Wyniki wyszukiwania - Biblioteka Nauki

1

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

100%

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

Archives of Mechanics

|

2016

|

tom 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.

2

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

88%

Woźniak H.

|

2015

|

tom 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.

3

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

88%

Svanadze M. M.

|

tom 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.

4

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

75%

Svanadze M.

|

tom 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.

5

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

63%

Kumar R. , Vohra R.

Mechanics and Mechanical Engineering

|

2019

|

tom 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.

6

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

63%

Liszka K. , Stopa J.

|

tom 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.