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Search results for: SYSTEM OF EQUATIONS
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Simulation of the remanence influence on the transient states in a single-phase multiwinding transformer
PublicationThis paper presents the mathematical model of a single-phase multi-winding core type transformer taking into account magnetic hysteresis phenomenon based on the feedback Preisach model (FPM). The set of loop differential equations was developed for a K-th winding transformer model where the flux linkages of each winding includes flux Φ common to all windings as a function of magneto motive force Θ of all windings. The first purpose...
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Straightened characteristics of McKendrick-von Foerster equation
PublicationWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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Finite element modeling of plastic hinges based on ductility demand-capacity method using nonlinear material for dynamic analysis
PublicationThe article discusses modeling plastic hinges in reinforced concrete interme-diate supports using finite elements methods. The ductility demand-capacitymethod was used to determine the geometrical parameters of cross-section plas-ticization zones, their ability to move and rotate, as well as their ductility. Dueto the varied geometry and stiffness of the supports and their nonlinear behav-ior under dynamic load, this method was...
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Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler–Pasternak elastic foundation using a new refined beam theory: an analytical approach
PublicationIn this article, a new refined beam theory, namely one variable first-order shear deformation theory, has been employed to study the vibration and buckling characteristics of nonlocal beam. The beam is exposed to an axial magnetic field and embedded in Winkler–Pasternak foundation. The von Kármán hypothesis along with Hamilton’s principle has been implemented to derive the governing equations for both the vibration and buckling...
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Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates
PublicationThe vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin–Voigt model is employed to describe...
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Maximum transportation growth in energy and solute particles in Prandtl martial across a vertical 3D-heated surface: Simulations achieved using by finite element approach
PublicationThe goal of this study is to determine the maximum energy and solute particles' transportation growth in a 3D-heated region of Prandtl martial through a dynamic magnetic field. The effects of this field on the properties of solvent molecules and heat conduction are studied. A correctly stated functional method and a finite element approach are comparable to a certain type of differential equations. In order demonstrate the effects...
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Balance error generated by numerical diffusion in the solution of Muskingum equation
PublicationIn the paper the conservative properties of the lumped hydrological models with variable parameters are discussed. It is shown that in the case of the non-linear Muskingum equation the mass balance is not satisfied. The study indicates that the mass balance errors are caused by the improper form of equation and by the numerical diffusion which is generated in the solution. It has been shown that the classical way of derivation...
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Features of Nonlinear Sound Propagation in Vibrationally Excited Gases
PublicationWeakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to...
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A Measurement-Based Approach for Speed Control of Induction Machines
PublicationThis paper presents an approach to design a measurement-based controller for induction machines. The proposed control approach is motivated by the fact that developing an appropriate mechanical model of such induction machines is a challenging task. Since our proposed control methodology is only on the basis of measured data, the controller design does not require any information about the model of the mechanical part. The control...
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A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
PublicationThe paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the...
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Buckling of thin-walled columns accounting for initial geometrical imperfections
PublicationThe paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The...
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Nonlinear phenomena of small-scale sound in a gas with exponential stratification
PublicationThe nonlinear dynamics of perturbations, quickly varying in space, with comparatively large characteristic wavenumbers k: k>1/H, is considered. H is the scale of density and pressure reduction in unperturbed gas, as the coordinate (H is the so-called height of the uniform equilibrium gas). Coupling nonlinear equations which govern the sound and the entropy mode in a weakly nonlinear flow are derived. They describe the dynamics...
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On Wrinkling in Sandwich Panels with an Orthotropic Core
PublicationThis paper deals with the local loss of stability (wrinkling) problem of a thin facing of a sandwich panel. Classical solutions to the problem of facing instability resting on a homogeneous and isotropic substructure (a core) are compared. The relations between strain energy components associated with different forms of core deformations are discussed. Next, a new solution for the orthotropic core is presented in detail, which...
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AN OVERVIEW OF HEAT TRANSFER ENHANCEMENT BASED UPON NANOPARTICLES INFLUENCED BY INDUCED MAGNETIC FIELD WITH SLIP CONDITION VIA FINITE ELEMENT STRATEGY
PublicationThe mathematical model of heat generation and dissipation during thermal energy transmission employing nanoparticles in a Newtonian medium is investigated. Dimensionless boundary layer equations with correlations for titanium dioxide, copper oxide, and aluminium oxide are solved by the finite element method. Parameters are varied to analyze their impact on the flow fields. Various numerical experiments are performed consecutively...
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Mathematical modeling and prediction of pit to crack transition under cyclic thermal load using artificial neural network
PublicationThe formation of pitting is a major problem in most metals, which is caused by extremely localized corrosion that creates small holes in metal and subsequently, it changes into cracks under mechanical load, thermo-mechanical stress, and corrosion process factors. This research aims to study pit to crack transition phenomenon of steel boiler heat tubes under cyclic thermal load, and mathematical modeling...
