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2
Content available remote Obchody roku Jana Czochralskiego
PL
Jan Czochralski to jedna z najbardziej niezwykłych I postaci w historii nauki w Polsce i na świecie. Uczony ogromnie utalentowany i przedsiębiorczy, odważny i niezależnie myślący, niedający się wpisać w standardowe modele kariery akademickiej, zarówno w okresie międzywojennym, kiedy zadziwił świat swymi odkryciami dotyczącymi wzrostu monokryształów, jak i zaraz po wojnie, kiedy zaczął się jego osobisty dramat jako człowieka, uczonego i Polaka. Jeszcze niedawno, ku zdumieniu wielu naukowców zagranicznych odwiedzających Polskę, ten twórca technologii umożliwiającej budowę komputerów, badacz o dokonaniach na miarę Nagrody Nobla, był stosunkowo mało znany w swoim ojczystym kraju.
3
Content available remote On the Shape of Eigen-Forms of Columns Under Non-Conservative Loads
EN
In many structures of civil engineering, rotating machinery, flying objects with rocket propulsion and other systems, problems of stability arise and have to be addressed. The optimal cross-section layout in maximization of critical loads of such systems needs a deep knowledge concerning their modal properties and stability behavior, to enable one to effectively control them. The present paper is devoted to discussion of the relations between the eigenfrequencies and the eigen-modes of selected discrete and continuous models of columns subjected to conservative and non-conservative follower loads.
EN
The paper is concerned with transverse dynamics of a rigid rotor supported in a semi-active slide bearing lubricated with a magnetic fluid. Attention is focused on modeling and simulation of forced vibrations of an asymmetric rotor supported in a rolling bearing at one end and in a slide bearing, on the other one. The slide bearing is treated as a nonlinear flexible support with visco-elastic properties controlled by an external magnetic field via a ferrofluid used as a bearing lubricant. The considered dynamical system is a discrete model of real rotor of Rotor Kit RK-4 by Bentley Nevada, a laboratory device being used for educational and research purposes. The aim of the study is to find how a magnetically induced modification of the magnetic fluid affects the resonant behavior of the rotor under harmonic kinematic excitation by the rotor housing movement. Computer simulations are used to obtain resonant curves of nonlinear relative rotor/housing vibrations. The effects of magnetically controlled viscosity of the lubricant fluid are presented as changes of shape and maximum values of the resonant curves as well as a shift of the resonance zone in the excitation frequency domain.
EN
The paper is devoted to the analysis of influene of configuration of characteristic curves on the eigen-forms and stability of continuous and discrete columns subjected to the circulatory load. Special attention is paid to Beck's and Ziegler's columns elastically supported on the top of column. It is pointed out that in both cases there exsist some singular points where transition from the first to the second eigen-form occurs.
PL
Pracę poświęcono analizie wpływu krzywych charakterystycznych na postaci własne i stabilność rozważanych kolumn ciągłych i dyskretnych poddanych obciążeniu cyrkulacyjnemu. Szczególną uwagę zwrócono na kolumny Becka i Zieglera sprężyście podpartych na końcach. Wykazano istnienie szczególnych punktów osobliwych na płaszczyźnie siła-częstość, w których następuje zmiana z pierwszej na drugą postać własną.
EN
The classic Ziegler column under compressive follower force is considered now in a generalized form including a stabilizing spring acting at the end of the column. Damping in the joints is neglected. With increasing spring stiffness from zero to infinity one can observe evolution of the dynamic properties of the column from the original free-end form to the limit configuration with the end simply supported. Attention is focused not only on the stability of the straight-form equilibrium of the column but also on the eigen-frequencies, eigen-values and eigen-forms of motion of the column near the equilibrium. The follower force is responsible for loss of stability but the stabilizing spring considerably affects the stability boundary. The most interesting phenomena occur in the low zone of the spring stiffness where quite complicated interactions between flatter and divergence is observed under increasing follower force. Detailed analysis of the eigen-values is presented in the four regions of the parameter space to demonstrate new phenomena not reported in the literature.
