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Search results for: NONLINEAR ANALYSIS
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Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force
PublicationIn this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the...
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Nonlinear Interaction of Magnetoacoustic Modes in a Quasi-Isentropic Plasma Flow
PublicationThe nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till . The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting....
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Parametric analysis of Istanbul's Ring Road viaduct for three levels of seismic load
PublicationThe paper presents a parametric analysis of the Istanbul's ring road viaduct that is currently under construction within the Northern Marmara Highway project. The structure, due to its location on seismic prone areas is exposed to seismic loads of different strengths and different return periods. The study is focused on concrete bridge supports that are design to work in nonlinear range. The parametric study, conducted in MATLAB...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Nonlinear increase in bubbles radii caused by sound in a bubbly liquid
PublicationThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is considered. The reasons for interaction are both nonlinearity and dispersion. In the field of intense sound, a decrease in the mixture density is predicted. That corresponds to the well-established growth of bubbles volumes due to rectified diffusion. The nonlinear interaction of modes as a reason for a bubble to grow due to sound, is discovered. The...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublicationThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Nonlinear fuzzy control of the dissolved oxygen in activated sludge processes
PublicationWastewater treatment plant is generally a complex, multivariable, time varying and nonlinear large scale industrial system. Moreover, interactions between the components are very strong. The dissolved oxygen tracking problem is one of the most complex and fundamental issues of biological processes. Air for the aerated tanks is supplied by aeration system (blowers, pipes, diffusers). It is a complex dynamic system. The new control...
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Certain family of analytical solutions of nonlinear von Neumann equations
PublicationIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Elastoplastic material law in 6-parameter nonlinear shell theory
PublicationWe develop the elastoplastic constitutive relations for nonlinear exact 6-parameter shell theory. A J2-type theory with strain hardening is formulated that takes into account asymmetric membrane strain measures. The incremental equations are solved using implicit Euler scheme with closest point projection algorithm. The presented test example shows the correctness of the proposed approach. Influence of micropolar material parameters...
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Control of nonlinear and linearized model of self-balancing electric motorcycle
PublicationSelf-Balancing Electric Motorcycle (SBEM) is a dynamic and nonlinear electro-mechanical system. In this paper, the process of mathematical modelling and line-arization of SBEM is presented. The model of the control system in Matlab envi-ronment is implemented. The control system using the PID controller is designed. The operation of particular structures of the PID controller on the simulation model is compared. Due to simulation...
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Laminated plates and shells - first ply failure analysis within 6-parameter shell theory
PublicationThis work describes Tsai-Wu and Hashin criteria modifications, dictated by nonlinear 6-parameter shell theory with asymmetric strain measures and drilling rotation. The material law is based on standard orthotropic elastic constants for a non-polar continuum, under plane state of stress. First ply failure loads of cylindrical panel subjected to pressure and flat compressed plate are estimated by means of Finite Element Analysis....
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Numerical analysis on axial capacity of steel built-up battened columns
PublicationThis paper deals with the numerical analysis aimed at study the bearing capacity of pinended steel built-up columns under axial compression. Finite element (FE) models were performed for the columns presented in the literature. The main problem discussed in the article is the shape and magnitude of geometric imperfections introduced into the numerical FE model, necessary to obtain the load capacity consistent with the experimental...
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Ship Dynamic Positioning Based on Nonlinear Model Predictive Control
PublicationThe presented work explores the simulation test results of using nonlinear model predictive control algorithm for ship dynamic positioning. In the optimization task, a goal function with a penalty was proposed with a variable prediction step. The results of the proposed control algorithm were compared with backstepping and PID. The effect of estimation accuracy on the control quality with the implemented algorithms was investigated....
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Novel analysis methods of dynamic properties for vehicle pantographs
PublicationTransmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should...
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Nonlinear control systems modelling: global vs. local
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Structural pounding models with Hertz spring and nonlinear damper
PublicationW artykule przedstawiono porównanie możliwości wykorzystania dwóch modeli zderzeń: nieliniowego modelu lepkosprężystego i modelu Hertz'a z dodatkowym tłumieniem. Efektywność każdego z modeli zbadano porównując wyniki analiz numerycznych z wynikami badań eksperymentalnych. Wyniki pracy pokazują, iż zastosowanie nieliniowego modelu lepkosprężystego prowadzi do mniejszych błędów w przebiegach czasowych siły zderzenia oraz do mniejszych...
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Numerical methods for systems of nonlinear differential functional equations
PublicationPraca dotyczy zagadnień początkowo brzegowych dla nieliniowych układów różniczkowo funkcyjnych. Rozważana jest aproksymacja rozwiązań rozważanego problemu różniczkowo funkcyjnego przez rozwiązania odpowiedniego problemu różnicowego. W pracy analizowana jest zbieżność prezentowanych metod. Dowód zbieżności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perron'a dla danych operatorów.