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Direct-contact condensation from vapour- gas mixture in a spray ejector condenser for negative CO2 power plant
PublicationDirect-contact condensation of vapour containing the inert gas on a spray of subcooled liquid exists in a number of technical applications. For example, it may be found in the nuclear industry (e.g. pressurized jet under normal operating conditions, in safety analyses) or in the chemical industry (e.g. mixing-type heat exchanger, degasser, sea water desalting). The problem is also essential to modelling and analysis of some...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Relativity of arithmetic as a fundamental symmetry of physics
PublicationArithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters ‘plus’ or ‘times’ one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in...
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Analysis of the process of water entry of an amphibious vehicle
PublicationThe paper presents a method of computational and experimental analysis of the process of water entry of an amphibious vehicle. The computational method is based on the Reynolds Averaged Navier-Stokes Equations (RANSE) solver and the xperiment was carried out in the towing tank at Ship Design and Research Centre S.A. with the use of a scale model. The analysis was focused on the safety of water entry, i.e. the maximum pitch and...
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Propagation of acoustic pulses in some fluids with yield stress
PublicationThis study is devoted to the derivation of approximate equations governing acoustic pulses in flows with yieldstress, including some time-dependent flows with a slow dependence on time of yield stress and apparent viscosity. Themodeling of yield stress and apparent viscosity in the vicinity of a zero deformation rate allows us to consider a thixotropicfluid as a Bingham plastic with coefficients that are dependent on time. The...
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Tuning matrix-vector multiplication on GPU
PublicationA matrix times vector multiplication (matvec) is a cornerstone operation in iterative methods of solving large sparse systems of equations such as the conjugate gradients method (cg), the minimal residual method (minres), the generalized residual method (gmres) and exerts an influence on overall performance of those methods. An implementation of matvec is particularly demanding when one executes computations on a GPU (Graphics...
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Novel Interpolation Method of Multi-DFT-Bins for Frequency Estimation of Signal with Parameter Step Change
PublicationThe IpDFT(Interpolation Discrete Fourier Trans-form) method is one of the most commonly used non-parametric methods. However, when a parameter (frequency, amplitude or phase) step changes in the DFT period, the DFT coefficients will be distorted seriously, resulting in the large estimation error of the IpDFT method. Hence, it is a key challenge to find an IpDFT method, which not only can eliminate the effect of the step-changed...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Local and global response of sandwich beams made of GFRP facings and PET foam core in three point bending test
PublicationIn the paper behaviour of laminated sandwich beams (FRP face sheet – PET foam core – FRP face sheet) subjected to three point bending is studied. The paper aim is to find practical descriptions enabling effective and accurate estimation of the elastic response, damage and failure of the beams, basing on experiments and static calculations. Therefore a number of tests are described, that were done on laminated coupons and foam specimens...
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Laplace domain BEM for anisotropic transient elastodynamics
PublicationIn this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained....
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Excitation of Non-Wave Modes by Sound of Arbitrary Frequency in a Chemically Reacting Gas
PublicationThe nonlinear phenomena in the field of high intensity sound propagating in a gas with a chemical reaction, are considered. A chemical reaction of A → B type is followed by dispersion and attenuation of sound which may be atypical during irreversible thermodynamic processes under some conditions. The first and second order derivatives of heat produced in the chemical reaction evaluated at the equilibrium temperature, density and...
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Experimental and numerical studies on the mechanical response of a piezoelectric nanocomposite-based functionally graded materials
PublicationThis work presents an experimental study of piezoelectric structures reinforced by graphene platelets, based on the concept of the functionally graded materials (FGMs). The assumed model is a rectangular beam/plate and the composition is due to the Halpin-Tsai rule. The model is also simulated in the Abaqus software which is the first time that such a structure has been modelled in an FEM package. In addition, a mathematical model...
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Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory
PublicationThe present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential...
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Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
PublicationIn the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a...
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Higher harmonics of the intensity modulated Photocurrent/Photovoltage spectroscopy response - a tool for studying photoelectrochemical nonlinearities
PublicationIn this work, a higher harmonic analysis (HHA) of the intensity modulated photocurrent/photovoltage (IMPS/IMVS) spectroscopy data is proposed as a potent tool for studying nonlinear phenomena in photoelectrochemical and photovoltaic systems. Analytical solutions of kinetic equations were constructed for cases of single and double resonance accounting for various sources of higher harmonics. These sources correspond to the physical...
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A subdomain model for armature reaction field and open‐circuit field prediction in consequent pole permanent magnet machines
PublicationIn this paper, the machine quantity, such as electromagnetic torque, self and mutual inductances, and electromotive force, is analytically calculated for non-overlapping winding consequent pole slotted machine for open-circuit field and armature reaction. The sub-domain approach of (2-D) analytical model is developed using Maxwell's equations and divide the problem into slots, slot-openings, airgap and magnets region, the magnet...
