Acta Mechanica Sinica
Acta Mechanica Sinica
 Acta Mechanica Sinica--2011, 27 (1)   Published: 18 February 2011
 Foreword
 Foreword J. Awrejcewicz Abstract This Special Issue of Acta Mechanica Sinica (AMS) publishes a few papers selected and recommended by The Scientific Committee, The 10th International Conference on Dynamical Systems - Theory and Applications, which was held in Lodz, Poland, between December 7-10, 2009. The conference hosted 120 participants from 26 countries all over the world. Among them are numerous groups of outstanding scientists and engineers, who deal with widely understood problems of dynamics met in both engine...
 Review
 Dissipation-induced instabilities and symmetry Oleg N. Kirillov F. Verhulst Abstract The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler's paradox (1952), has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary, associated with Whitney's umbrella. The first explanation of Ziegler's paradox...
 Research papers
 Dynamical behavior of a mobile system with two degrees of freedom near the resonance Klaus Zimmermann Igor Zeidis Abstract The design of mobile robots that can move without wheels or legs is an important engineering and technological problem. Self-propelling mechanisms consisting of a body that has contact with a rough surface and moveable internal masses are considered. Mathematical models of such systems are presented in this paper. First, a model of a vibration driven robot that moves along a rough horizontal plane with isotropic dry friction is studied. It is shown that by changing the off-resonance freq...
 Dynamics in large generators due to oval rotor and triangular stator shape Niklas L.P.Lundstrom Jan-Olov Aidanpaa Abstract Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse responses due to certain deviations of shape in the rotor and the stator. In particular, the perturbation on the rotor is considered to be of oval character, and ...
 Representation of robotic fractional dynamics in the pseudo phase plane Miguel F.M.Lima J.A. TenreiroMachado Abstract This paper analyses robotic signals in the perspective of fractional dynamics and the pseudo phase plane (PPP). It is shown that the spectra of several experimental signals can be approximated by trend lines whose slope characterizes their fractional behavior. For the PPP reconstruction of each signal, the time lags are calculated through the fractal dimension. Moreover, to obtain a smooth PPP, the noisy signals are filtered through wavelets. The behavior of the spectra reveals a relation...
 Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods J. Awrejcewicz A.V. Krysko J. Mrozowski O.A. Saltykova M.V. Zhigalov Abstract Chaotic vibrations of flexible non-linear Euler--Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov--Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler--Bernoull...
 Dynamic analysis of an offshore pipe laying operation using the reel method Marek Szczotka Abstract A system designed for a rigid and flexible pipe laying purposes is presented in the paper. Mathematical and numerical models are developed by using the rigid finite element method (RFEM). The RFEM is an efficient solution in the time domain. Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method. Large deformations of the pipe during spooling and when it is reeled out at sea are considered. A...
 Elastically restrained Bernoulli--Euler beams applied to rotary machinery modelling Tiago A.N.Silva Nuno M.M.Maia Abstract Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh's quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained throug...
 Spectral properties and identification of aerostatic bearings Jan Kozanek Ladislav Pust Abstract Modified rotor kit Bently Nevada was used for dynamic characteristics measurements of new developed aerostatic bearings. Mathematical model of these bearings is considered as linear. Model was identified with the help of harmonic force excitation independently from the speed of journal rotation. The stiffness and damping matrices were identified for different air inlet pressures. The calculated spectral properties allow to determine the stability boundary for suitable variation of model ...
 Modified Muravskii model for elastic foundations Igor V. Andrianov Yurii A. Kirichek J. Awrejcewicz Abstract A frequency equation for the vibration of an engine seating and an equation for pressure under the bottom of the engine are obtained. The present approach extends the so called Muravskii model possessing high practical accuracy of the ground modeling with its simultaneous simplicity.
 Comparison of methods for vibration analysis of electrostatic precipitators Iwona Adamiec-Wojcik Andrzej Nowak Stanislaw Wojciech Abstract The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators. The first, called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features, which is called the hybrid finite element method. As a result, a model with a diagonal mass matrix is obtained. Due to a specific geometry of the electrodes,...
 Precracking and interfacial delamination in a bi-material structure: Static and dynamic loadings Barbara Gambin Jordanka Ivanova Varbinka Valeva Gergana Nikolova Abstract The behavior of a precracked bi-material structure interface under given static and dynamic axial loading is an interest object in the present paper. Firstly, it is shown that the shear-lag model is a proper tool to analyze a delamination process in a precracked bi-material structure undergoing static loading. Secondly, the shear-lag model'' is applied to the structure under dynamic loading. To solve the problem for an interface delamination of the structure and to determine the deb...
 Analytical study of the interface in bre-reinforced 2D composite material Igor V. Andrianov J. Awrejcewicz Dieter Weichert Abstract Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures. An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibre-reinforced composite materials are proposed. The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems. All solutions are obtained in a closed analytical form. The obtained results can be used for the calculation ...
 Transient vibration of thin viscoelastic orthotropic plates J. Soukup F. Vales J. Volek J. Skocilas Abstract This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flugge and Timoshenko--Mindlin. The linear model, a general standard viscoelastic body, of the rheologic properties of a viscoelastic material was applied. The time and coordinate curves of the basic quantities displacement, rotation, velocity, stress and deformation are compared. The results obtained by an approximate analytic met...
 A discrete model of a rope with bending stiffness or viscous damping Pawel Fritzkowski Henryk Kaminski Abstract A discrete model of a rope is developed and used to simulate the plane motion of the rope fixed at one end. Actually, two systems are presented, whose members are rigid but non-ideal joints involve elasticity or dissipation. The dissipation is reflected simply by viscous damping model, whereas the bending stiffness conception is based on the classical curvature-bending moment relationship for beams and simple geometrical formulas. Equations of motion are derived and their complexity is di...
 On new chaotic mappings in symbol space Inese Bula Janis Bula Irita Rumbeniece Abstract A well known chaotic mapping in symbol space is a shift mapping. However, other chaotic mappings in symbol space exist too. The basic change is to consider the process not only at a set of times which are equally spaced, say at unit time apart (a shift mapping), but at a set of times which are not equally spaced, say if the unit time can not be fixed. The increasing mapping as a generalization of the shift mapping and the k$-switch mapping are introduced. The increasing and$k-switch ma...
 Rhythmic precipitate patterns and fractal structure Rabih F. Sultan Abstract Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix. The sparingly soluble salt formed, displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis. The Liesegang structures are analyzed from the viewpoint of their fractal nature. Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time, band spacing and band width...
 Tensegrity applied to modelling the motion of viruses Simona-Mariana Cretu Gabriela-Catalina Brinzan Abstract A considerable number of viruses’ structures have been discovered and more are expected to be identified. Different viruses’ symmetries can be observed at the nanoscale level. The mechanical models of some viruses realised by scientists are described in this paper, none of which has taken into consideration the internal deformation of subsystems. The authors’ models for some viruses’ elements are introduced, with rigid and flexible links, which reproduce the movements of viruses includin...
 An analytical and numerical study of chaotic dynamics in a simple bouncing ball model Andrzej Okninski Boguslaw Radziszewski Abstract Dynamics of a ball moving in gravitational field and colliding with a moving table is studied in this paper. The motion of the limiter is assumed as periodic with piecewise constant velocity—it is assumed that the table moves up with a constant velocity and then moves down with another constant velocity. The Poincar′e map, describing evolution from an impact to the next impact, is derived and scenarios of transition to chaotic dynamics are investigated analytically and numerically.
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