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EN
This article presents a modified incremental model describing pre-failure deformations of granular soils under classical triaxial conditions. The original shape of equations has been proposed by Sawicki and Świdziński [40, 41]. A new form of equations that are consistent with the proposed definitions of deviatoric loading and unloading is suggested. Triaxial tests necessary for calibrating the proposed model have been performed. The modified model is used to simulate the deformations and stability of sand for every pre-failure loading path and makes it possible to describe the behaviour of granular soil under both drained and undrained conditions. A comparison of experimental and numerical results is presented. All investigations were performed in a classical tri-axial apparatus.
PL
W artykule przedstawiono uwagi do przepisów, którym powinny odpowiadać hydrotechniczne budowle piętrzące w nawiązaniu do zasad podziału budowli piętrzących na klasy, zgodne z innowacyjną środowiskową klasyfikacją hydrotechnicznych budowli piętrzących wodę opartą na kryterium prędkości krytycznej. Klasyfikacja środowiskowa ma na celu minimalizację wpływu procesów biologicznych, erozji, sedymentacji oraz zatorów lodowych na środowisko w rejonie stopni wodnych, dla zapewnienia bezpiecznych warunków przepływu wód przez zbiornik oraz budowle przelewowo-upustowe stopnia wodnego podczas użytkowania. Podano zasady utrzymywania piętrzenia wody gwarantujące sterowanie procesami ruchu rumowiska. Proponowana klasyfikacja ma na celu zwrócenie uwagi na fakt istnienia ścisłej zależności między parametrami korytowymi a zasadami projektowania budowli piętrzących, które muszą być uwzględniane podczas projektowania i użytkowania. Podano ogólne i szczegółowe propozycje do opracowania nowych przepisów, którym powinny odpowiadać hydrotechniczne budowle piętrzące wodę.
EN
We deal with the investigation of L2-stability of the trivial solution to the system of difference equations with coefficients depending on a semi-Markov chain. In our considerations, random transformations of solutions are assumed. Necessary and sufficient conditions for L2-stability of the trivial solution to such systems are obtained. A method is proposed for constructing Lyapunov functions and the conditions for its existence are justified. The dynamic system and methods discussed in the paper are very well suited for use as models for protecting information in cyberspace.
PL
Opisano wyniki własnej metody badania niestabilności stanów wody oraz wielkości przepływów, wprowadzając innowacyjną klasyfikację budowli piętrzących wodę. Podział budowli piętrzących na klasy oparto na kryterium prędkości krytycznej, mając na względzie minimalizację wpływu procesów biologicznych, erozji, sedymentacji oraz zatorów lodowych na środowisko w rejonie stopni wodnych, w celu zapewnienia przepustowości budowli przelewowo-upustowych stopnia wodnego podczas użytkowania.
EN
The results of author’s method for evaluation of water levels (and discharges) instability as the function of time are described and new environmental classification of water headworks is proposed, based on design criteria with application “instability factors” for determination water levels (and discharges). The classification is based on the assumption, that local channel processes and risks (biological, erosion, sedimentation, ice control and others) within the environment of hydraulic works will be eliminated or bed impacts limited. The main aim of applied classification is to protect the structure from aggradations and deterioration.
EN
This study investigates the effects of inertia on the hydroelastic instability of a pressure- -driven Herschel-Bulkley fluid passing through a two-dimensional channel lined with a polymeric coating. The no-viscous hyperelastic polymeric coating is assumed to follow the two-constant Mooney-Rivlin model. In this work, analytical basic solutions are determined for both the polymeric gel and the fluid at very low Reynolds numbers. Next, the basic solutions are subjected to infinitesimally-small, normal-mode perturbations. After eliminating the nonlinear terms, two 4-th order differential equations are obtained. The equations with appropriate boundary conditions are then numerically solved using the shooting method. The results of the solution show that the inertia terms in the perturbed equations destabilize the pressure-driven Herschel-Bulkley fluid flow. The investigation reveals that the elastic parameter has a stabilizing effect on the flow. Also, based on the obtained results, the yield stress, depending on the power-law index, has a stabilizing or destabilizing effect on the flow. Since in this work the inertia terms are included in the pertinent governing equations, therefore, the results of this study are much more realistic and reliable than previous works in which inertia terms were absent. In addition, unlike the previous works, the present study considers both the shear-thinning and shear-thickening types of fluids. Hence, the results of this work embrace all the fluids which obey the Herschel-Bulkley model.
