Latin American Journal of Solids and Structures, Volume: 10, Issue: 1, Published: 2013
  • Preface

    Alves, Marcílio
  • Modeling and analysis of continuous dynamical systems

    Awrejcewicz, Jan
  • Prototypes and modulation functions of classical and novel configurations of optical chopper wheels

    Duma, Virgil-Florin

    Abstract in English:

    Optical choppers with rotating wheels are some of the most used macroscopic optomechatronic devices for the controlled modulation, attenuation or obscuration of light in a wide area of applications. We discuss and compare the modulation functions produced by two types of chopper wheels: the classical device, with windows with linear edges, and the eclipse chopper (with windows with circular edges) that, to the best of our knowledge, we have introduced. This discussion is based on the analysis and the design we have previously developed for these various devices, for top-hat (constant over the entire section) light beam distributions. While the comparison of the different shapes of transmitted signals allows for the proper choice of the most appropriate device and parameters to obtain the modulation function that is fit for a certain application, the present work also presents the mechanical setup we have designed and manufactured for testing choppers with rotating wheels. A series of prototype wheels with different, optimized profiles were obtained for the purpose. The simulation and the electro-erosion programs for the wire electro-erosion of aluminum plates to manufacture the wheels are presented. An advantageous double wheel solution has been developed to obtain wheels with windows of different shapes and sizes, and the testing of this final assembly concludes the study.
  • Numerical verification and experimental validation of the FEM model of collecting electrodes in a dry electrostatic precipitator

    Nowak, Andrzej

    Abstract in English:

    The subject of the present work is the numerical verification and experimental validation of the FEM model which would enable us to analyse the vibrations of collecting electrodes. The effectiveness of electrostatic precipitators (ESP) depends on many factors. One of these factors is the efficiency of periodic cleaning of the collecting electrodes; thus the dust is removed by inducing vibrations. These vibrations are caused by the axial impact of a hammer on an anvil beam. In the course of the impact, and afterwards, the stresses due to the impact are produced in both the rapper system and in the collecting electrode section. The paper presents a modified finite element method which can be used in simulations and to analyse the vibrations of collecting electrodes. In the verification process the calculation results obtained were compared with those from commercial software (Abaqus). The calculations and measured results were compared for validation. The comparisons were made using peak and RMS (root-mean-squared) values as well as special factors and hit rates. An acceptable compatibility of the results proves that the model can be applied in the analysis of vibrations of electrodes in design practice.
  • Vibrations of beams with a variable cross-section fixed on rotational rigid disks

    Zolkiewski, Slawomir

    Abstract in English:

    The work is focused on the problem of vibrating beams with a variable cross-section fixed on a rotational rigid disk. The beam is loaded by a transversal time varying force orthogonal to an axis of the beam and simultaneously parallel to the disk's plane. There are many ways of usage of the technical moveable systems composed of elements with the variable cross-sections. The main applications are used in numerous types of turbines and pumps. The paper is a kind of introduction to the dynamic analysis of above mentioned beam systems. The equations of motion of rotational beams fixed on the rigid disks were derived. After introducing the Coriolis forces and the centrifugal forces, the transportation effect in the mathematical model was considered. This particular project is the first stage research, where there were proposed certain solutions of problems connected with the linear variable cross-sections systems. The further investigation considering the nonlinear systems has been proceeding. The results, analysis and comparison will be presented in the future works.
  • On dynamic self-organization: examples from magmatic and other geochemical systems

    Sultan, Rabih F.; Abdel-Fattah,; Abdel-Rahman, M.

    Abstract in English:

    Standard Liesegang banding is the display of parallel bands of precipitate formed periodically when co-precipitate ions interdiffuse in a gel medium. The most striking resemblance with Liesegang patterns in Nature lies in the diverse scenery of banded textural features commonly observed in some geological materials, such as geodes, agates, malachites, as well as stratigraphic units of certain rock formations. Here, we explore the possible relationship between the Liesegang banding scenario and magmatic-type pattern formation, such as zonations in km-scale circular zoned plutons and anorogenic ring complexes, cyclic layering in large mafic - ultramafic layered intrusions and orbicular granites, as well as in mm-scale crystal zonations. We also investigate magmatic processes such as fractional crystallization, and the ranges of T and p that are compatible with operating conditions for Liesegang banding. For geochemical self-organization to operate via a Liesegang-type mechanism, a necessary condition is that the system be transiently out of equilibrium, and be described by complex nonlinear kinetic laws. We examine the viability of the development of geochemical patterns, in relation with the various requirements for the growth of Liesegang structures.
  • Investigation of the memorization process