EN
The paper is concerned with stability analysis of slender thin-walled cantilever beam subjected to axial distributed follower load, modelled as Leipholz columns and made of functionally gradient materials. Both transverse and longitudinal material gradients are studied as a result of different phase mixture with inclusion of thermo-active shape memory alloy (SMA). Attention is focused on the effect of phase transformation in SMA caused by increase of temperature and resulting in considerable changes of the local visco-elastic material properties which in turn affect system stability. Equivalent homogeneous beam stiffness and internal Kelvin-Voigt loss factor are determined using Kirchhoff's hypothesis and the visco-elastic principle. Partial equation of transverse column vibration is transformed to ordinary equations by means of two-mode Galerkin's discretisation based on the cantilever beam functions. Eigen-value behaviour and critical follower force are studied for various material gradient configurations. A concept of intelligent column is proposed utilizing longitudinal material functionality induced by non-uniform temperature distribution.
10
Content available remote Resonant Vibration of a Rotor with Magnetic
EN
The paper is concerned with the dissipative effect of the magnetic hysteresis in transverse dynamics of a rigid rotor supported in hydrodynamic bearings with magnetic actuation. Attention is focused on the influence of magnetic damping induced in the ferromagnetic core of a single magnetic actuator on the stability domain and the resonant behaviour of a rotor under constant gravity load and harmonic excitation. The dynamic relation between the magnetic field and magnetic induction in the core is described in form of a differential equation based on the hypothesis of magneto-rheologic analogy. Nonlinear magnetization curve reflecting magnetic saturation is included.
11
Content available remote Stability of Composite Rotors with Massive Discs and Follower Load
EN
The paper is concerned with a new approach to the stability behaviour of a rotating composite shaft with two supports and massive disc at the end using dynamic eigenvalues and eigenform for bifurcation analysis. The shaft subjected to tip-concentrated axial follower load and discussion is focused on the influence of gyroscopic effect on the critical rotation speed and post-critical behaviour of the system. Dynamic base functions are applied in Galerkin's discretization procedure. Two mechanisms of flutter instability exhibited by the system are studied and explained for prospective applications in industrial machinery like compressors, pumps and turbines.
12
Content available remote Modelling and Analysis of Wave Propagation in Railway Wheel Rims
EN
The paper is concerned with railroad wheel rim behavior under concentrated transverse contact forces. Design of underframe elements of modern high-speed railway vehicles requires detailed understanding of the behaviour of wheelsets, especially wave propagation in wheel rims, responsible for noise emitted, wear, corrugation, wheel poligonalisation etc. (Bogacz, 1995). In the present study, a wheel rim is treated as a curved beam of various beam models like curved Bernoulli-Euler beam, curved Rayleigh beam and curved Timoshenko beam (Bogacz, Kocjan, Kurnik 2003). They are compared with the Mahrenholtz approach based on the straight beam theory (Mahrenholtz, 2000). The influence of wheel radius on transverse wave propagation in the rim is studied. The wheel plate is modelled as a viscoelastic Winkler-type foundation (Bogacz, Dżuła, 1998). Travelling waves are analyzed with special attention paid to the velocity of propagation. The beam equations are solved using Fourier transformation, and the results are presented in form of time-space graphs. The effect of the vehicle speed is studied as well. The results obtained indicate important criteria to be taken into account in design of modern high-speed railroad wheelsets and bogies. It is shown that in general curved beam theory should be applied, but under some particular conditions the straight beam model is accurate enough. The influence of the internal stresses combined with wheel plate stiffness on wave propagation is presented as well.
13
Content available remote Damping of Mechanical Vibrations Utilising Shunted Piezoelements
EN
The paper is concerned with damping of beam and shaft vibrations using piezoelements with external shunting circuits. Usually, distributed piezoactuators are applied to beams or plates to contact curvature occuring during transverse vibrations. Here, an alternative concept of vibration control is explored consisting in utilising additional dissipation in shunting circuits of piezoelements bonded to a beam or shaft surface. Attention is focused on a cantilever beam subject to tip-concentrated follower load (Beck's column) and/or to kinematic excitation by clamped edge motion. Efficiency of piezodamping is studied in both stabilising the equilibrium and reduction of resonance. On the other hand, the effect of shunting is examined in case of ring-like piezotransducers controlling torsional vibrations of a shaft under harmonic excitation. A shift of resonance zone and reduction of top vibration amplitudes are shown as functions of shunting parameters.
