Determining the resonance frequencies of forced vibrations of turbogenerators with foundations

The model method for determination of dynamic properties of framed foundations on plastic scale models is elaborated. Position shifting of resonance peaks has been found by evaluation of different response curves, measured on models. Theoretical and experimental analysis of forced vibrations of complex damped mechanical system with several degrees of freedom has shown that resonance peaks, measured at different points of the same system, correspond to various frequencies of exciting force. To locate eigen frequencies and dangerous resonances from results of measurements, it is necessary to plot the envelope of the set of curves and to determine the positions of its peaks, or, at least, to find the concentration of resonance maxima of all individual curves.     

Zur Frage der Analogie zwischen Wärme- und Stoffaustausch

Zusammenfassung Bei der Beantwortung der Frage nach der Analogie des Wärme- und Stoffaustausches muß man berücksichtigen, daß beide Vorgänge durch den Massenstrom beeinflußt werden. Als Kriterium für die Analogie wurde daher das Verhältnis a^*/^*: a/ (a^*/^* mit zu a/ ohne Massenstrom-beeinflussung) definiert, wobei für ^* eine in der angelsächsischen Literatur übliche Definition verwendet wurde. Dieses Verhältnis ist sowohl nach der einfachen Filmtheorie (ohne Veränderung der Grenzschicht durch den Massenstrom) als auch nach der Grenzschichttheorie berechenbar. Grundsätzlich kann man nach beiden Theorien nur für a/D=1 von einer strengen Analogie sprechen. Die Abweichungen sind jedoch bei der Verdunstung der meisten Lösungsmittel 0,8 < a/D < 3 und bei den erreichbaren Massenströmen (Gastemperatur <250°C) so klein, daß sie innerhalb der Meßgenauigkeit liegen. Es erscheint daher zulässig, mit den berechneten Abweichungen von der Analogie auch bei hier von abweichenden Größen für a/D und größeren Massenströmen das Verhältnis von Wärme- zu Stoffübergangskoeffizienten bei laminaren Grenzschichten zu bestimmen und für Berechnungen zu benutzen. Bei turbulenten Grenzschichten liegen noch nicht genügend Untersuchungen vor, doch scheint die Abweichung von der Analogie noch kleiner als bei laminaren Grenzschichten zu sein.

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The analogy of heat- and mass transfer

Considering the analogy of heat and mass transfer it has to be taken into account that both processes are influenced by the mass-flow. As a criterion for the analogy a ratio a^*/(3^*: a/ was defined (a^*/^* with, to a/ without a mass-flow influence) with ^* being used according to a definition common in English literature. This ratio may be calculated by both the simple film theory (without alterations in boundary layer caused by the mass-flow) and the boundary layer theory. In principle, in both theories, only for a/D=1 we can speak of strict analogy. Deviations in the evaporation of most solvents with 0.8 < a/D < 3 and with the attainable mass-flow-rates (gas temperature <250° C) are small enough, however, to fall within the accuracy of measurement. It appears permissable therefore, with deviations to the analogy calculated, for deviating quantities of a/D, and higher mass-flow-rates, to determine the ratio of heat- and mass-transfer coefficients for laminar boundary layers and use it for calculations. For turbulent boundary layers not enough data are available, but it seems that, deviations to the analogy are even smaller than in laminar boundary layers.

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Bezeichnungen a Temperaturleitzahl - C_p, c_p molare bzw - spez Wärme c=P/RT - D Diffusionskoeffizient - M relative Molmasse - ¯m Massen ström - ¯N Mengenstrom - P Gesamtdruck - P Partialdruck - q Wärme strom - R allgemeine Gaskonstante - T abs Temperatur - u Geschwindigkeit - x Ordinate in Strömungsrichtung - y=p/P Molanteil - z Ordinate senkrecht zur Strömung - Wärmeübergangskoeffizient - Stoffübergangskoeffizient - Grenzschichtdicke - Wärmeleitkoeffizient - v=y / kinematische Zähigkeit - Dichte - u·x Re_x=u.x/v Reynoldszahl - Pr=v/a Prandtlzahl - Sc=v/D Schmidtzahl - Nu_x=·x/v Nusseltzahl - Sh_x=·x/D Sherwoodzahl Indizes D diffundierender Dampf - G Trägergas - th thermisch - Konz Konzentration - * Größe durch Mengenstrom beeinflußt - , Zustand an der Wand bzw. im Gasstrom - - Mittelwert Prof. Dr.-Ing. U. Grigull zum 60. Geburtstag.     

