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Search results for: NONLINEAR MODELLING
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Nonlinear modelling of eathquake induced pounding.
PublicationZaprezentowano nieliniowy model lepkosprężysty siły zderzenia w czasie kontaktu między konstrukcjami podczas trzęsień ziemi. Efektywność modelu sprawdzono przez porównanie wyników analizy numerycznej z wynikami eksperymentalnymi. Wyniki badań pokazują, iż rozważany model najdokładniej symuluje siłę zderzenia w czasie.
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Nonlinear Analysis-Modelling and Control
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A nonlinear approach to modelling gas bubble deformation.
PublicationPrzedstawiono model wyjaśniający wpływ deformacji pęcherzyka na występowanie zjawiska chaosu podczas generowania pęcherzyków gazowych z pojedynczej dyszy zanurzonej w cieczy.
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Nonlinear control systems modelling: global vs. local
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Adaptive fuzzy modelling and control for discrete-time nonlinear uncertain systems
PublicationReferat przedstawia metodę adaptacyjnego rozmytego modelowania i sterowania dla nieliniowego systemu dyskretnego z niepewnością. Proponowana metoda adaptacyjna składa się z dwóch części: rozmyte modelowanie on-line z zastosowaniem systemu Takagi - Sugeno (T-S) oraz sterowanie adaptacyjne z modelem referencyjnym. Model rozmyty T-S posiada samoorganizującą się strukturę, tzn. reguły rozmyte mogą być dodawane, zamieniane lub usuwane...
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Modelling water flow in unsaturated porous media: Accounting for nonlinear permeability and material heterogeneity
PublicationW pracy przedstawiono problematykę matematycznego modelowania przepływów w nienasyconych ośrodkach porowatych, ze szczególnym uwzględnieniem dwóch aspektów. Pierwszym z nich jest obliczanie średniego współczynnika przewodności hydraulicznej między węzłami siatki w numerycznym rozwiązaniu równania przepływu nienasyconego. Drugim zagadnieniem jest wpływ lokalnej zmienności parametrów ośrodka porowatego (współczynnika przewodności...
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Volterra series usefulness in modelling of the time-domain cross-talk phenomena in coupled microstrip lines with nonlinear termination
PublicationW pracy przedyskutowano możliwość wykorzystania szeregów Volterry do analizy zjawiska przesłuchu w sprzężonych liniach mikropaskowych z nieliniowym obciążeniem. Apracowano algorytm metody, zaś uzyskane wyniki numeryczne zweryfikowano poprzez porównania z wynikami badań eksperymentalnych linii obciążonych w torze transmisyjnym diodą Schottky'ego.
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Analytical method of modelling the geometric system of communication route
PublicationThe paper presents a new analytical approach to modelling the curvature of a communication route by making use of differential equations. The method makes it possible to identify both linear and nonlinear curvature. It enables us to join curves of the same or opposite signs of curvature. Solutions of problems for linear change of curvature and selected variants of nonlinear curvature in polynomial and trigonometric form were analyzed....
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Modelling of joining route segments of differential curvature
PublicationThe paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph...
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Modelling of Geared Multi-Rotor System
PublicationIn the paper the method of modelling a speed-varying geared rotor system is presented. The proposed approach enables us to obtain an accurate low-order lumped parameter representation of the investigated system. The final model consists of reduced modal models of an undamped beam/torsional shaft system as well as a spatially lumped model of other linear and nonlinear phenomena including gear mesh interaction.
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The application of nonlinear curvature sections in the turnout diverging track
PublicationThe paper presents the analytical method of modelling the diverging track of railway turnout with nonlinear curvature sections. These sections were used for smoothing the graph of curvature in the extreme areas of turnout. The problem of the curvature distribution was identified with the use of differential equations. The resulting solutions are of universal nature for example the ability of assuming any values of curvature at...
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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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Nonlinear Model of Synchronous Generator for Autonomous Electrical Power Systems Analysis
PublicationThis paper presents the nonlinear lookup table model for synchronous generator (SG) analysis. The saturation effects of the SG magnetic circuit have been considered. The saturated characteristic of the SG magnetic circuit are based on the open circuit saturation curve for magnetizing inductances. The model has been implemented into the Synopsys/Saber software using the MAST modelling language. To implement the no-load voltage characteristic...