    Cretu, Simona-Mariana

    Abstract in English:

    Memorizing involves many processes that are not fully known. This research area is just as exciting for contemporary scientists as well as it was for the ones in antiquity, considering the crucial importance of memory in human life and personality. In the last decades important steps in the knowledge of the memorization process were made by cognitive neuroscience. The paper focuses on the analysis of this process with references to its early known beginning. The study first analyses this topic in Plato's work and continues with opinions of other scientists/philosophers. Analogies between earlier and current theories, including dynamic aspects of the store, retain and recall of information, drive us to a personal point of view referring to the interpretation of Plato's book, The Republic; therefore, new directions of investigation referring to the entities and processes from human body can occur in the next future.
  • Non-linear dynamics of a hanging rope

    Fritzkowski, P.; Kaminski, H.

    Abstract in English:

    Two-dimensional motion of a hanging rope is considered. A multibody system with elastic-dissipative joints is used for modelling of the rope. The mathematical model based on the Lagrange formalism is presented. Results of some numerical simulations are shown for the mechanical system with kinematic excitation. Basic tools are used to qualify dynamics of the rope: the maximum Lyapunov exponent (MLE) is estimated numerically by the two-particle method, frequency spectra are generated via the Fast Fourier Transform (FFT) and bifurcation diagrams are produced. Influence of the excitation amplitude and frequency as well as damping on behaviour of the system is analyzed. The work can be treated as the first step in more advanced analysis of regular and chaotic motion of the complex system.
  • Application of the rigid finite element method to modelling ropes

    Kaminski, Henryk; Fritzkowski, Pawel

    Abstract in English:

    Two-dimensional motion of a rope fixed at one end is considered. The Rigid Finite Element Method (RFEM) is reviewed and applied to obtain a model of the rope, including its elastic and dissipative properties. Equations of motion are derived without the small displacement assumption, using the Lagrange equations. The resulting model is compared to another one, being derived within the framework of standard analytical mechanics methods and the Lagrange formalism. Advantages of the RFE approach are discussed from a computational point of view. The presented, alternative model can be a basis for e cient numerical simulations, which seem to be useful in further, comparative studies of the rope dynamics.
  • Study of cluster formation in a model of nanotechnology development

    Balyakin, Artem; Domnich, Anna; Zhulego, Vladimir; Ivanova, Anna

    Abstract in English:

    Mathematical model describing the development of science (nanotechnology) in Russian Federation is proposed. Results of numerical simulations are presented and discussed in the context of socio-economical interpretation.
  • Analysis of flexibility of the support and its influence on dynamics of the grab crane

    Urbaś, A.

    Abstract in English:

    Dynamic analysis of the model of the grab crane with the flexibly supported base is presented in the paper. The analyzed grab crane is the structure of the open-loop kinematic chain with rigid links. Joint coordinates and homogenous transformations are used in order to describe dynamic behavior of the system. Equations of the motion of the systems are derived using Lagrange's equations of the second order and integrated Newmark's method with iterative procedure. The commercial package MSC.ADAMS is used in order to verify own program. The range of analysis concerns influence of different values of vertical stiffness coefficients in the supports and means of fixing of the load on its motion.
  • The asymptotic solutions for boundary value problem to a convective diffusion equation with chemical reaction near a cylinder

    Maksimova, N. V.; Akhmetov, R. G.

    Abstract in English:

    The work deals with a boundary value problem for a quasilinear partial elliptical equation. The equation describes a stationary process of convective diffusion near a cylinder and takes into account the value of a chemical reaction for large Peclet numbers and for large constant of chemical reaction. The quantity the rate constant of the chemical reaction and Peclet number is assumed to have a constant value. The leading term of the asymptotics of the solution is constructed in the boundary layer as the solution for the quasilinear ordinary differential equation. In this paper, we construct asymptotic expansion of solutions for a quasilinear partial elliptical equation in the boundary layer near the cylinder.
  • Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms

    Litak, Grzegorz; Kecik, Krzysztof; Rusinek, Rafal

    Abstract in English:

    We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.
  • Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed

    Pielorz, A.; Sado, D.

