Search results for: nonlinear system
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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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Linear and nonlinear impedance of alkali and iron doped silicate-lead glasses
Open Research DataLinear and nonlinear impedance was studied for lead-silicate glass samples doped with iron ions and alkaline oxides. The compositions of glasses were as follows: (in %mol) 50% SiO2, 25% PbO, 15% Fe2O3 and 15% one of alkaline oxides: Na2O, K2O, Li2O. All samples were prepared by the conventional melt quenching technique. The substrates were powdered...
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Performance-Driven Surrogate Modeling of High-Frequency Structures
PublicationThe development of modern high-frequency structures, including microwave and antenna components, heavily relies on full-wave electromagnetic (EM) simulation models. Notwithstanding, EM-driven design entails considerable computational expenses. This is especially troublesome when solving tasks that require massive EM analyzes, parametric optimization and uncertainty quantification be-ing representative examples. The employment of...
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Linear and nonlinear impedance of iron containing silicate glasses
Open Research DataThe linear and nonlinear impedance ofglasses doped with iron oxide were measured. Glass samples (50 SiO2-50-xPbO-xFe2O3 in mol%) were prepared by the conventional melt quenching technique. The substrates were powdered in a mortar and melted in Al2O3 crucibles. The melting was conducted in air at 1623K. The melts were poured out on plate heated up to...
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Nonlinearity shaping in nanostructured glass-diamond hybrid materials for optical fiber preforms
PublicationNanodiamond integration with optical fibers has proved a compelling methodology for magneto-optics. We reveal that the applicability of nanodiamonds in nonlinear optics goes beyond the previous demonstrations of frequency converters. Instead, we exploit the recently reported volumetric integration of nanodiamonds along the optical fiber core and show that the nonlinear response of glasses can be manipulated by nanodiamonds. By...
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Low-Cost Quasi-Global Optimization of Expensive Electromagnetic Simulation Models by Inverse Surrogates and Response Features
PublicationConceptual design of contemporary high-frequency structures is typically followed by a careful tuning of their parameters, predominantly the geometry ones. The process aims at improving the relevant performance figures, and may be quite expensive. The reason is that conventional design methods, e.g., based on analytical or equivalent network models, often only yield rough initial designs. This is especially the case for miniaturized...
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Unusual streaming in chemically reacting gases
PublicationNonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in the chemically reacting gas, is considered. The instantaneous dynamic equation which describes the nonlinear generation of the vorticity mode, is derived. It includes a quadratic nonlinear acoustic source. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. In the non-equilibrium regime of the chemical reaction,...
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Numerical Methods
e-Learning CoursesNumerical Methods: for Electronics and Telecommunications students, Master's level, semester 1 Instructor: Michał Rewieński, Piotr Sypek Course description: This course provides an introduction to computational techniques for the simulation and modeling of a broad range of engineering and physical systems. Concepts and methods discussed are widely illustrated by various applications including modeling of integrated circuits,...
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The equations for interactions of polarization modes in optical fibres including the kerr effect
PublicationWe have derived coupled nonlinear Schro¨ dinger equations (CNLSE) for arbitrary polarized light propagation in a single-mode fibre employing electromagnetic field complete description. We used a basis of transverse eigenmodes with appropriate projecting; hence, the nonlinear constants depend on the waveguide geometry. Accounting for a weak nonlinearity, which is connected to the Kerr effect, we have given explicit expressions for...
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas
PublicationA weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exotericchemical reaction of A->B type, which takes place in a gas, may be reversible or not. Two types of sound areconsidered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction.For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiencyof...
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approximation of photonic crystal fibres with large air holes by the step index fibre model
PublicationAn equivalent step index fibre with a silica core and air cladding is used to model photonic crystal fibres with large air holes. We model this fibre for linear polarisation (we focus on the lowest few transverse modes of the electromagnetic field). The equivalent step index radius is obtained by equating the lowest two eigenvalues of the model to those calculated numerically for the photonic crystal fibres. The step index parameters...