EN
The paper is concerned with stability analysis of a flexible rotating shaft supported as a cantilever beam and subjected to tip-concentrated follower load. Such systems exhibit two mechanisms of instability of flutter type, different in physical nature and, what is most important, interacting to produce complicated stability regions in the space of rotation speed and follower load. In such systems even for high-speed working conditions, the rotary inertia as well as the gyroscopic effect is usually neglected like in slender beams. However, in some regions of parameters, especially in slightly internally dissipative shafts the gyroscopic effect can considerably change the boundaries of the stability domain. Moreover, an interesting phenomenon can be observed when two pairs of eigenvalues with different speeds at the same time intersect the imaginary axis of the complex plane. This leads to bifurcation with four critical eigenvalues similar to that studied by Iooss in the Navier-Stokes equations.
15
Content available remote Dynamics of wheel-tyre subjected to moving oscillating force
EN
The subject of the paper is analysis of wheel of a moving railway vehicle which is subjected to a moving oscillating force. Rail ring is treated as a beam of small curvature connected to wheel axle with a Winkler foundation. Bernoulli-Euler and Timoshenko beam model is used. Results are gained using Fourier transformation. Space and space-time graphs, showing wave propagation in subcritical and supercritical zones of excitation, concerning resonance of transverse vibrations, are included.
16
Content available remote Stability of Rotor with Hybrid Magnetohydrodynamic Support
EN
The paper is concerned with the transverse stability of a rigid rotor symmetrically supported in hydrodynamic bearings aided by magnetic actuators. Fluid-lubricated bearings provide desired transverse load capacity and small-gap magnetic actuators stabilise the rotor which thus can run smoothly with higher angular speeds being supported in what is called hybrid magnetohydrodynamic bearing. In the present paper attentions is focused on additional damping of rotor vibrations related to the magnetic hysteresis in the core of the magnetic actuator. That kind of energy disspation is usually neglected in actively controlled magnetic bearings. In hybrid, magnetohydrodynamic bearing the magnetic hysteresis has been found to be a considerable source of additional damping due to extremely small air gap in the magnetic circuit. The dynamic relation of the magnetic field and the magnetic induction has been described in this paper in form of a differential equation. The magnetic hysteresis is simulated numerically. The dissipative effect of the magnetic hysteresis in transverse stability of the rotor is presented in two control strategies - open-loop control and parametric control. In both a considerable increase of the critical rotation speed at the flutter instability threshold has been found.
17
EN
The stability and dynamics of elastic and viscoelastic models of column and inverted double pendulum, subject to a generalized follower force is considered in the paper. The analysis has confirmed the existence of the fixed point in frequency domain, revealing in a value of loading for which the frequency of natural vibration occurs independent of variety of the system parameters. The detailed analysis of modal forms reveals, that at the fixed point, the structural eigenmode changes, the first eigenmode varies into the second one. Finally the critical force appears with the second eigenmode which, however corresponds to the fundamental eigenfrequency. The higher eigenmode relates to the shorter buckle lenght, what reveals in multiply higher values of the critical load, comparing it with the Euler critical load.
18
Content available remote Stability and bifurcation of a rotating articulated shaft
EN
The subject of the paper fis concerned with analysis of dynamics of a rotating articulated shaft in terms of problems related to stability and near-critical bifurcating vibration. The shaft is supported on a flexible tail boom, is divided, and contains its structure three cruciform foints that yield a local loss of flexural stiffness of the shaft. in the first part of the work the problem of stability has been taken up, i.e. critical rotation speed at which self-excited vibration appears has been determined. The factor responsible for the self-excitation is presence of internal friction in material of the shaft. The friction, under continuous supply of the energy that maintains a constant angular velocity, leads to dynamic loss of stability in the form of the occurrence of an additional precession of the shaft around a certain equilibrium position. When the gravity force is taken into account (horizontal axis of rotation) the equilibrium becomes non-trivial.