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Composite shells in 6-field nonlinear shell theory
PublicationW pracy przedstawiono równanie konstytutywne uwzględniające wielowarstwowość materiału powłoki. Równania wyprowadzono bazując na podejściu Equivalent Single Layer
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CdS Nanocrystallines: Synthesis, Structure and Nonlinear Optical Properties
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Direct measurement of nonlinear properties of bipartite quantum states
PublicationNieliniowe własności stanów kwantowych, takie jak entropia, splątania, określają ilość ważnych fizycznych źródeł i są często używane w informatyce kwantowej. Na ogół są one obliczane z pełnego opisu stanu kwantowego, pomimo tego, że zależą od niewielkiej ilości parametrów opisujących dany stan. Wyciągamy nielokalną i nieliniową wielkość, mianowicie entropię Renyi, z lokalnych pomiarów dwóch par fotonów splątanych polaryzacyjnie.
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Quasilinearization methods for nonlinear parabolic equations with functional dependence
PublicationRozważamy problem Cauchy`ego dla nieliniowych równań parabolicznych z zależnością funkcyjną. Dowodzimy twierdzeń o szybkiej zbieżności ciągów kolejnych przybliżeń określonych w metodzie quasilinearyzacji w dwóch przypadkach: (i) argumentem funkcyjnym jest funkcja niewiadoma, (ii) zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej.
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Tollmien- Shlichting and sound waves interaction: nonlinear resonances.
PublicationRozpatruje się oddziaływanie różnych typów modów hydrodynamicznych w warstwie lepkiej. Stwierdzono możliwość istnienia oddziaływania rezonansowego.Dokładne równania ewolucyjne kierujące dynamiką warstwy lepkiej zostały wypisane.
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Nonlinear waves in optical waveguides and soliton theory applications
PublicationRównania teorii solitonów zastosowano do propagacji impulsów światła w falo-wodach dielektrycznych.Wyprowadzono i zbadano rozwiazania równań oddziaływa-nia (z uwzględnieniem tłumienia) trzech fal Maxwella-Blocha.
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Towards homoscedastic nonlinear cointegration for structural health monitoring
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Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines
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Nonlinear and fluctuation phenomena as reliability predictors for foil capacitors
PublicationW trakcie procesu produkcyjnego kondensatorów przeciwzakłóceniowych wymagane jest przeprowadzenie testów jakości i trwałości. Do tego celu bardzo przydatna byłaby procedura szybkich testów nieniszczących. Rozwiązaniem problemu może być implementacja w systemie realizującym testy produkcyjne dodatkowych zadań związanych z bezpośrednimi pomiarami nieliniowości i/lub fluktuacji. Wybór wskaźnika trzeciej harmonicznej (THI), parametru...
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Numerical modeling of the nonlinear wave propagation in a bubble layer
PublicationRozważano zagadnienie propagacji fali wewnątrz warstwy z pęcherzykami. Omówiono model matematyczny, przedstawiono przykładowe wyniki badań teoretycznych. Analizowano zmiany ciśnienia wewnątrz warstwy, falę odbitą i bieżącą w ośrodku otaczającym, badano gęstość widmową mocy. Badania teoretyczne przeprowadzono dla różnych grubości warstwy, koncentracji pęcherzyków i wartości parametrów fali padającej.
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Laminated shells in nonlinear six-parameter shell theory
PublicationW pracy proponowany jest związek konstytutywny dla powłoki warstwowej w ramach 6-paramatrowej nieliniowej teorii powłok z miarami odkształceń jak w ośrodku Cosseratów. Zaletą podejścia jest bezpośrednie zastosowanie inżynierskich stałych materiałowych.
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Numerical investigations of the nonlinear waves generation in a bubble layer
PublicationRozważano zagadnienie propagacji fal różnych częstotliwości wewnątrz warstwy z pęcherzykami. Przedstawiono model matematyczny zjawiska oraz wyniki badań teoretycznych. Badano zmiany widma fali bieżącej i odbitej jak również zmiany amplitud wybranych harmonicznych ciśnienia tych fal w funkcji grubości warstwy i koncentracji pęcherzyków.
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Theoretical studies of nonlinear generation efficiency in a bubble layer
PublicationCelem pracy jest teoretyczna analiza propagacji fal o dużym natężeniu w warstwie z pęcherzykami. Przedstawiono model matematyczny zjawiska w tym omówiono problem wyznaczania prędkości fazowej, współczynnika tłumienia i częstotliwości rezonansowej pęcherzyków. Badano zmiany amplitud pierwszej i drugiej harmonicznej ciśnienia fali odbitej i bieżącej w funkcji grubości warstwy oraz względnej koncentracji pęcherzyków. Rozważano pęcherzyki...
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On coertia and inertia in aspects of Natanson’s nonlinear extended thermodynamics
PublicationIn this article, the previously underrepresented contributions of Natanson to the field of thermodynamics have been presented. In order to identify a source of irreversibility at Nature, Natanson introduced the concept of Coertia, which is similar to inertia. Natanson’s Coertia is a fundamental property of space that is responsible for every irreversible phenomena in matter, as well as in the electromagnetic and gravitational fields....