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Interaction between acoustic and non-acoustic mode in bubbly liquid
PublicationThe nonlinear interaction of acoustic and entropy modes in a bubbly liquid is the subject of investigation. Thedynamic equation governing an excess density of the entropy mode is derived. Nonlinearity and dispersion are the reasons forexcitation of the entropy mode. The nonlinear interaction of modes as a reason for bubble to grow due to sound, is discovered.Some numerical examples of the modes interactions are made.
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Interaction of Acoustic and Thermal Modes in the Gas with Nonequilibrium Chemical Reactions: Possibilities of Acoustic Cooling
PublicationNonlinear generation of thermal mode during propagation of dominative sound in a chemically reacting gas is considered. The dynamic equation of excess temperature associated with the thermal mode is derived. It is instantaneous and includes quadratic nonlinear acoustic source reflecting the nonlinear character of interaction between acoustic and non-acoustic types of gas motion. Both periodic and aperiodic sound may be considered...
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Combined environmental testing device for picosatellites
PublicationAs access to space conditions becomes more available, both technically and economically, scientists’ interest in launching finer and more sophisticated experiments grows. To be qualified for launch, such experiments need to be carefully tested prior to the event. The tests should represent actual launch conditions as closely and in a detailed manner. Typical tests for payload include: vibration tests, thermal and vacuum tests,...
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Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions
PublicationThe weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium...
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Self-refraction of acoustic pulses with shock fronts in some nonequilibrium media
PublicationThe nonlinear self-refraction of acoustic pulsed beams, which include shock fronts, is studied. The medium of sound propagation is a gas where thermodynamically nonequilibrium processes take place, such as exothermic chemical reaction or excitation of vibrational degrees of a molecule’s freedom. Comparative analysis of the features of sound propagation over gases where pure nonlinear attenuation of the shock wave occurs, and gases...
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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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Can we really solve an arch stability problem?
PublicationWe bring attention to the problem of solving nonlinear boundary-value problems for elastic structures such as arches and shells. Here we discuss a classical problem of a shear-deformable arch postbuckling. Considering a postbuckling behaviour of a circular arch we discuss the possibility to find numerically a solution for highly nonlinear regimes. The main attention is paid to the problem of determination of all solutions. The...
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Acoustic heating produced in the boundary layer
Publication: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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Karolina Lademann mgr
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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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Enriched buckling for beam-lattice metamaterials
PublicationWe discuss two examples of beam-lattice metamaterials which show attractive mechanical properties concerning their enriched buckling. The first one considers pantographic beams and the nonlinear solution is traced out numerically on the base of a Hencky’s model and an algorithm based on Riks’ arc-length scheme. The second one concerns a beam-lattice with sliders and the nonlinear solution is discussed in analytic way and, finally,...
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A Novel Method for Intelligibility Assessment of Nonlinearly Processed Speech in Spaces Characterized by Long Reverberation Times
PublicationObjective assessment of speech intelligibility is a complex task that requires taking into account a number of factors such as different perception of each speech sub-bands by the human hearing sense or different physical properties of each frequency band of a speech signal. Currently, the state-of-the-art method used for assessing the quality of speech transmission is the speech transmission index (STI). It is a standardized way...
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Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation
PublicationInstantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in...
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Acoustic heating produced in the thermoviscous flow of a bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Acoustic heating produced in the thermoviscous flow of a Bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Mixed 4-node shell element with assumed strain and stress in 6-parameter theory
PublicationWe propose a mixed hybrid 4-node shell elements based on Hu-Washizu principle. Apart from displacements both strains and stress fields are treated as independent fields. The element is derived in the framework of a general nonlinear 6-field shell theory with drilling rotation which is dedicated to the analysis of multifold irregular shells with intersections. The novelty of the presented results stems from the fact that the measures...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublicationInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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Mixed 4-node shell element with assumed strain and stress in 6-parameter theory
PublicationWe propose a mixed hybrid 4-node shell elements based on Hu-Washizu principle. Apart from displacements both strains and stress fields are treated as independent fields. The element is derived in the framework of a general nonlinear 6-field shell theory with drilling rotation which is dedicated to the analysis of multifold irregular shells with intersections. The novelty of the presented results stems from the fact that the measures...
