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Number of results: 85
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Abstract

Large elongation in one de?nite direction of a crystal of cubic symmetry is considered. The equations of second order elasticity theory are applied. In this approximation three constants of the second order and six constants of the third order characterize the crystal. The stress is a function of the elongation direction. The elongation directions for which the stress reaches an extreme value have been analyzed.

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Authors and Affiliations

Z. Wesołowski
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Abstract

Considering concrete nonlinearity, the wave height limit between small and large amplitude sloshing is defined based on the Bernoulli equation. Based on Navier-Stokes equations, the mathematical model of large amplitude sloshing is established for a Concrete Rectangle Liquid-Storage Structure (CRLSS). The results show that the seismic response of a CRLSS increases with the increase of seismic intensity. Under different seismic fortification intensities, the change in trend of wave height, wallboard displacement, and stress are the same, but the amplitudes are not. The areas of stress concentration appear mainly at the connections between the wallboards, and the connections between the wallboard and the bottom.

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Authors and Affiliations

X. Cheng
D. Li
P. Li
X. Zhang
G. Li
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Abstract

The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.

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Authors and Affiliations

Anna Perelomova
Paweł Wojda
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Abstract

Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.

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Authors and Affiliations

Majid Jamal-Omidi
Mahdi Shayanmehr
Saeid Sazesh
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Abstract

An application of nonlinear optimisation methods to the solution of optimal brake torques for the ESP system is presented. The plane model of a vehicle is worked out and then used in the optimisation process. Two tasks are considered; the first when the vehicle motion is disturbed by bumps and ruts, the second when the vehicle changes the lane. The results of numerical calculation are included.
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Authors and Affiliations

Witold Grzegożek
Stanisław Wojciech
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Abstract

The above-threshold operation of a Fabry-Perot laser with a nonlinear PT (parity time) mirror is investigated. For the first time, the analysis accounts for gain saturation of an active medium as well as gain and loss saturation effects in the PT mirror. The obtained laser output intensity characteristics have been demonstrated as a function of various PT mirror parameters such as: the ratio of the PT structure period to laser operating wavelength, number of PT mirror primitive cells, and gain and loss saturation intensities of the PT mirror gain and loss layers. Two functional configurations of the laser have been considered: laser operating as a discrete device, and as a component of an integrated circuit. It has been shown that, in general, the laser operation depends on the PT mirror orientation with respect to the active medium of the laser. Moreover, when the laser radiation is outcoupled through the PT mirror to the free space, bistable operation is possible, when losses of the mirror’s loss layer saturate faster than gain of the gain layer. Furthermore, for a given saturation intensity of the mirror loss layers, the increase of the saturation intensity of the mirror gain layers causes increasing output intensity, i.e., the PT mirror additionally amplifies the laser output signal.
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Bibliography

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Authors and Affiliations

Agnieszka Mossakowska-Wyszyńska
1
ORCID: ORCID
Piotr Witoński
1
ORCID: ORCID
Paweł Szczepański
1 2
ORCID: ORCID

  1. Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
  2. National Institute of Telecommunications, ul. Szachowa 1, 04-894 Warsaw, Poland
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Abstract

The time period of a jet engines full acceleration (from idle run rotating speed to full thrust) is a very important operational parameter. Minimization of this period is an important problem to be solved during the design of the fuel supply and control system. There are many methods of acceleration process control, especially in the case of engines with complicated design configurations. This work presents the problem of acceleration of a simple, single spool turbine jet engine with a so-called stable geometry, in which only one input (control) signal exists - fuel flow rate. Two methods of acceleration control consisting of limitation of the maximum allowable temperature of working medium in front of and behind the turbine in transient states were analyzed. In order to avoid difficulties associated with the direct measurement of actual temperatures, the so-called nonlinear engine observer was applied. With the use of the computer simulation method it was proven that the control algorithm with the limited maximum temperature in front of the turbine makes it possible the shortening of the acceleration time period significantly in comparison with a similar algorithm, that realizes the limitation of temperature behind the turbine.
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Authors and Affiliations

Wojciech I. Pawlak
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Abstract

Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.

