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1
Content available Exact and approximate methods in analysis of one-dimensional mechanical systems
Płaczek M.
Selected Engineering Problems
|
2016
|
nr 7
37--42
EN
Paper presents comparison of an exact Fourier method and an approximate Galerkin method in analysis of one-dimensional vibrating mechanical systems. Assumptions of the approximate method are presented. The considered systems are beams with different methods of fixing - different boundary conditions. Values of natural frequencies and dynamic flexibilities of considered systems are designated using the approximate method and compared with results obtained using the exact method.
2
Content available An approximate method for calculating total ship resistance on a given shipping route under statistical weather conditions and its application in the initial design of container ships
Szelangiewicz T., Żelazny K.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
|
2015
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nr 44 (116)
99--106
EN
During ship design, its service speed is one of the crucial parameters that determine its future operational profitability. As sufficiently exact calculation methods applicable to preliminary design stage are lacking, the so-called contract speed, the speed a ship reaches in calm water, is usually specified during the draft stage. The service speed obtainable by a ship under real weather conditions (mainly wind and waves) is one of the most important parameters influencing a ship’s profitability on a given shipping route. This paper presents a parametric model of calculating total ship resistance on a given shipping route under actual weather conditions (wind, waves, sea current), that could be useful in the initial design of container ships.
3
Content available remote Formulating of Diverse Task of Chosen Class of Vibrating Mechatronic Systems
Buchacz A
Mechanics and Mechanical Engineering
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2011
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Vol. 15, nr 4
31--41
EN
In this paper the modeling by different category graphs and analysis of vibrating clamped – free mechatronic system by the approximate method called Galerkin’s method has been presented. The frequency – modal analysis and assignment of amplitude - frequency characteristics of the mechatronic system is considered. The aim was to nominate the relevance or irrelevance between the characteristics obtained by exact – only for shaft – and approximate method. Such formulation especially concerns the relevance the relevance of the natural frequencies-poles of characteristics both of mechanical subsystem and the discrete – continuous clamped – free vibrating mechatronic system. This approach is a fact, that approximate solutions fulfill all conditions for vibrating mechanical and/or mechatronic systems and can be an introduction to synthesis of these systems modeled by different category graphs. Using of the hypergraph methods of modeling and synthesis methods of torsionally vibrating bars to the synthesis of discrete–continuous mechatronic systems is originality of such formulation problems.
4
Weryfikacja dokładności metody przybliżonej Galerkina w modelowaniu i badaniu drgających układów mechatronicznych
Buchacz A., Płaczek M.
Modelowanie Inżynierskie
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2010
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T. 8, nr 39
41-48
PL
W pracy przedstawiono zagadnienia weryfikacji dokładności przybliżonej metody Galerkina i jej przydatności w modelowaniu i badaniu drgających układów mechatronicznych. Weryfikacja metody przybliżonej jest istotna ze względu na brak możliwości stosowania metody dokładnej w odniesieniu do układów mechatronicznych. Dokładność metody przybliżonej określono, zestawiając wyniki badania układu mechanicznego otrzymane tą metodą z wynikami metody dokładnej. W efekcie porównania obu metod wprowadzono współczynniki korekcyjne metody przybliżonej.
EN
This paper presents problem of the verification of accuracy of approximate Galerkin method in the vibrating mechatronic system research works. The considered mechatronic system is one-dimension vibrating bending beam with piezoelectric transducer bonded to the beam surface and external shunting circuit adjoined to the clamps of the transducer. In order to assign dynamic characteristic of the considered system approximate Galerkin method was used, where approximate solution of differential motion equation was defined as a product of time and displacement eigenfunctions which meet defined boundary conditions.
5
Content available remote Analysis of probability as an impulse to synthesis of a beam-system represented by hypergraphs
Buchacz A.
Journal of Achievements in Materials and Manufacturing Engineering
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2010
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Vol. 38, nr 1
72-79
EN
Purpose: of this paper is to analyze vibrating beam by an exact and approximate methods and to create hypergraphs of the beam in case of two methods of analysis. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by the considered methods - especially concerning the relevance of the natural frequency-poles of beam characteristics. The main subject of the research is a continuous free beam as a subsystem of vibrating beam-system with constant cross sections. Findings: this approach is that approximate solutions fulfil all conditions for vibrating beams and can be an introduction to synthesis of these systems modelled by hypergraphs. Research limitations/implications: linear continuous flexibly vibrating free beam is considered Practical implications: of this study is mainly the introduction to synthesis of flexibly vibrating continuous beam-systems. Originality/value: of this approach is about application of approximate methods of analysis of a beam and modelling the one of transformed hypergraph.