    Abstract in English:

    In the paper irregular vibrations of discrete-continuous systems consisting of an arbitrary number rigid bodies connected by shafts torsionally deformed are studied. In the systems a local nonlinearity described by the polynomial of the third degree is introduced. It is assumed that the characteristic of the local nonlinearity is of a hard type. Governing equations are solved using the wave approach leading to equations with a retarded argument. Exemplary numerical calculations are done for the three-mass system. The possibility of occurring of irregular vibrations is discussed on the basis of the Poincaré maps, bifurcations diagrams and the exponents of Lyapunov.
  • Large amplitude free vibration of orthotropic shallow shells of complex shapes with variable thickness

    Awrejcewicz, Jan; Kurpa, Lidiya; Shmatko, Tatiyana

    Abstract in English:

    The present formulation of the analysed problem is based on Donell's nonlinear shallow shell theory, which adopts Kirchhoff's hypothesis. Transverse shear deformations and rotary inertia of a shell are neglected. According to this theory, the non-linear strain-displacement relations at the shell midsurface has been proposed. The validity and reliability of the proposed approach has been illustrated and discussed, and then a few examples of either linear or non-linear dynamics of shells with variable thickness and complex shapes have been presented and discussed.
  • Chaotic synchronization of vibrations of a coupled mechanical system consisting of a plate and beams

    Awrejcewicz, J.; Krysko, A.V.; Yakovleva, T.V.; Zelenchuk, D.S.; Krysko, V.A.

    Abstract in English:

    In this paper mathematical model of a mechanical system consisting of a plate and either one or two beams is derived. Obtained PDEs are reduced to ODEs, and then studied mainly using the fast Fourier and wavelet transforms. A few examples of the chaotic synchronizations are illustrated and discussed.
  • Dynamical stability and parametrical vibrations of the laminated plates with complex shape

    Kurpa, Lidiya; Mazur, Olga; Tkachenko, Victoria

    Abstract in English:

    The problem of nonlinear vibrations and stability analysis for the symmetric laminated plates with complex shape, loaded by static or periodic load in-plane is considered. In general case research of stability and parametric vibrations is connected with many mathematical difficulties. For this reason we propose approach based on application of R-functions theory and variational methods (RFM).The developed method takes into account pre-buckle stress state of the plate. The proposed approach is demonstrated on testing problems and applied to laminated plates with cutouts. The effects of geometrical parameters, load, boundary conditions on stability regions and nonlinear vibrations are investigated.
  • Determination of the rheological properties of thin plate under transient vibration

    Skočilas, Jan; Skočilasová, Blanka; Soukup, Josef

    Abstract in English:

    The article deals with systematic analysis of the transient vibration of rectangular viscoelastic orthotropic thin 2D plate. The analysis is focused on specific deformation models of plate and for specific linear models of rheological properties. The viscoelastic isotropic and anisotropic (orthotropic) materials were investigated. The plate is loaded by general transient impulse. The time and coordinate dependencies of the fundamental quantities - displacements, rotations, stress and deformations in arbitrary points of plate under transient vibration, e. g. the analysis of stress and deformation waves in plates were investigated. The selected models are defined by constitutive equations for stress and deformation dependence. The isotropic and orthotropic model is considered. The analysis results depend on quality of the determined mechanical properties of the materials. The standard methods commonly used are time-consuming and not accurate enough. The new methodology of determining the material parameters directly from investigated plate is proposed and proven.
  • Application of an improved three-phase model to calculate effective characteristics for a composite with cylindrical inclusions

    Andrianov, Igor V.; Awrejcewicz, Jan; Starushenko, Galina A.

    Abstract in English:

    A modified three-phase composite model yielding reliable effective characteristics of composite structures has been proposed. In particular, the problem of effective heat transfer coefficient of the composite structure with periodically located inclusions of circular cross-sections located on a square net is solved. Advantages of the proposed model in comparison to the classical three-phase model are illustrated and discussed.
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