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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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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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Software tool for modelling of mechatronic systems with elastic continua
PublicationThe paper presents a systematic computational package for modelling and analysis of complex systems composed of multiple lumped and distributed parameter subsystems. The constructed computer program enables the frequency domain analysis of a class of linear systems and to obtain reduced order model in the form of bond graph. Obtained modal bond graph can be directly exported into 20-Sim package to further processing including nonlinear...
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A Review of Hyperelastic Constitutive Models for Dielectric Elastomers
PublicationDielectric elastomers are smart materials that are essential components in soft systems and structures. The core element of a dielectric elastomer is soft matter, which is mainly rubber-like and elastomeric. These soft materials show a nonlinear behaviour and have a nonlinear strain-stress curve. The best candidates for modelling the nonlinear behaviour of such materials are hyperelastic strain energy functions. Hyperelastic functions...
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Modelling of Nuclear Power Plant Steam Turbine
PublicationThe paper describes the approach to a Nuclear Power Plant steam turbine modelling which would enable on-line optimal process control (model based) and diagnosis over wide range of operating conditions caused by changing power demand. Presented model is static, multivariable and nonlinear. Such model enables analyzing the heat cogeneration aspects. Developed model is validated and verified by using archive data gained from researches...
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Modelling of Nuclear Power Plant Steam Turbine
PublicationThe paper describes the approach to a Nuclear Power Plant steam turbine modelling which would enable on-line optimal process control (model based) and diagnosis over wide range of operating conditions caused by changing power demand. Presented model is static, multivariable and nonlinear. Such model enables analyzing the heat cogeneration aspects. Developed model is validated and verified by using archive data gained from researches...
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Experimentation, material modelling and simulation of bonded joints with a flexible adhesive
PublicationThe paper deals with material parameters identification of a flexible adhesive and the numerical simulation of its behaviour in a single lap bonded joint. The material modelling was based on the simple shear and tensile-shear laboratory tests of the bonded joints made of thin aluminium and polyurethane plates with the flexible adhesive Terostat MS 9360 manufactured by Henkel AG & Co. The adhesive was considered as a hyperelastic...
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Computational modelling of historic masonry railroad arch bridges
PublicationThe problems encountered during the analyzes of structural response of historic masonry railroad arch bridges are described in this paper. The attention is mainly focused on the stiffness of the masonry arches, their strengths and appropriate estimation of railroad load intensity. Issues related to computational modelling of two, existing, almost 130 years old masonry arch railroad bridges are presented in this context. The main...
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Nonlinear model of a synchronous generator for analysis of more electric aircraft power systems
PublicationA nonlinear model for studying a variable-speed synchronous generator (SG) in more electric aircraft (MEA) power system has been developed. The saturation effects of the SG magnetic circuit have been considered. The model has been implemented in the Synopys/Saber simulation environment. The modelling language MAST has been used to elaborate the SG model. The model exhibit a network with the same number of external terminals/ports...
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Modelling of wastewater treatment plant for monitoring and control purposes by state - space wavelet networks
PublicationMost of industrial processes are nonlinear, not stationary, and dynamical with at least few different time scales in their internal dynamics and hardly measured states. A biological wastewater treatment plant falls into this category. The paper considers modelling such processes for monitorning and control purposes by using State - Space Wavelet Neural Networks (SSWN). The modelling method is illustrated based on bioreactors of...
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FEM analysis of composite materials failure in nonlinear six field shell theory
PublicationThe monography deals with the problem of failure initiation in thin laminated composites. Known techniques of laminate structures modelling are briefly characterised. Eventually, shell based approach is chosen for the purpose of the description of the composite structures behaviour, as it predicts their deformation and states of stress effectively in a global sense. The nonlinear six parameter shell theory (6p theory) with asymmetric...