6
Content available remote Dynamical flexibility of torsionally vibrating mechatronic system
Buchacz A.
Journal of Achievements in Materials and Manufacturing Engineering
|
2008
|
Vol. 26, nr 1
33-40
EN
Purpose: of this paper is the application of the approximate method called Galerkin's method to solve the task of assigning the frequency-modal analysis and characteristics of a mechatronic system. Design/methodology/approach: was the formulated and solved as a problem in the form of a set of differential equations of the considered mechatronic model of an object. To obtain the solution, Galerkin's method was used. The discussed torsionally vibrating mechatronic system consists of mechanical system, which is a continuous bar of circular cross-section, clamped on its ends. The electrical subsystem of the considered mechatronic system is a ring transducer to be perfectly bonded to the bar surface. Findings: this study is that the parameters of the transducer have an important influence on the values of natural frequencies and on the form of the characteristics of the said mechatronic system. The results of the calculations were not only presented in a mathematical form but also as transients of the examined dynamical characteristic which are a function of frequency of the assumed excitation. Research limitations/implications: is that the linear mechatronic system was considered, for this type of systems, such approach is sufficient. Practical implications: of this researches was that another approach is presented, that means in the domain of frequency spectrum analysis. The method used and the obtained results can be of some value for designers of mechatronic systems. Originality/value: of this paper is that the mechatronic system, created from mechanical and electrical subsystems with electromechanical bondage was examined. This approach is other than those considered elsewhere.
7
Content available remote Calculation of characteristics of torsionally vibrating mechatronic system
Buchacz A.
Journal of Achievements in Materials and Manufacturing Engineering
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2007
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Vol. 20, nr 1-2
327-330
EN
Purpose: of this paper is the application of the approximate method to solve the task of assigning the frequency - modal analysis and characteristics of a mechatronic system. Design/methodology/approach: was the formulated and solved as a problem in the form of a set of differential equations of motion and state equations of the considered mechatronic model of an object. To obtain the solution, Galerkin's method was used. The discussed torsionally vibrating mechanical system is a continuous bar of circular cross-section, clamped on its ends. A ring transducer, which is an integral part of the mechatronic system is assumed to be perfectly bonded to the bar surface. Findings: this study is that the parameters of the transducer have an important influence on the values of natural frequencies and on the form of the characteristics of the said mechatronic system. The poles of the dynamical characteristic calculated with the use of mathematical exact method and Galerkin's method have approximately the same values. The results of the calculations were not only presented in a mathematical form but also as transients of the examined dynamical characteristic which are a function of frequency of the assumed excitation. Research limitations/implications: is that the linear mechatronic system was considered, but for this type of systems, such approach is sufficient. Practical implications: of this researches was that another approach is presented, that means in the domain of frequency spectrum analysis. The method used and the obtained results can be of some value for designers of mechatronic systems. Originality/value: of this paper is that the mechatronic system, created from mechanical and electrical subsystems with electromechanical bondage was examined. This approach is other than those considered elsewhere.
8
Content available remote Singularity behavior of flow in a curved pipe
Khan M. A. H.
International Journal of Applied Mechanics and Engineering
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2006
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Vol. 11, no 3
699-704
EN
Singularity behavior of flow in a curved pipe is analyzed. A series related to a similarity parameter is obtained by using algebraic programming language MAPLE. The series is then analyzed by various generalizations of the approximate methods. The result is not conclusive, but we show approximately the dominating behavior of the flow near the (unphysical) singularity point.
9
Ocena nieuszkadzalności ESŁ na podstawie niepewnych danych
Prażewska M. J.
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
|
2002
|
nr 4
231--236
PL
Opisano metodę wyznaczania dystrybuanty czasu funkcjonowania przy niepewnych danych. Przedstawiono zasadę metody oraz na przykładzie pokazano sposób obliczeń. Wyniki zilustrowano wykresami.
EN
The paper presents the method to calculate probability distribution of operating time on the basic incomplete observed data. The principles of this methodology are presented. Results are illustrated by the numerical example the practical application.
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