EN
In the article, basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reactiondiffusion systems are investigated. Such solutions, called autosolitons, arise in a stability region of the system and can coexist with the spatially homogeneous states. By a linear stability analysis and computer simulation, it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model. A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented. The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.
PL
W artykule poruszony został problem gruntów antropogenicznych pochodzących z termicznego przetwarzania odpadów pod kątem ich wykorzystania w budownictwie drogowym. W ramach prowadzonych badań określono podstawowe własności fizyczne oraz własności mechaniczne przedstawionych gruntów antropogenicznych. Norma PN-S-02205:1998 analizowany materiał gruntowy (grupa - popioły lotne i mieszaniny popiołowo-żużlowe) kwalifikuje jako przydatne do wbudowania w dolne warstwy nasypu poniżej strefy przemarzania, pod warunkiem, że zalegają one w miejscach suchych lub są izolowane od wody. Kolejnym krokiem było modelowanie w programie MIDAS GTS NX przykładowego nasypu drogowego znajdującego się w stanie niestateczności. Otrzymane wyniki pokazują, że własności fizyczno-wytrzymałościowe badanych gruntów antropogenicznych dają możliwości ich wykorzystania przy zabezpieczaniu niestabilnych nasypów drogowych przy prostych warunkach gruntowo-wodnych. Należy pamiętać, że analizowane grunty antropogeniczne powinny zostać poddane również rygorystycznym badaniom ich składu chemicznego. Uzyskane wyniki pozwolą określić możliwości ich wykorzystania w budownictwie drogowym pod kątem ich właściwości wytrzymałościowych.
EN
In the article the problem of anthropogenic soils from thermal treatment of waste in terms of their use in road construction is discussed. As part of the research, the basic physical and mechanical properties of the anthropogenic soils were determined. PN-S-02205: 1998, the analyzed ground material (fly ash and slag mixture) qualifies as useful for embedding into the lower layers of the embankment below the freezing zone, provided they are in dry places or are insulated from water. The next step was to model an exemplary, unstable road embankment in the MIDAS GTS NX. The results point out that the strength and physical properties of the anthropogenic soils may be used to secure unstable road embankments with simple soil and water conditions. It should be remembered that analysed anthropogenic soils should also be subjected to rigorous testing for their chemical composition. The obtained results will allow us to determine the possibilities of their use in road construction in terms of their strength properties.
EN
This study examined the mechanical properties of a para-aramid filament according to the processing conditions of air-jet textured yarns (ATY). The specimens were prepared by changing the yarn speed, over feed ratio, air pressure, and heater temperature, which are important processing factors in the ATY process. The basic physical properties of the ATY, such as denier, tenacity, breaking strain, and initial modulus, were measured and their thermal shrinkage, such as dry and wet shrinkage, were measured to determine the thermal stability of the aramid ATY. In addition, the instability of para-aramid ATY were measured and assessed with the loop formation of ATY, according to the ATY process parameters. An examination of the effects of process parameters on the physical properties of aramid ATY revealed the core overfeed and air pressure to be the main factors. A high core overfeed and air pressure make the aramid ATY crimpy in the yarn core and entangle the fluffy loops on the yarn surface, resulting in an increase in the yarn linear density and breaking strain as well as a decrease in the tenacity and initial modulus. In contrast, these yarn physical properties were unaffected by the yarn speed, heater temperature, and wetting treatment. In addition, the dry and wet thermal shrinkage were unaffected by the process parameters of ATY. On the other hand, the instability decreased with increasing core overfeed and heater temperature and increased with increasing air pressure. These results showed that a high core overfeed makes the aramid ATY crimpy with an entangled yarn structure, and high air pressure helps provide small loops on the yarn surface. Finally, a high heater temperature makes the crimpy ATY structure more stable due to the strong heat set, which results in low instability.
EN
The article deals with the issue of nonlinearity and instability of the architecture language which is manifested in modern architectural trends: architecture as performance, show, attraction. The research apparatus of the article includes elements of the systematic approach, the theory of architectural composition, methods and means of a synergetic approach in architecture.