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An enhanced method in predicting tensile behaviour of corroded thick steel plate specimens by using random field approach
PublicationThe present work investigates the possibility of using random field techniques in modelling the mechanical behaviour of corroded thick steel plate specimens. The nonlinear Finite Element method, employing the explicit dynamic solver, is used to analyse the mechanical properties of typical specimens. A material model considering full nonlinearity is used to evaluate the stress-strain response. The influence of major governing parameters...
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Estimation of Failure Initiation in Laminated Composites by means of Nonlinear Six-Field Shell Theory and FEM
PublicationThe monography deals with the problem of failure initiation in thin laminated composites. Known techniques of laminate structures modelling are briefly characterised. Eventually, shell based approach is chosen for the purpose of the description of the composite structures behaviour, as it predicts their deformation and states of stress effectively in a global sense. The nonlinear six parameter shell theory (6p theory) with asymmetric...
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Modelling and analysis of medium frequency transformers for power converters
PublicationThe evolutions in power systems and electric vehicles, related to the economic opportunities and the environmental issues, bring the need of high power galvanically isolated DC-DC converter. The medium frequency transformer (MFT) is one of its key components, enabled by the increasing switching frequency of modern power semiconductors like silicon carbide transistors or diodes. The increased operating frequency offers small...
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FE analysis of support-specimen interaction of compressive experimental test
PublicationThe objective of this work is to investigate the support-specimen interaction during the compressive experimental testing of stiffened plates. The interaction is analyzed employing the nonlinear Finite Element Method using the commercial software ANSYS. The connection between the stiffened plate and testing supports is modelled with the use of contact elements, where several possible interaction scenarios are investigated, and...
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Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublicationInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
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Marek Czachor prof. dr hab.
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Mathematical and numerical modelling,W,IDE-EMSS,IIst,sem.01,lato,2023/24 (PG_00057379)
e-Learning CoursesModelling of controlled mechanical systems by the mixed method of rigid and flexible finite elements: The finite element volume problems. Dynamics of multibody systems. Modelling of stationary closed loop systems. Modelling of systems whose configuration changes with time. Modelling of nonlinear controlled systems. Optimal control at energy performance index: Control of continuous nonstationary systems in domain of generalised...
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Mathematical and Numerical Modelling, L, IDE IInd, sem.01, summer, 2022/23(00057379)
e-Learning CoursesModelling of controlled mechanical systems by the mixed method of rigid and flexible finite elements: The finite element volume problems. Dynamics of multibody systems. Modelling of stationary closed loop systems. Modelling of systems whose configuration changes with time. Modelling of nonlinear controlled systems. Optimal control at energy performance index: Control of continuous nonstationary systems in domain of generalised...
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Optimal state feedback controller for balancing cube
PublicationIn this paper, a nonlinear balancing cube system is considered, the concept for which is based on an inverted pendulum. The main purpose of this work was the modelling and construction of a balancing cube with the synthesis of the control system. The control objectives included swing-up and stabilization of the cube on its vertex at an unstable equilibrium. Execution of the intended purpose required, first, deriving a cognitive...
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Synthesis of a state feedback controller for an averaging tank with variable filling
PublicationIn paper, a nonlinear averaging tank with variable filling is considered. The main purpose of this research work was the modelling and control system synthesis of an averaging tank. The control objectives included ensuring stability and zero steady-state error of the system and achieving settling time as short as possible, while maintaining a minimal overshoot. In order to achieve the intended purpose, firstly a mathematical model...
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CONTROL OF THE WAVES IN A TOWING TANK WITH THE USE OF A BLACK-BOX MODEL
PublicationThe paper describes an adaptive control system of the waves, implemented in the Ship Design and Research Centre, CTO S.A. The purpose of generating the waves in the towing tank is the modelling of the environmental conditions during hydrodynamic model tests. The tests are performed on scale models of towed or free running ships, anchored structures like oil rigs or bottommounted structures, e.g. wind turbines. In the towing tank...
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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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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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Half-Order Modeling of Saturated Synchronous Machine
PublicationNoninteger order systems are used to model diffusion in conductive parts of electrical machines as they lead to more compact and knowledge models but also to improve their precision. In this paper a linear half-order impedance model of a ferromagnetic sheet deduced from the diffusion of magnetic field is briefly introduced. Then, from physical considerations and finite elements simulation, the nonlinear half-order impedance model...
