Search results for: nonlinear dynamics
-
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...
-
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.
-
Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas
PublicationTwo dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place. are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into...
-
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....
-
Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublicationThe paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of...
-
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...
-
Effectiveness of a mathematical model in simulating nonlinear mechanical behaviour of a seismic isolation system made of polymeric bearings
PublicationThe present study was focused on determining the effectives of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system made of Polymeric Bearings. The proposed mathematical model defines the lateral force as a nonlinear function of the shear displacement and the deformation velocity. The effectiveness of the proposed mathematical model was verified by comparing the seismic response...
-
NONLINEAR VIBRATION ANALYSIS OF BEAM AND PLATE WITH CLOSED CRACK: A REVIEW
PublicationThe effect of nonlinearity is high sensitivity in damage detection, especially for closed cracks and delamination. This review illustrates the results of several researchers dealing with nonlinear effects caused by the closure of cracks in the structure, i.e., beam and plate structures. Early detection of damage is an important aspect for the structure and, therefore, continuous progress is being made in developing new and effective...
-
The nonlinear effects of sound in a liquid with relaxation losses
PublicationThe nonlinear effects of sound in electrolyte with a chemical reaction are examined. The dynamic equations that govern non-wave modes in the field of intense sound are derived, and acoustic forces of vortex, entropy, and relaxation modes are determined in the cases of low-frequency sound and high-frequency sound. The difference in the nonlinear effects of sound in electrolyte and in a gas with excited vibrational degrees of molecules,...
-
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...
-
Sensorless Multiscalar Control of Five-Phase Induction Machine with Inverter Output Filter
PublicationThe paper presents a complete solution for speed sensorless control system for five-phase induction motor with voltage inverter, LC filter and nonlinear control of combined fundamental and third harmonic flux distribution. The control principle, also known as multiscalar control, nonlinear control or natural variables control, is based on a use of properly selected scalar variables in control feedback to linearize controlled system....
-
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...
-
Robust output prediction of differential – algebraic systems – application to drinking water distribution system
PublicationThe paper presents the recursive robust output variable prediction algorithm, applicable for systems described in the form of nonlinear algebraic-differential equations. The algorithm bases on the uncertainty interval description, the system model, and the measurements. To improve the algorithm efficiency, nonlinear system models are linearised along the nominal trajectory. The effectiveness of the algorithm is demonstrated on...
-
Nonlinear Fuzzy Control System for Dissolved Oxygen with Aeration System in Sequencing Batch Reactor
PublicationBiological processes at a wastewater treatment plant are complex, multivariable, time varying and nonlinear. Moreover, interactions between the components are very strong. Control of dissolved oxygen is one of most important task at the plant. The level of dissolved oxygen in aerobic tanks has significant influence on behaviour and activity of microorganisms at the plant. Air for aerated tanks is supplied by the aeration system...
-
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...
-
Low Cost Method for Location Service in the WCDMA System
PublicationA new and low cost method for a location service (LCS) in the Wideband Code Division Multiple Access (WCDMA) system is outlined. This method, which is called TDOA + RTT, enables calculation of the geographical position of a mobile station (MS) without knowledge of relative time differences (RTDs) between base stations (BSs). The TDOA+RTT method is based on the measurement of round trip times (RTTs) between the MS and the serving...
-
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...
-
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...
-
Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
-
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...
-
Nonlinear and linear impedance of bismuth vanadate ceramics and its relation to structural properties
PublicationThe nonlinear and linear electrical properties, topography, and microstructure of bismuth-vanadate ceramics, were studied. The structurewas observed with the use of X-ray diffraction (XRD), scanning electronmicroscopy (SEM), atomic force microscopy (AFM) and confocal microscopy methods. The obtained results showed that ceramic is porous. Two phase transitionswere determinedwith the use of DSC measurements. The linear and nonlinear ac...
-
Standing Acoustic Waves and Relative Nonlinear Phenomena in a Vibrationally Relaxing Gas-Filled Resonator
PublicationStanding acoustic waves in one-dimensional resonator filled with vibrationally relaxing gas, are studied. Two regimes of excitation of molecular vibrational degrees of freedom are considered, equilibrium and nonequilibrium. The acoustic energy enlarges with time in the non-equilibrium regime and decreases otherwise before formation of discontinuity. After that, it decreases due to nonlinear absorption and tends to zero in equilibrium...