PL
Adnotacja. W artykule rozpatrzona została kwestia nieliniowość i niestabilności architektonicznego języka, przejawiającego się we współczesnych architektonicznych tendencjach – architektura jako działanie, show, atrakcja. Naukowo-badawczy aparat artykułu zawiera elementy podejścia systemowego, teorii architektonicznej kompozycji, metodyki i środków synergetycznego podejścia w architekturze.
10
EN
We study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network (GJN for short), assuming its stability. For the two-station case, this problem has recently been solved in the logarithmic sense for the marginal stationary distributions under the setting that arrival processes and service times are of phase-type. In this paper, we study similar tail asymptotic problems on the stationary distribution, but problems and assumptions are different. First, the asymptotics are studied not only for the marginal distribution but also the stationary probabilities of state sets of small volumes. Second, the interarrival and service times are generally distributed and light tailed, but of phase-type in some cases. Third, we also study the case that there are more than two stations, although the asymptotic results are less complete. For them, we develop a martingale method, which has been recently applied to a single queue with many servers by the author.
EN
In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams is investigated based on the Timoshenko beam theory. The material properties of the beam are considered to change gradually through thickness of the beam by a simple power law. By using the principle of minimum total potential energy, governing equations of the beam are derived. Stability behavior of the beam is predicted by solving the governing equations of the FGP beam. The results show that the homogeneity of boundary conditions plays a critical role in the stability of the FGP beam. While non-homogeneous boundary conditions lead to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the beam is obtained for the beams that have unstable behavior. Finally, the effects of various parameters on the buckling load of the unstable beam, such as power law index, temperature, applied voltage and aspect ratio are investigated, and the results are compared with the Euler-Bernoulli beam theory.
EN
A two-dimensional incompressible flow model is presented to study the occurrence of rotating stall in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. The linearized 2D Euler equations for an incompressible flow in a fixed frame of the coordinate system are considered. After discretization by a spectral collocation method based on Chebyshev-Gauss-Lobatto points, the generalized eigenvalue problem is solved through the QZ algorithm. The compressor stability is judged by the imaginary part of the eigenvalue obtained. Based on the 2D stability analysis, the influence of inflow angle, radius ratio and wave number are studied. The results from the present stability analysis are compared with some experimental measurement and Shen’s model. It is showed that diffuser instability increases rapidly and the stall rotational speed decreases quickly with an increase in the diffuser radius ratio. The largest critical inflow angle can be obtained when the wave number is around 3 ∼ 5 for the radius ratio between 1.5 to 2.2. It is also verified that the stability model proposed in this paper agrees well with experimental data and has the capability to predict the onset of rotating stall, especially for wide diffusers.
EN
In this paper the results of numerical studies on natural vibration frequency and stability of a slender supporting system loaded by external force directed towards a positive pole are presented. In the investigated structure the failure in the form of crack is present. The boundary problem is formulated on the basis of the principle of minimum action – Hamilton’s principle. The results in the non-dimensional form are plotted as the characteristic curves in the external load – natural vibration frequency plane as well as the maximum loading capacity is discussed.
PL
W artykule omówiono działania podjęte przez Laboratorium Masy Głównego Urzędu Miar w okresie od 1997 r. do 2015 r. w celu weryfikacji zagrożenia związanego z niestabilnością – dryfem – materialnych wzorców odniesienia wykorzystywanych w procesie przekazywania jednostki miary masy.
EN
This paper discusses the action taken by the Mass Laboratory of the Central Office of Measures in the period 1997–2015 to verify the risks of the instability (drift) of the stainless steel reference mass standards used in the mass unit dissemination process.
EN
This article discusses the problem of the instability of road embankments. Two types of landslides located in various geotechnical conditions were analysed. The first case is where the stability of the road embankment itself is lost, in which the soil layers under the embankment have no influence. In the other case, the instability of the embankment is connected with landslides of the soil on which a given embankment is situated (slope stability loss). The authors proposed original solutions which were later on verified by MIDAS GTS NX®. The conducted studies show that the proposed protection strategies for both slopes are effective, thus yielding a high coefficient of general stability (FoS).