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On the Nonlinea Distortions of Sound and its Coupling with Other Modes in a Gasesous Plasma with Finite Electric Conductivity in a Magnetic Field
PublicationNonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic...
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Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow
PublicationA thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also...
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Evaluation of pounding effects between reinforced concrete frames subjected to far-field earthquakes in terms of damage index
PublicationIn this paper, three different damage indexes were used to detect nonlinear damages in two adjacent Reinforced Concrete (RC) structures considering pounding effects. 2-, 4- and 8-story benchmark RC Moment Resisting Frames (MRFs) were selected for this purpose with 60%, 75%, and 100% of minimum separation distance and also without any in-between separation gap. These structures were analyzed using the incremental dynamic analysis...
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Parabolic Equations with Functional Dependence
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.
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Magnetosonic Excitation of the Entropy Perturbations in a Plasma with Thermal Conduction Depending on Temperature
PublicationNonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle (0 B B ) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear...
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Parametric analysis of Istanbul's Ring Road viaduct for three levels of seismic load
PublicationThe paper presents a numerical 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 magnitude and different return periods. The study is fo-cused on concrete bridge supports that are design to work in nonlinear range. The study, conducted in SOFISTIK environment,...
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Nonlinear impedance of vanadate glasses containing BaTiO3
Open Research DataThe nonlinear impedance of vanadate glasses doped with BaTiO3 was measured. Samples of the composition of x[BaO,TiO2]–(80 − x)V2O5–20Bi2O3 where x = 5, 10 and 15 in mol% were prepared by a conventional melt quenching technique. The melting was performed in alumina crucibles at the temperature of 1273 K–1373 K. The melts were poured on a preheated (573...
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Acoustic heating produced in resonators filled by a newtonian fluid
PublicationAcoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a...
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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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Systems of boundary value problems of advanced differential equations
PublicationThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets
PublicationWe construct an adaptive estimator of a density function on d dimensional unit sphere Sd (d ≥ 2), using a new type of spherical frames. The frames, or as we call them, stereografic wavelets are obtained by transforming a wavelet system, namely Daubechies, using some stereographic operators. We prove that our estimator achieves an optimal rate of convergence on some Besov type class of functions by adapting to unknown smoothness....
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Nonlinear impedance of vanadate glass-ceramics containing BaTiO3
Open Research DataThe nonlinear impedance of vanadate glasses doped with BaTiO3 was measured. Samples of the composition of x[BaO,TiO2]–(80 − x)V2O5–20Bi2O3 where x = 5, 10 and 15 in mol% were prepared by a conventional melt quenching technique. The melting was performed in alumina crucibles at the temperature of 1273 K–1373 K. The melts were poured on a preheated (573...
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Isogeometric Shell FE Analysis of the Human Abdominal Wall
PublicationIn this paper a nonlinear isogeometric Kirchhoff-Love shell model of the human abdominal wall is proposed. Its geometry is based on in vivo measurements obtained from a polygon mesh that is transformed into a NURBS surface, and then used directly for the finite element analysis. The passive response of the abdominal wall model under uniform pressure is considered. A hyperelastic membrane model based on the Gasser-Ogden-Holzapfel...
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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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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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Inline Microwave Filters With N+1 Transmission Zeros Generated by Frequency-Variant Couplings: Coupling-Matrix-Based Synthesis and Design
PublicationA general coupling-matrix-based synthesis methodology for inline Nth-order microwave bandpass filters (BPFs) with frequency-variant reactive-type couplings that generate N+1 transmission zeros (TZs) is presented in this brief. The proposed approach exploits the formulation of the synthesis problem as three inverse nonlinear eigenvalue problems (INEVPs) so that the coupling matrix is built from their sets of eigenvalues. For this...