PL
Przedmiotem pracy jest analiza dynamiki wirującego wału przegubowego w kontekście problemu stateczności i okołokrytycznych drgań bifurkacyjnych. Wał jest zamocowany na podatnej belce ogonowej, jest dzielony, a wswojej strukturze zawiera tzy przeguby krzyźakowe wnoszące lokalną zmianę sztywności giętnej wału. W pierwszej części pracy zajęto się problemem stateczności takiego wału, tj. wyznaczono prędkość krytyczną, przy której pojawiają się drgania samowzbudne. Czynnikiem odpowiedzialnym za samowzbudzenie jest obecność tarcia wewnętrznego w materiale wału. Tarcie to przy ciądłym doprowadzaniu energii utrzymującej stałą prędkość kątową, powoduje utratę stateczności w postaci wystąpienia dodatkowego ruchu precesyjnego wokół pewnego położenia równowagi. Przy uwzględnieniu sił ciężkości (pozoioma oś wirowania) położenie to jest nietrywialne. Do określenia progu krytycznego wyznaczono funkcje własne wału z uwzględnieniem podatności podpór i lokalnych zmian sztywności.
19
Content available remote Piezoelectric Stabilisation of Leipholz Columns
EN
The paper is concerned with a concept of flutter suppression in slender columns subjected to tangential follower forces. The mechanism of self-excitation of such systems is more or less recognised what enables a designer to apply proper stabilisation methods including active techniques. Promissing results have been obtained in numerical experiments with distributed piezoelectric actuators contracting column curvature occurring as a disturbance of the strait-line equilibrium position. Piezoelements can also be used in what is called shunting effect to additionally dissipate energy of transverse vibration. The method has been successfully applied in reduction of resonat vibrations of transversely loaded beams and plates. In the present paper the shunting effect is modelled and examined from the point of view of application in a non-conservative self-excited system being the Leipholz column.
20
Content available remote Stability of a Viscoelastic Shaft in Fluid-Film
EN
An analysis of dynamic stability of a rotating system consisting of a flexible shaft and two hydrodynamic bearings is presented with special attention paid to the interaction of two instability sources - the internal friction in the shaft material and the fluid-film action in the bearings. Stability is determined and the critical speed of rotation is calculated from the eigenvalue analysis of the rotor system locally linearized around a nontrivial speed- and load-dependent static equilibrium. Journals of the bearings are assumed to be lumped-mass elements performing plane motion, so that the shaft and bearing equations are coupled by the shaft end shear force. A single-mode Galerkin's discretization is performed leading to an 8-dimensional problem incorporating 14 geometric and physical system parameters. It is shown that generally shaft and bearing compliances destabilize the system, although it is also possible that a flexible shaft in fluid-film bearings is more stable than in rigid supports. An interesting effect is related to the double Hopf bifurcation which consists in simultaneous loss of stability by two eigenvalues. It appears for certain parameter values and is expected to lead to complicated postcritical behaviour.
PL
W pracy przedstawiono analizę stateczności dynamicznej układu wirującego złożonego z odkształconego wału i podpierających ten wał łożysk hydrodynamicznych. Celem pracy jest zbadanie interakcji dwóch różnych fizycznych przyczyn niestateczności - tarcia wewnętrznego w wirującym podatnym wale i oddziaływania dynamicznego filmu olejowego w łożyskach. Krytyczną prędkość wirowania układu na granicy obszaru niestateczności typu "flatter" wyznaczono rozwiązując zagadnienie własne początkowe układu wirnika lokalnie zlinearyzowanego wokół nietrywialnego położenia równowagi, zależnego od obciążenia poprzecznego wału. Założono, że czopy łożysk ślizgowych są elementami sztywnymi poruszającymi się ruchem płaskim, co oznacza, że równania wału i czopów są sprzężone poprzez siłę poprzeczną w końcowych przekrojach wału. Zastosowano jednomodalną dyskretryzację Galerkina dla wału, co doprowadziło do układu ośmiu równań zwyczajnych z czternastoma parametrami fizycznymi i geometrycznymi. Pokazano, że podatność wału i łożysk ogólnie destabilizuje układ, chociaż jest również możliwe, że odkształcony wał w łożyskach ślizgowych jest bardziej stateczny niż taki samk wał na podporach sztywnych. Występuje interesujący efekt związany z podwójną bifurkacją Hopfa, która polega na jednoczesnym przekroczeniu granicy stateczności przez dwie różne wartości własne układu. Zjawisko to występuje dla pewnych wartości parametrów i może prowadzić do skomplikowanych pokrytycznych zachowań dynamicznych układu.
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