PL
W artykule został poruszony problem niestateczności nasypów w drogownictwie. Analizie zostały poddane dwa rodzaje osuwisk drogowych zlokalizowanych w różnych warunkach geotechnicznych. W pierwszym przypadku doszło do utraty stateczności samego nasypu drogowego, na którą wpływu nie mają warstwy gruntu zalegające pod nasypem. W drugim przypadku niestateczność nasypu komunikacyjnego związana jest z osuwaniem się gruntów, na którym przedmiotowy nasyp się znajduje (utrata stateczności zbocza). Zostały zaproponowane autorskie rozwiązania, które następnie zweryfikowano w programie MIDAS GTS NX®. Przeprowadzone badania wykazały, że projektowane zabezpieczenia obu skarp są poprawne, co przekłada się na wysokie wartości współczynników stateczności ogólnej (FoS).
EN
The paper analyses the complementarity of electrical energy field, using a multiannual, monthly and daily approach, for a small hydroelectric power station, wind turbine and photovoltaic plant. The results obtained point to the existence of a strong negative correlation between the solar industry and the wind industry from the perspective of monthly changes. The energy yield generated by a hydroelectric power station is significantly correlated with the generation yield of wind sources. When considering a multiannual perspective, the existence of a correlation between small-scale water and solar power plants was identified. The conclusions of this study may serve as vital rationales when planning the contribution of these sources to the Polish National Power System (KSE).
PL
W pracy dokonano analizy komplementarności uzysku energii elektrycznej w ujęciu wieloletnim, miesięcznym oraz dobowym dla małej elektrowni wodnej, turbiny wiatrowej oraz farmy fotowoltaicznej. Uzyskane wyniki pozwalają stwierdzić istnienie silnej ujemnej korelacji pomiędzy energetyką słoneczną oraz wiatrową z perspektywy miesięcznych zmian. Uzysk energii z elektrowni wodnej jest istotnie skorelowany z generacją źródeł wiatrowych. Dla wieloletniego horyzontu czasowego wskazano na istnienie korelacji pomiędzy małą energetyką wodną a słoneczną. Płynące z opracowania wnioski mogą być istotnymi przesłankami na etapie planowania udziału tych źródeł w Krajowym Systemie Elektroenergetycznym.
17
Content available remote Modal analysis of thermoelastic behavior of friction clutches and brakes
EN
Thermoelastic contact problem in sliding systems such as friction clutches and brakes is discussed in the paper. Frictional heat induces thermal deformations of clutch components. Deformations modify contact pressure distribution at sliding interfaces, which in turn defines distribution of frictional heat. This fully coupled thermoelastic contact problem is known to exhibit instability if the sliding speed is sufficiently high. Practical manifestation of instability is development of hot spots at contact interfaces. In the paper a modal approach to this problem is presented. The formulation leads to an eigenvalue problem with eigenmodes representing patterns of temperature distribution and real parts of eigenvalues indicating stability/instability of the mode.
PL
W artykule prezentowane jest zagadnienie kontaktu termosprężystego w układach z tarciem ślizgowym takich jak sprzęgła i hamulce cierne. Ciepło wydzielane wskutek tarcia powoduje deformacje termiczne elementów sprzęgła. Deformacje te modyfikują rozkład nacisków kontaktowych na powierchniach ciernych, które z kolei określają rozkład ciepła generowanego tarciem. To w pełni sprzężone zagadnienie kontaktu termosprężystego cechuje się niestatecznością przy dostatecznie dużych prędkościach poślizgu. Praktycznym skutkiem niestateczności są gorące plamy tworzące się na powierzchniach kontaktu. W artykule zaprezentowana jest analiza modalna tego problemu. Sformułowanie to prowadzi do zaganienia własnego, w którym postacie własne reprezentują rozkłady temperatur a części rzeczywiste wartości własnych wskazują czy postać jest stateczna.
EN
In this publication the nonlinear slender cantilever column composed of two rods in which the cracks are present is investigated. The cracks are simulated by means of rotational springs with linear characteristic. Additionally the external compressive load is located at the free end to the structure. In order to predict the static behaviour of the column the boundary problem is being formulated by means of the principle of total potential energy. The results of numerical simulations are concern on influence of the locations of cracks on loading capacity. On the basis of the analysis of the results the most dangerous (lowest loading capacity) regions are found.
EN
A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.
20
Content available remote Instability in multi delay functional differential equations of fourth order
EN
A vector functional differential equation of the fourth order with multiple deviating arguments is considered. New sufficient conditions are established to guarantee the instability of the zero solution of the equation to be considered. We give an example to illustrate the subject.
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