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Authors and Affiliations

Robert Nebeluk
Piotr Marusak
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Abstract

In this study we investigate the appearance of combination tones in violins. Most authors in recent times have emphasised that combination tones occur inside the ear exclusively (intra-aural). This assumption will be subjected to scrutiny based on evidence found in an empirical study in which combination tones were measured outside the ear (extra-aural).

Measurements were performed in which a violinist played two tones of a particular musical interval simultaneously. This was recorded and subsequently analysed using a Fourier Transformation. In addition to the partial tones of the primary interval, the resulting spectrum showed frequencies corresponding to combination tones. Similar measurements on the viola and violoncello also revealed the existence of extra-aural combination tones. Such frequencies may influence the timbre of simultaneous intervals played on string instruments. In another experiment the violin was excited using an electrodynamic mini-shaker with the aim of localising the origin of extra-aural combination tones. A newly devised tone matrix was used as a theoretical approach which computes all potential combination tones that may occur between any pair of partial tones. The detailed analysis of musical intervals by both the frequency spectrum and the tone matrix shows characteristic mirror and point symmetries in the partial tone structure. The discussion focuses mainly on the audibility of extra-aural combination tones and on ‘the combination tone 1’. This research opens up new perspectives and questions relevant for interpreters, composers, violin makers and violin acousticians.

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Authors and Affiliations

Angela Lohri
Sandra Carral
Vasileios Chatziioannou
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Abstract

The nonlinearity parameter B/A, internal pressure, and acoustic impedance are calculated for a room temperature ionic liquid, i.e. for 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide for temperatures from (288.15 to 318.15) K and pressures up to 100 MPa. The B/A calculations are made by means of a thermodynamic method. The decrease of B/A values with the increasing pressure is observed. At the same time B/A is temperature independent in the range studied. The results are compared with corresponding data for organic molecular liquids. The isotherms of internal pressure cross at pressure in the vicinity of 70 MPa, i.e. in this range the internal pressure is temperature independent.
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Authors and Affiliations

Edward Zorębski
Michał Zorębski
Marzena Dzida
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Abstract

Weakly 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 the inverse time of relaxation. Additional nonlinear terms increase standard nonlinearity of the high-frequency sound in the equilibrium regime of vibrational excitation and decrease otherwise. As for the nonlinearity of the low-frequency sound, the conclusions are opposite. Appearance of a non-oscillating additional part which is a linear function of the distance from the transducer is an unusual property of nonlinear distortions of harmonic at the transducer high-frequency sound
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Authors and Affiliations

Anna Perelomova
Magdalena Kusmirek
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Abstract

The paper describes the construction, operation and test results of three most popular interpolators from a viewpoint of time-interval (TI) measurement systems consisting of many tapped-delay lines (TDLs) and registering pulses of a wide-range changeable intensity. The comparison criteria include the maximum intensity of registered time stamps (TSs), the dependency of interpolator characteristic on the registered TSs’ intensity, the need of using either two counters or a mutually-complementing pair counter-register for extending a measurement range, the need of calculating offsets between TDL inputs and the dependency of a resolution increase on the number of used TDL segments. This work also contains conclusions about a range of applications, usefulness and methods of employing each described TI interpolator. The presented experimental results bring new facts that can be used by the designers who implement precise time delays in the field-programmable gate arrays (FPGA).

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Authors and Affiliations

Dariusz Chaberski
Robert Frankowski
Maciej Gurski
Marek Zieliński
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Abstract