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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublicationWe discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only...
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In-plane shear nonlinearity in failure behavior of angle-ply laminated shells
PublicationThe paper concerns the progressive failure analysis of laminates with the in-plane shear nonlinearity accounted for.The nonlinear shear response of the layer is described by the constitutive relation treating the stresses as a function of strains. Thus it can be easily incorporated into the displacement-based FEM codes. The brittle failure mechanisms of the fibers and the matrix of the layer are recognized with the use of the Hashin...
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On the Nonlinear Effects of Magnetoacoustic Perturbations in Optically Thin Quasi-Isentropic Plasmas
PublicationNonlinear effects of planar magnetosound perturbations in a plasma are discussed. Plasma is non-adiabatic due to optically thin radiation and external heating. For these reasons, thermal instability of a plasma may appear which makes it acoustically active. The plasma is assumed to be initially homogeneous ideal gas with infinite electrical conductivity permeated by a straight magnetic field which is orthogonal to the trajectories...
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Dynamic Analysis of the Turnout Diverging Track for HSR with Variable Curvature Sections
PublicationThe paper presents an analytical method of identifying the curvature of the turnout diverging track consisting of sections of varying curvature. Both linear and nonlinear (polynomial) curvatures of the turnout diverging track are identified and evaluated in the paper. The presented method is a universal one, it enables to assume curvature values at the beginning and end point of the geometrical layout of the turnout. The results...
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Sensitivity analysis of simple random beam models by means of Monte Carlo Methods using Variance Reductions Techniques
PublicationA probabilistic sensitivity analysis of two nonlinear bar structures is presented. The analysis is carried out on the basis of the Monte Carlo method. The imperfections of the structures and the applied loads are adapted as random variables. Based on all of the generated input variables, an output response of the system is sought. Afterwards, a coefficient responsible for the structure failure is calculated and the limit state...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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Examination of selected failure criteria with asymmetric shear stresses in the collapse analysis of laminated shells
PublicationThe paper is concerned with failure analysis of composite shells performed with the usage of the nonlinear 6‐parameter shell theory with drilling rotation degree of freedom. This special theory embodies naturally unlim-ited translations and rotations and is suitable for analysis of irregular shells for instance with various, partic-ularly orthogonal, intersections. The presence of the drilling rotation is inherently accompanied...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Searching of the buried objects into the sea bottom by means of nonlinear acouctic methods
PublicationThe main goal of this paper is to introduce the methodology of preparing the area for investigations that will be carried out at the sea. As the first step there is recognition of the basic method both in the theory as well as experimental investigation. There were taken into account the nonlinear methods. These ones are very promising methods that have very interesting features, very convenient for examinations of the seabed structure....
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Random field modelling of mechanical behaviour of corroded thin steel plate specimens
PublicationThe objective of this work is to explore the possibility of corrosion degradation modelling of thin steel plate specimens with the use of random field approach. The mechanical properties are obtained via the nonlinear Finite Element Analysis with the use of an explicit dynamic solver. The fully nonlinear material model is adopted to obtain the proper stress-strain response. Sensitivity analysis considering the main statistical...
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Analysis of ultimate compressive strength of cracked plates with the use of DOE techniques
PublicationThe objective of this work is to investigate the structural compressive response of plates with locked cracks accounting for all relevant factors and correlation between them. The nonlinear FE model considering both geometric and material nonlinearities is employed herein, and the FE model of the structural response of intact plates is validated with the available experimental data. In the common studies, based on One Factor at...
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Nonlinear Control of a Doubly Fed Generator Supplied by a Current Source Inverter
PublicationNowadays, wind turbines based on a doubly fed induction generator (DFIG) are a commonly used solution in the wind industry. The standard converter topology used in these systems is the voltage source inverter (VSI). The use of reverse-blocking insulated gate bipolar transistor (RB-IGBT) in the current source inverter topology (CSI), which is an alternative topology, opens new possibilities of control methods. This paper presents...
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On the Nonlinear Effects of Magnetoacoustic Perturbations in a Perfectly Conducting Viscous and Thermoconducting Gas
PublicationNonlinear effects of planar and quasi-planar magnetosound perturbations are discussed. The plasma is as- sumed to be a Newtonian thermoconducting gas with infinite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. Generation of the non-wave modes (magnetoacoustic heating and streaming) in the field of periodic and aperiodic magnetoacoustic perturbations is discussed. The results...
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Investigations of the optical activity of nonlinear crystals by means of dual-wavelength polarimeter
PublicationA dual-wavelength method in high accuracy polarimetry has been successfully tested and applied to measure optical activity (OA) of nonlinear crystals. In proposed polarimetric scheme two neighboring semiconductor laser wavelengths (635 and 650 nm) are used, which increases number of parameters measured simultaneously and improves the data processing. By neglecting dispersion of eigen wave ellipticity in crystals, more efficient...
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Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation
PublicationThe nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic...