The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear mathematical model solved by bond graph, the ranges of excitation frequency were determined, in which the movement of the couplings is chaotic. For three couplings, the 3D distributions of the largest Lyapunov exponent and correlation dimension diagram (CDD) were plotted. The proposed diagram (CDD) illustrates how the geometric structure of the attractor changes when the conditions of excitation change. The classic Poincare cross-section, completed by us with the density of points distribution, significantly enhances information about geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. The areas with the highest densification of the Poincaré cross section are most often located in places where the chaotic attractor is curved. Untersuchung der nichtlinearen Dynamik flexibler Kopplungen mit Hilfe von Bondgraphen ZusammenfassungZiel dieser Arbeit ist es, die Dynamik von elastischen Kupplungen zu modellieren. Anhand eines durch einen Bindungsgraphen gelösten nichtlinearen mathematischen Modells wurden die Bereiche der Anregungsfrequenz bestimmt, in denen die Bewegung der Kopplungen chaotisch ist. Für drei Kopplungen wurden die 3D-Verteilungen des größten Lyapunov-Exponenten und das Korrelationsdimensionsdiagramm (CDD) aufgezeichnet. Das vorgeschlagene Diagramm (CDD) zeigt, wie sich die geometrische Struktur des Attraktors ändert, wenn sich die Anregungsbedingungen ändern. Der von uns vervollständigte klassische Poincaré-Querschnitt mit der Dichte der Punkteverteilung verbessert die Informationen über geometrische Strukturen fremder Attraktoren erheblich. Es hat sich gezeigt, dass in Bezug auf große Änderungsbereiche der Steuerparameter die geometrische Struktur des seltsamen Attraktors gedehnt und gebogen wird. Die Bereiche mit der höchsten Verdichtung des Poincaré-Querschnitts befinden sich am häufigsten an Stellen, an denen der chaotische Attraktor gekrümmt ist.
This paper investigates the nonlinear dynamics of a flexible tyre coupling via computer modelling and simulation. The research mainly focused on identifying basins of attraction of coexisting solutions of the formulated phenomenological coupling model. On the basis of the derived mathematical model, and by assuming ranges of variability of the control parameters, the areas in which chaotic clutch movement takes place are determined. To identify multiple solutions, a new diagram of solutions (DS) was used, illustrating the number of coexisting solutions and their periodicity. The DS diagram was drawn based on the fixed points of the Poincaré section. To verify the proposed method of identifying periodic solutions, the graphic image of the DS was compared to the three-dimensional distribution of the largest Lyapunov exponent and the bifurcation diagram. For selected values of the control parameter ω, coexisting periodic solutions were identified, and basins of attraction were plotted. Basins of attraction were determined in relation to examples of coexistence of periodic solutions and transient chaos. Areas of initial conditions that correspond to the phenomenon of unstable chaos are mixed with the conditions of a stable periodic solution, to which the transient chaos is attracted. In the graphic images of the basins of attraction, the areas corresponding to the transient and periodic chaos are blurred.
Abstract. The article analyzes foundations associated with risk management. The research part is based on a potential risks identification analysis, impact and probability of occurrence and significance assessment for the company performing multimodal transportation services of intermodal transport units (ITU). For this purpose a risk map analysis method was used. Identification of the twenty-four most significant threats led to the identification of the most important elements of the process of ITU carriage, which proper handling allows to minimize possible losses.Keywords: risk analysis, multimodal transport, intermodal transport unit (ITU), risk map analysis, risk assessment ZARZĄDZANIE RYZYKIEM W TRANSPORCIE INTERMODALNYM NA PODSTAWIE MAPOWANIA RYZYKA Streszczenie. W artykule przeanalizowano zagadnienia związane z podstawami zarządzania ryzykiem. Część badawczą oparto na analizie identyfikacji potencjalnego ryzyka, oceny skutków i prawdopodobieństwa wystąpienia oraz oceny istotności dla przedsiębiorstwa realizującego usługi transportu zintegrowanych jednostek ładunkowych (ZJŁ) w przewozach międzygałęziowych. W tym celu posłużono się metodą mapy ryzyka. Wyodrębnienie dwudziestu czterech najbardziej istotnych zagrożeń pozwoliło na identyfikację najważniejszych elementów procesu przewozu ZJŁ, których prawidłowe wykonanie pozwala na minimalizację możliwych strat.Słowa kluczowe: zarządzanie ryzykiem, transport intermodalny, zintegrowana jednostka ładunkowa (ZJŁ), metoda mapy ryzyka, ocena ryzyka 32 M. Cieśla, B. Mrówczyńska, T. Opasiak
The scientific purpose of this paper was to analyse the problem related to intermodal transportation of mining components packed in containers or other cargo transport units coupled with the problem of its proper securing. In this article, the issue of exposing the load to the effects of inertia forces which might cause unintentional movement is presented. The methods of securing the heavy load in cargo transport units are reviewed in the context of cargo immobilisation possibilities while reducing the load sensitivity to mechanical forces. The research part of this article presents the methods of packing and securing an atypical load, which is a part of a mining machine weighing 18t. This paper presents the results of calculations of inertia forces acting on the transported cargo, packed on a container platform. Based on the results, the cross fixing method was selected to secure the cargo and further decisions were made on the type and quantity of conveyor lashings necessary for the safe and correct carriage of the atypical load.
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