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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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A review on analytical models of brushless permanent magnet machines
PublicationThis study provides an in-depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite-element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time-consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent...
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Generalized Chebyshev Bandpass Filters With Frequency-Dependent Couplings Based on Stubs
PublicationThis paper presents an accurate synthesis method for inline and cross-coupled generalized Chebyshev bandpass filters with frequency-dependent couplings implemented via open and short stubs. The technique involves the synthesis of a lumped-element prototy pe in the form of a coupling matrix with a frequency-dependent term and the conversion of this prototype to a distributed-element mode l composed of sections of TEM lines. This...
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Effects of subfilter velocity modelling on dispersed phase in LES of heated channel flow
PublicationA non-isothermal turbulent flow with the dispersed phase is modelled using the Large Eddy Simulation (LES) approach for fluid, one-way coupled with the equations of point-particle evolution. The channel is heated at both walls and isoflux boundary conditions are applied for fluid. Particle velocity and thermal statistics are computed. Of particular interest are the r.m.s. profiles and the probability density function of particle...
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Monitoring of breast tissue thermo-ablation by means of impedance measurements
PublicationW pracy przedstawiono rozważania dotyczące monitorowania jakości termoablacji zmian nowotworowych w piersi przy pomocy pomiarów impedancyjnych. Pokazano prototypowe konstrukcje sond do termoablacji jak również zaprezentowano wyniki symulacji i pierwszych eksperymentów. A usefulness of a developed probe combining power delivery to ablated breast tumour and simultaneous impedance measurements is discussed in the paper. It consists...
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Application tool for IP QoS network design
PublicationDespite the fact that differentiated-service-aware network implementation has been a widely discussed topic for quite some time, network design still proofs nontrivial. Well developed software could put an end to network designer's problems. This chapter describes work, which has been aimed at creating a comprehensive network design tool, offering a fair range of functionality and high reliability. The presented tool is able to...
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A grey box model of glucose fermentation and syntrophic oxidation in microbial fuel cells
PublicationIn this work, the fermentative and oxidative processes taking place in a microbial fuel cell (MFC) fed with glucose were studied and modeled. The model accounting for the bioelectrochemical processes was based on ordinary, Monod-type differential equations. The model parameters were estimated using experimental results obtained from three H-type MFCs operated at open or closed circuits and fed with glucose or ethanol. The experimental...
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Nonreciprocal cavities and the time-bandwidth limit: comment
PublicationIn their paper in Optica 6, 104 (2019), Mann et al. claim that linear, time-invariant nonreciprocal structures cannot overcome the time-bandwidth limit and do not exhibit an advantage over their reciprocal counterparts, specifically with regard to their time-bandwidth performance. In this Comment, we argue that these conclusions are unfounded. On the basis of both rigorous full-wave simulations and insightful physical justifications,...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures
PublicationWe focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon,...
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Discrete-continuous optimisation of an axial flow blood pump
PublicationThis paper presents results of discrete-continuous optimisation of an axial flow blood pump. Evolution Strategies (ES) are used as a global optimisation method in order to localise the optimal solution in relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump is performed by means of the Reynolds-Average Navier-Stokes...
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The Discrete-Continuous, Global Optimisation of an Axial Flow Blood Pump
PublicationThis paper presents the results of the discrete-continuous optimisation of an axial flow blood pump. Differential evolution (DE) is used as a global optimisation method in order to localise the optimal solution in a relatively short time. The whole optimisation process is fully automated. This also applies to geometry modelling. Numerical simulations of the flow inside the pump are performed by means of the Reynolds-Average Navier-Stokes...
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Recycled Polyurethane as a Second Phase in Thermoset Blends and Its Effect on Thermal Degradation Kinetics Studies
PublicationA new approach is introduced in the modification of thermosetting polymer by using different amount of polyurethane of waste origin. The post consumer polyurethane foam coatings are degraded using glycolysis process and the recycled product is further converted into new polyurethane. The blending of recycled polyurethane with epoxy exhibits transparency and produces nanostructures. The effective interaction between two polymers...
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Smoothed transition curve for railways
PublicationThe work draws attention to the existing situation in the area of transition curves used in the geometric layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this situation was the excessive...
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Effective configuration of a double triad planar parallel manipulator for precise positioning of heavy details during their assembling process
PublicationIn the paper, dynamics analysis of a parallel manipulator is presented. It is an atypical manipulator, devoted to help in assembling of heavy industrial constructions. Few atypical properties are required: small workspace; slow velocities; high loads. Initially, a short discussion about definition of the parallel manipulators is presented, as well as the sketch of the proposed structure. In parallel, some definitions, assumptions...
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublicationIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....