Spectrophotometric determination of various polyanions with polymeric film optodes using microtiter plate reader

Polycation-sensitive membrane optodes based on the chromoionophore 2′,7′-dichlorofluorescein octadecylester (DCFOE) have previously been developed and used for determination of heparin via a titrimetric method. In this study, it is shown that some other important polyanions such as PPS (pentosan polysulfate), DNA, xanthan, Na-alginate, and carrageenan (food additive) can also be readily determined by using DCFOE-based microtiter plate-format optodes (MPOs) and polycationic titrants that bind these polyanionic species. The optical sensors are prepared with poly(vinyl chloride) (PVC), polyurethane (PU), bis(2-ethylhexyl)sebacate (DOS), and 2′,7′-dichlorofluorescein octadecylester (DCFOE) and exhibit reproducible and sensitive absorbance changes in response to the varying polycationic titrant concentrations. Three different polycations; protamine, poly-l-lysine and poly-l-arginine, are employed as titrants. The method has a detection limit of 1 μg mL⁻¹, and a dynamic range of 1–40 μg mL⁻¹. After the quantitative determinations are successfully demonstrated in buffered solutions, similar titrations are also performed in real samples. The method is validated by recovery studies in these samples. The average polyanion recoveries were quantitative [99.7(±1.3) % for pastry cream with vanillin (protamine titrant); 100.4 (±3.3) % for pastry gel with strawberry(PLA titrant), and 102.9(±2.0) % for pastry gel with strawberry (PLL titrant)].     

Synthesis of Some Novel 1,3,4- and 1,2,4-Thiadiazole Derivatives

Synthesis and spectral characterization of novel 1,3,4-thiadiazole derivatives including one organo-mercury compound are described. Their structure elucidation was performed by means of spectroscopic and physical methods (IR, ¹H NMR, ¹³C NMR, MS, X-ray).     

Integration of H?lder forms and currents in snowflake spaces

For an oriented n-dimensional Lipschitz manifold M we give meaning to the integral ${\int_M f \, dg_1 \wedge \cdots \wedge dg_n}$ in case the functions ${f, g_1, \ldots, g_n}$ are merely H?lder continuous of a certain order by extending the construction of the Riemann?CStieltjes integral to higher dimensions. More generally, we show that for ${\alpha \in (\tfrac{n}{n+1},1]}$ the n-dimensional locally normal currents in a locally compact metric space (X, d) represent a subspace of the n-dimensional currents in (X, d ^?? ). On the other hand, for ${n \geq 1}$ and ${\alpha \leq \tfrac{n}{n+1}}$ the vector space of n-dimensional currents in (X, d ^?? ) is zero.     

Ueber die Einrichtungen des elektrolytischen Laboratoriums der Actien-Gesellschaft zu Stolberg-Westfalen

Ohne Zusammenfassung     

Transformation of the Wiener measure under non-invertible shifts

Summary In this paper we consider the transformation of measure induced by a not-necessarily-invertible perturbation of the identity. The Radon-Nikodym density for the image of the Wiener measure and the associated Girsanov-type density are derived. An application of these results yields an extension of the degree theorem.     

Test of vibrational current distributions in transverse electron scattering

The transition current distribution for the low-lying 2⁺ state at 4.085 MeV in ²⁰⁸Pb obtained in a realistic cranked shell-model calculation is used to calculate the transverse PWBA form factor for inelastic electron scattering to this state. By keeping the same density but changing the velocity field to that of irrotational, incompressible flow the sensitivity of the form factor to the dynamics of nuclear vibrational motion is explored. It is found that the two flow patterns lead to significant, observable differences in the form factors.     

When is a Coalgebra a Generator?

Let C be a coalgebra over a field k. The aim of this paper is to study the following problem : (P) If C is a k-coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive.     

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.