngenetycznej porowatości międzziarnowej i postgenetycznej porowatości szczelinowej, co ujawnia się w odmiennych wynikach próbnych pompowań, wahaniach zwierciadła wód podziemnych i wydajności źródeł. Formacja Twin Creek charakteryzuje się wyraźnie większymi wahaniami sezonowymi zwierciadła wód podziemnych, silniejszymi wpływami granic nieprzepuszczalnych, anizotropowością i mniejszą pojemnością warstwy wodonośnej. Wartości przewodnictwa wodnego zawierają się w przedziale 10–100 m[sup]2[/sup]/dobę i są zazwyczaj niższe w formacji Twin Creek; zależą od litologii i charakterystyki szczelin.

EN

Fractured bedrock aquifers are becoming increasingly utilized in rapidly developing parts of the western USA, including the Emigration Canyon near Salt Lake City, Utah. The emigration Canyon area is located physiographically in the Wasatch Mountains (western province of the Rocky Mountains), and structurally within the Idaho–Utah–Wyoming thrust belt. The study area is characterized by a series of thrust faults and associated folds that transported a thick section of sedimentary rocks eastward to southeastward during the Cretaceous to Early Tertiary Sevier Orogeny. Locally developed cleavage, minor folds, and minor fault and fracture networks produce additional internal deformation. Stratigraphically, sedimentary rocks in the study area include steeply dipping Pennsylvanian to Early Cretaceous limestone, dolostone, sandstone, mudstone and shale, locally capped with gently dipping Late Cretaceous conglomerate. Shale and mudstone intervals are characterized by smaller-scale, bed-parallel partings, while thicker-bedded limestone, dolostone and sandstone units typically have larger-scale fractures of variable orientation. Sandstones and carbonate intervals have generally higher hydraulic conductivity, whereas shale and mudstones are primary confining layers. The water flow system is also strongly affected by local topography. Two major fractured aquifers are the Lower Jurassic Nugget aquifer and the Middle Jurassic Twin Creek aquifer. The Nugget aquifer consists of thick-bedded sandstone with prominent primary porosity and secondary fracture porosity. The Twin Creek aquifer consists mostly of thin-bedded limestone and shaley limestone, with mostly secondary fracture porosity. The aquifers are separated by a shale interval. Based on results of long-term pumping tests, long-term monitoring of water table elevation and variability of spring discharges, the aquifers react independently and differently to fluid stresses, indicating variable effects of primary grain porosity and secondary fracture porosity. The Twin Creek aquifer is characterized by significantly greater seasonal variations of hydraulic head, stronger effects of impermeable boundaries and anisotropy, and lower storage. Typical values of transmissivity are 10–100 m[sup]2[/sup]/day, for the Twin Creek and Nugget aquifers, but vary with changes in lithology and fracture characteristics.

15

Theoretical and laboratory investigations on oil displacement from the rock matrix under capillary forces

Liszka K., Stopa J.

Archives of Mining Sciences

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2000

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Vol. 45, nr 4

543-553

EN

The paper contains two parts. The theoretical basis for the process of oil displacement through the water from the fractured porous medium, due to capillary forces, has been discussed in the part No. 1. The functional equation describing the relative water content increase in the fractured rock matrix, surrounded by the water layer, has also been introduced. This may reflect the actual reservoir conditions, if a fractured oil reservoir is flooded with water, at the moment when the rock matrix porous block has already been surrounded by the water forced in as a result if shifting of watering front in the fractures system. The impact of particular parameters of this process on its performance has also been determined. This equation is non-linear, and may be solved using numerical methods, in general case. The analytical solution may be arrived at when the constant value of the mass exchange coefficients has been assumed, as well as simple geometry, such as spherical geometry and process symmetry. Having assumed as above, the analytical solution has been arrived at and compared with a numerical solution. Taking into consideration the assumptions, the error committed has been slight, in order of few percent. The results of the theoretical contemplations have been compared with laboratory experiments' results, in the second part of the paper. The detailed description of performed research and its methodology have been given. The experiments have confirmed theoretical results.

PL

Zjawisko wnikania wody do przestrzeni porowych wypełnionych ropą pod wpływem sił kapilarnych jest istotnym czynnikiem wpływającym na efektywność nawadniania złóż ropy, zwłaszcza w przypadku, gdy skalą zbiornikową jest skała porowato-szczelinowata. Z punktu widzenia hydromechaniki złoże takie składa się z systemu spękań i szczelin oraz bloków ośrodka porowatego przepuszczalności wielokrotnie mniejszej od systemu szczelin. Bloki te noszą nazwę matrycy skalnej. Front wypierania ropy przez wodę przemieszcza się przede wszystkim (szybciej) w systemie szczelin, następnie zaś następuje proces wymiany masy pomiędzy szczelinami a porami matrycy skalnej. Według modeli znanych z literatury, np. Greenkorn (1983), M a r 1 e (1981), wypieranie ropy przez wodę następuje pod wpływem sił kapilarnych. W niedawno opublikowanej pracy Zhang X. i Morrow N. R. (1996) wykazali na podstawie prób laboratoryjnych, że przebieg procesu kapilarnego wypierania ropy przez wodę zależny jest od kształtu próbki, warunków brzegowych w czasie eksperymentu, stosunku lepkości cieczy, napięcia powierzchniowego na granicy ropa-woda oraz przepuszczalności względnych i przepuszczalności absolutnej. Interpretacja wyników laboratoryjnych jest jednak utrudniona, gdyż model matematyczny procesu jest silnie nieliniowy. W niniejszej pracy rozważono pojedynczy blok matrycy ośrodka porowatego o podwójnej porowatości i przepuszczalności. Blok ten nasycony jest cieczą węglowodorową (ropą lub naftą), zaś jego powierzchnia boczna znajduje się w kontakcie z wodą, która jest cieczą wypierającą. Przy założeniu, że ciśnienie kapilarne jest jedynym czynnikiem powodującym wypieranie ropy otrzymano równanie (22) opisujące względny przyrost nasycenia wodą bloku matrycy w czasie trwania procesu wypierania. W równaniu tym występuje współczynnik dyfuzji D określony wzorem (14). Określono wpływ poszczególnych parametrów tego procesu na jego przebieg. Równanie (22) jest nieliniowe i w ogólnym przypadku może być rozwiązane metodami numerycznymi. Rozwiązanie analityczne może być znalezione przy przyjęciu stałego współczynnika dyfuzji i prostych geometrii i symetrii procesu. Po przyjęciu takich założeń otrzymano rozwiązanie analityczne i porównano je z numerycznym. Jak widać z wykresu na rys. 3 różnica otrzymanych wyników jest niewielka. Wynik otrzymany na drodze rozważań teoretycznych porównano następnie z wynikami badań laboratoryjnych wymienionego zagadnienia. Podano szczegółową metodykę przeprowadzonych badań. Ich wyniki potwierdziły słuszność rozważań teoretycznych. Wyniki pomiarów oraz dopasowanie krzywych teoretycznych do danych pomiarowych pokazano na rys. 4 i 5.