The central theme of this work was to analyze high aspect ratio structure having structural nonlinearity in low subsonic flow and to model nonlinear stiffness by finite element-modal approach. Total stiffness of high aspect ratio wing can be decomposed to linear and nonlinear stiffnesses. Linear stiffness is modeled by its eigenvalues and eigenvectors, while nonlinear stiffness is calculated by the method of combined Finite Element-Modal approach. The nonlinear modal stiffness is calculated by defining nonlinear static load cases first. The nonlinear stiffness in the present work is modeled in two ways, i.e., based on bending modes only and based on bending and torsion modes both. Doublet lattice method (DLM) is used for dynamic analysis which accounts for the dependency of aerodynamic forces and moments on the frequency content of dynamic motion. Minimum state rational fraction approximation (RFA) of the aerodynamic influence coefficient (AIC) matrix is used to formulate full aeroelastic state-space time domain equation. Time domain dynamics analyses show that structure behavior becomes exponentially growing at speed above the flutter speed when linear stiffness is considered, however, Limit Cycle Oscillations (LCO) is observed when linear stiffness along with nonlinear stiffness, modeled by FE-Modal approach is considered. The amplitude of LCO increases with the increase in the speed. This method is based on cantilevered configuration. Nonlinear static tests are generated while wing root chord is fixed in all degrees of freedom and it needs modification if one requires considering full aircraft. It uses dedicated commercial finite element package in conjunction with commercial aeroelastic package making the method very attractive for quick nonlinear aeroelastic analysis. It is the extension of M.Y. Harmin and J.E. Cooper method in which they used the same equations of motion and modeled geometrical nonlinearity in bending modes only. In the current work, geometrical nonlinearities in bending and in torsion modes have been considered.

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Authors and Affiliations

Kamran Ahmad
Shigang Wu
Hammad Rahman
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Abstract

The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.

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Authors and Affiliations

Tadeusz Kaczorek
ORCID: ORCID
Andrzej Ruszewski
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Abstract

Nonlinear 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 θ (0≤θ≤π) 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 excitation of the entropy mode. A dynamic equation is derived which describes excitation of perturbation in the entropy mode in the field of dominant magnetosonic mode. Effects associatiated with temperature dependent and anisotropic thermal conduction are considered and discussed.
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Bibliography

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Authors and Affiliations

Anna Perelomova
1

  1. Gdansk University of Technology, Faculty of Applied Physics and Mathematics, Gdansk, Poland
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Abstract

The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.

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Authors and Affiliations

T. Kaczorek
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Abstract

The article is a continuation of a study on the synthesis of matching multi-terminal networks, also known as compensators. The reactive four-terminal-network compensators for linear loads were introduced in previous publications, but it appeared that they operate effectively with nonlinear loads too. The methods to create a compensator for a mono-harmonic source, which allows complete independence of input from output waveforms, ensuring optimal operating conditions for the source, are presented herein. The work for the first time presents the optimal four-terminal-network compensator applied to a nonlinear load.

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Authors and Affiliations

M. Jaraczewski
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Abstract

The integration of chaos theory and history has been an issue ofmany scientific discussions, but failed to produce any results. Author reexamines the discussions, mathematical features of the theory and claims that proposed ways of integration couldn't have been used practically. Author asks if such integration is possible and i fit can have any intrinsic value for advancement of historical knowledge. Proposed solution is to use chaos theory as a tool, which enables historians to analyze causal relations in the past.
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Authors and Affiliations

Maciej Gablankowski
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Abstract

Reliable evaluation of stress-strain characteristics can be done only in the laboratory where boundary conditions with respect to stress and strain can be controlled. The most popular laboratory equipment is a triaxial apparatus. Unfortunately, standard version of triaxial apparatus can reliable measure strain not smaller than 0.1 %. Such accuracy does not allow to determine stiffness referred to strain range most often mobilized in situ i.e. 10-3 ÷ 10-1%, in which stiffness distribution is highly nonlinear. In order to overcome this problem fundamental modifications of standard triaxial apparatus should be done. The first one concerns construction of the cell. The second refers to method of measurement of vertical and horizontal deformation of a specimen. The paper compares three versions of triaxial equipment i.e. standard cell, the modified one and the cell with system of internal measurement of deformation. The comparison was made with respect to capability of stiffness measurement in strain range relevant for typical geotechnical applications. Examples of some test results are given, which are to illustrate an universal potential of the laboratory triaxial apparatus with proximity transducers capable to trace stress-strain response of soil in a reliable way.

