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1

Implementation of A Geometric Constraint Regularization For Multibody System Models

Müller A.

Archive of Mechanical Engineering

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2014

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Vol. LXI, nr 2

365--383

EN

Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

PL

Nadmiarowe więzy w układach wieloczłonowych (MBS) poważnie pogarszają wydajność obliczeniową i dokładność numerycznych metod symulacji systemów MBS. Klasycznym podejściem do rozwiązania tego problemu jest numeryczna dekompozycja Jakobianu więzów w kolejnych krokach całkowania cyfrowego. Dekompozycje takie są jednak kosztowne obliczeniowo. W artykule zaprezentowano metodę eliminacji, która wymaga tylko pojedynczej dekompozycji na etapie wstępnego przetwarzania modelu, a nie w trakcie integracji czasowej. Metoda jest oparta na wyznaczaniu przestrzeni ruchu przy wykorzystaniu koncepcji grup Liego. Pozwala ona zredukować zbiór więzów pętli dla szerokiej klasy systemów technicznych, przy czym w każdym przypadku zachowuje ona dostateczną liczbę więzów. Metoda została wyprowadzona i zilustrowana dla pojedynczych pętli kinematycznych.

2

Introducing heterometal centers into a [XW9O33]9- - type building block: a first step for related derivatives

Botar B., Bögge H., Müller A.

Bulletin of the Polish Academy of Sciences. Chemistry

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2002

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Vol. 50, No. 2

139-144

EN

For the first time it was possible to introduce heterometals (V(IV)) into the important [XW(9)O(33)](9-)(III) and Bi(III) building block thereby offering new pathways for related chemistry. By reaction of a VOSO(4)-5H(2)O solution in high excess with [(SbW(9)O(33))(2)(WO(2))4(OH(2)](12)- (molar ratio of 12:1) in acetic buffer solution, a compound containing the basic-typeanionslike[(SbW(8)VO(33)(2)(VO(2)(H(2)O)(4)(WO2)(2)](14-) which in principle could be protonated with different degrees, can be obtained. This opens new perspectives for magnetochemistry and reactivity studies of these types of compounds.

3

Thermal properties of the molybdenum - oxide based {Mo154} giant wheel type cluster with methanol ligands bonded to its surface

Bielański A., Małecka-Lubańska A., Krickemeyer E., Bögge H., Schmidtmann M., Müller A.

Bulletin of the Polish Academy of Sciences. Chemistry

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2001

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Vol. 49, No. 3

245-254

EN

The thermal behaviour of the giant molybdenum ring cluster compound formula - containing H2O ligands partly substituted by methanol molecules - was studied using TG, DTG and DTA analyses simultaneously, and mass spectromet-ric analysis of the decomposition products. Methanol is released from the sample quite rapidly even at room temperature (and even before the experiments start) but small traces of methanol are still present which we tried to use for characterising the different stages of giant ring transformation. The initial rapid loss of mass of the sample was accompanied by the DTA and DTG peak at 75°C. A small DTA endothermic peak at 165°C was assigned to an MS maximum indicating the increased emission of methanol and formaldehyde. Double exothermic peaks at 352 and 366° C corresponded to the loss of water formed from the abundant OH groups. Simultaneously, peaks indicating trace emission of formaldehyde, methanol, carbon dioxide as well as traces of hydrocarbons containing 2-4 carbon atoms per molecule were registered mass spectrometrically. The exothermic effect was attributed to a kind of "recrystallisation" process of the completely dehydrated product.

4

The reaction of giant wheel polyoxomolybdate clusters with ethanol

Bielański A., Małecka-Lubańska A., Poźniczek J., Müller A., Krickemeyer E., Diemann E.

Bulletin of the Polish Academy of Sciences. Chemistry

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2001

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Vol. 49, No. 1

85-99

EN

The conversion of ethanol at 100-280° C was used in order to characterise the redox and acid centres present in Na15{0.5[Mo(152)O(457)H14(H(2)O)68] • 0.5[Mo(154)O(462)H(2)14 (H(2)O)(70]}-ca. 400 H(2)O (1). It is concluded that Mo(VI)/Mo pairs at the external surface of the rings, of which the structure of 1 is composed, are the redox centres active in ethanol dehydrogenation to acetaldehyde. Simultaneous ethanol dehydration to diethyl ether or ethylene is a typical reaction occurring on acid centres. It is suggested that OH groups situated in (u3-0)(2)0(2) tetrahedrons inside the ring structure play such role. The formation of ethane predominating at highest temperatures is attributed to secondary reactions of primary ethylene.

5

Trwałość zmęczeniowa wybranych żeliw przy kombinacji losowego rozciągania ze skręcaniem

Łagoda T., Macha E., Müller A., Niesłony A.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

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1999

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Z. 68, t. 2

25--32

PL

W pracy analizowane są wyniki badań zmęczeniowych próbek z trzech żeliw w warunkach proporcjonalnego i nieproporcjonalnego losowego rozciągania ze skręcaniem. Dane eksperymentalne z zakresu długotrwałej wytrzymałości zmęczeniowej są porównywane z obliczonymi według algorytmu wyznaczania trwałości zmęczeniowej przy użyciu zmodyfikowanego kryterium maksymalnego naprężenia normalnego w płaszczyźnie krytycznej. Nieprzydatna dla badanych żeliw i warunków obciążenia okazała się w tym algorytmie liniowa hipoteza kumulacji uszkodzeń Palmgrena - Minera. Natomiast zadawalające wyniki uzyskano stosując nieliniową hipotezę Serensena - Kogajeva.

EN

In the paper the results of fatigue tests for specimens made of three cast irons are analysed. The specimens were tested under proportional and non-proportional random tension and torsion. The experimental data have been compared with the calculation data obtained according to the algorithm for fatigue live determination using the modified criterion of maximum normal stress in the critical plane. The linear Palmgren - Miner hypothesis of damage cumulation is not applicable for the tested cast irons and loading conditions. Satisfactory results have been obtained with use of the nonlinear Serensen - Kogayev hypothesis.

6

From simple linkable building blocks to structures with increasing size and complexity

Müller A., Kögerler P.

Bulletin of the Polish Academy of Sciences. Chemistry

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1998

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Vol. 46, No. 3

207-219

EN

Polyoxometalates provide excellent models for the understanding of basic aspects of molecular growth processes: Using the same reaction, i.e., the acidification of the aqueous solution of oxoanions, the resulting products span three important areas of matter, from the micro-, through the meso- to the macro"cosmos", the latter of which is characterized by crystallinity or respectively, translational invariance. Upon different types of linking of well-defined building units an overwhelming variety of different species can be formed. Novel types of molecular growth processes (including those based on a type of induced cascade) are described leading to different ring-shaped, electron-rich, mixed-valence, giant polyoxomolybdates with nano-sized cavities. The recent synthesis of various large ring-cluster systems has, furthermore, opened new perspectives for a novel supramolecular chemistry in nano-scale dimensions.