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Pounding between Inelastic Three-Storey Buildings under Seismic Excitations
PublicationStructural interactions between adjacent, insufficiently separated buildings have been repeatedly observed during damaging ground motions. This phenomenon, known as the structural pounding, may result in substantial damage or even total collapse of structures. The aim of the present paper is to show the results of the nonlinear numerical analysis focused on pounding between inelastic three-storey buildings under seismic excitations....
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Secondary arc modelling for single pole reclosing analyses
PublicationThe paper discusses two evaluation methods of single pole auto-reclosing process effectiveness in HV transmission lines. Secondary arc current and recovery voltage calculation results obtained by load flow calculation are compared to the results obtained by the time domain simulations. Moreover, a nonlinear secondary arc model implementation is presented. The paper presents the study results for the three types of EHV transmission...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublicationThe validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed...
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Proportional-Derivative and Model-based Controllers used for a Serial Type Manipulator in case of a Variable Mass Payload
PublicationIn the paper, numerical analysis of dynamics of a variable mass system is considered. Its reference example is a serial-like manipulator composed of revolute joints and rigid bodies. Payload of its gripper is considered as its variable mass element (mass and inertia irregularly between subsequent payloads). For the rest of the system, inertia parameters are considered as known (precisely identified during the assembling process)....
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Static and dynamic modelling blow- out type trauma of orbital wall
PublicationAuthors of the paper present initial results of finite element analysis of a blow-out type trauma of orbital wall. The research is liked with laboratory tests for the Young’s modulus of bones evaluation. In the finite element analysis the neighbourhood of orbital wall is modelled by triangle thin shell finite elements. In the paper results of nonlinear static and transient dynamic analysis (including damping) are compared. The...
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Mathematical Modelling of a Seismic Isolation System to Protect Structures During Damaging Earthquakes
PublicationThe present study aims to determine the effectiveness of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system to protect structures during strong and damaging earthquakes. In order to construct the Polymeric Bearings considered in this research, a specially prepared flexible polyurethane elastomer with increased damping properties has been used. The usefulness of the proposed mathematical...
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Fluid–solid interaction on a thin platelet with high-velocity flow: vibration modelling and experiment
PublicationThe paper concerns the nonlinear behaviour of a thin platelet that is streamlined in an aerodynamic tunnel. The air velocity in the aerodynamic tunnel was at 858.9 km/h or 0.7 Ma (Ma—Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound). This experiment was numerically simulated using FSI (fluid–solid interaction) tools, namely the coupling...
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Incorporating installation effects into the probability analysis of controlled modulus columns
PublicationThis technical report presents the probabilistic analysis which integrates the Monte Carlo simulation (MCS) with random field theory to model the load–displacement behavior of Controlled Modulus Columns (CMCs) in overconsolidated Poznań clay. Presented study focuses on the practical aspects of statistical analysis of geotechnical data, numerical model development, and results evaluation. Variability and spatial distribution of...
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Design of three control algorithms for an averaging tank with variable filing
PublicationAn averaging tank with variable filling is a nonlinear multidimensional system and can thus be considered a complex control sys-tem. General control objectives of such object include ensuring stability, zero steady state error and achieving simultaneously shortest possible settling time and minimal overshoot. The main purpose of this research work was the modelling and synthesis of three control systems for an averaging tank. In...
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Selected local stability problems of channel section flanges made of aluminium alloys
PublicationThe paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Constitutive Modelling of Knitted Abdominal Implants in Numerical Simulations of Repaired Hernia Mechanics
PublicationThe paper presents a numerical approach to describe mechanical behavior of anisotropic textile material, which is a selected abdominal prosthesis. Two constitutive nonlinear concepts are compared. In the first one the material is considered composed from two families of threads (dense net model) and in the second one the material is homogeneous but anisotropic (as proposed by Gassel, Ogden, Holzapfel). Parameters of both models...