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Authors and Affiliations

Mirosław J. Lipiński
Małgorzata K. Wdowska
Anna Wudzka
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Abstract

This article discusses the performance of an algorithm for detection of defect centers in semiconductor materials. It is based on direct parameter approximation with nonlinear regression to determine the parameters of thermal emission rate in the photocurrent waveforms. The methodology of the proposed algorithm was presented and its application procedure was described and the results of its application can be seen in measured photocurrent waveforms of a silicon crystal examined with High-Resolution Photoinduced Transient Spectroscopy (HRPITS). The performance of the presented algorithm was verified using simulated photocurrent waveforms without and with noise at the level of 10 -2. This paper presents for the first time the application of the direct approximation method using modern regression and clustering algorithms for the study of defect centers in semiconductors.
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Authors and Affiliations

Witold Kaczmarek
1
Marek Suproniuk
1
Karol Piwowarski
1
Bogdan Perka
1
Piotr Paziewski
1

  1. Institute of Electronic Systems, Department of Electronics, Military University of Technology, ul. gen. Sylwestra Kaliskiego 2, 00-908 Warszawa, Poland
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Abstract

The implementation of a new, high-performance float flat glass manufacturing technology in Europe, in conjunction with the growing interest in new glass functions expressed by the construction industry, has led to significant developments in the theory of glass structures. Long time research conducted in the EU countries has been concluded by the technical document CEN/TC 250 N 1060, drawn up as a part of the work of the European Committee for Standardization on the second edition of Eurocodes (EC). The recommendations pertaining to the design of glass structures have been foreseen in the second edition of the Eurocodes, in particular the development of a separate design standard containing modern procedures for static calculations and stability of glass building structures (cf. works M. Feldmann, R. Kasper, K. Langosch and other).

In this paper new static analysis methods for glass plates made of monolithic and laminated glass, declared in th document CEN/TC 250 N 1060 (2014) and recommended in the national standarization document CNR-DT 210 (National Research Council of Italy, 2013) are presented. These static analysis methods are not commonly known in our national engineering environment, and thus require popularization and regional verification. Numerical and analytical simulations presented in this paper for rectangular plates made of monolithic and laminated glass and having various support conditions are of this character. The results of numerical calculations constitute a basis for the discussion of new static analysis methods for plates.

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Authors and Affiliations

Marian Gwóźdź
ORCID: ORCID
Piotr Woźniczka
ORCID: ORCID
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Abstract

Double-beam model is considered in many investigations both theoretical and typically engineering ones. One can find different studies concerning analysis of such structures behaviour, especially in the cases where the system is subjected to dynamic excitations. This kind of model is successfully considered as a reliable representation of railway track. Inclusion of nonlinear physical and geometrical properties of rail track components has been justified by various computational studies and theoretical analyses. In order to properly describe behaviour of real structures their nonlinear properties cannot be omitted. Therefore a necessity to search appropriate analytical nonlinear models is recognized and highlighted in published literature. This paper presents essential extension of previously carried out double-beam system analysis. Two nonlinear factors are taken into account and parametrical analysis of the semi-analytical solution is undertaken with special emphasis on different range of parameters describing nonlinear stiffness of foundation and layer between beams. This study is extended by preliminary discussion regarding the dynamic effects produced by a series of loads moving along the upper beam. A new solution for the case of several forces acting on the upper beam with different frequencies of their variations in time is presented and briefly discussed.
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Authors and Affiliations

Piotr Koziol
1
ORCID: ORCID
Rafał Pilecki
2
ORCID: ORCID

  1. PhD, DSc, Assoc. Prof., Cracow University of Technology, Faculty of Civil Engineering, ul. Warszawska 24, 31-155 Kraków, Poland
  2. MSc, Eng., former student of Cracow University of Technology
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Abstract

The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.

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Authors and Affiliations

Anna Perelomova
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Abstract

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. They should be based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows for iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.
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Authors and Affiliations

Natalia Staszak
1
ORCID: ORCID
Tomasz Garbowski
1
ORCID: ORCID
Barbara Ksit
2
ORCID: ORCID

  1. Poznan University of Life Sciences, Department of Biosystems Engineering, Wojska Polskiego 50, 60-627 Poznań
  2. Poznan University of Technology, Institute of Building Engineering, Piotrowo 5, 60-965 Poznan, Poland

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