-
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...
-
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...
-
On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution
PublicationAmong various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In...
-
Generation and Propagation of Nonlinear Waves in a Towing Tank
PublicationThe paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The...
-
Robust Model Predictive Control for Autonomous Underwater Vehicle – Manipulator System with Fuzzy Compensator
PublicationThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order to track desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performance can be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPC as a known proficient nonlinear control approach should be improved by the uncertainty estimator...
-
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...
-
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,...
-
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...
-
Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
-
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....
-
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...
-
Stress-driven nonlocal elasticity for nonlinear vibration characteristics of carbon/boron-nitride hetero-nanotube subject to magneto-thermal environment
PublicationStress-driven nonlocal theory of elasticity, in its differential form, is applied to investigate the nonlinear vibrational characteristics of a hetero-nanotube in magneto-thermal environment with the help of finite element method. In order to more precisely deal with the dynamic behavior of size-dependent nanotubes, a two-node beam element with six degrees-of freedom including the nodal values of the deflection, slope and curvature...
-
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...
-
Measurement system for nonlinear surface spectroscopy by atomic force microscopy for corrosion processes monitoring
PublicationIn addition to traditional imaging the surface, atomic force microscopy (AFM) enables wide variety of additional measurements. One of them is higher harmonic imaging. In tapping mode the nonlinear contact between tip and specimen results in higher frequency vibrations. More information available from the higher harmonics analysis proves to be helpful for more detailed imaging. Such visualization is especially useful for heterogeneous...
-
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...
-
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...
-
Asynchronous time difference of arrival (ATDOA) method
PublicationA new method for a location service in the asynchronous wireless sensor networks is outlined. This method, which is called asynchronous time difference of arrival (ATDOA), enables calculation of the position of a mobile node without knowledge of relative time differences (RTDs) between measuring sensors. The ATDOA method is based on the measurement of time difference of arrival between the node and the same sensor at the discrete...
-
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...
-
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...
-
Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers
PublicationSeismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them by using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and...
-
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...
-
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...
-
A measurement system for nonlinear surface spectroscopy with an atomic force microscope during corrosion process monitoring
PublicationIn addition to traditional imaging the surface, atomic force microscopy (AFM) enables wide variety of additional measurements. One of them is higher harmonic imaging. In tapping mode the nonlinear contact between tip and specimen results in higher frequency vibrations. More information available from the higher harmonics analysis proves to be helpful for more detailed imaging. Such visualization is espe-cially useful for heterogeneous...
-
Designing a ship course controller by applying the adaptivebackstepping method
PublicationThe article discusses the problem of designing a proper and efficient adaptive course-keeping control system for a seagoingship based on the adaptive backstepping method. The proposed controller in the design stage takes into account thedynamic properties of the steering gear and the full nonlinear static maneuvering characteristic. The adjustable parametersof the achieved nonlinear control structure were tuned up by using the...
-
On the geometrically nonlinear vibration of a piezo-flexomagnetic nanotube
PublicationIn order to describe the behavior of thin elements used in MEMS and NEMS, it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo-flexomagnetic elastic wall is considered. By the inclusion of Euler-Bernoulli beam and using Hamilton’s principle, the equations governing the system...
-
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...
-
Robust Model Predictive Control for Autonomous Underwater Vehicle–Manipulator System with Fuzzy Compensator
PublicationThis paper proposes an improved Model Predictive Control (MPC) approach including a fuzzy compensator in order totrack desired trajectories of autonomous Underwater Vehicle Manipulator Systems (UVMS). The tracking performancecan be affected by robot dynamical model uncertainties and applied external disturbances. Nevertheless, the MPCas a known proficient nonlinear control approach should be improved by the...
-
Simplified, multiregional fuzzy model of a nuclear power plant steam turbine
PublicationPower systems, including steam turbines and synchronous generators, are complex nonlinear systems with parameters varying over time. The paper presents the developed simplified, multiregional fuzzy model of the steam turbine of a nuclear power plant turbine generator set and compares the results with a full nonlinear model and commonly used linear input-output model of a steam turbine. The proposed model consist of series of linear...