Forced Response of Mistuned Bladed Disks: Quantitative Validation of the Asymptotic Description

The effect of small mistuning in the forced response of a bladed disk is analyzed using a recently introduced methodology: the asymptotic mistuning model. The asymptotic mistuning model is an extremely reduced, simplified model that is derived directly from the full formulation of the mistuned bladed disk using a consistent perturbative procedure based on the relative smallness of the mistuning distortion. A detailed description of the derivation of the asymptotic mistuning model for a realistic bladed disk configuration is presented. The asymptotic mistuning model results for several different mistuning patterns and forcing conditions are compared with those from a high-resolution finite element model. The asymptotic mistuning model produces quantitatively accurate results, and, probably more relevant, it gives precise information about the factors (tuned modes and components of the mistuning pattern) that actually play a role in the vibrational forced response of mistuned bladed disks.

INSTRUCCIO y formula per a la bona execucio de la pragmatica dels processos de absencia [Texto impreso]

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Asymptotic and computational analysis of mistuning effects on the dynamics of bladed disks

Es bien conocido que las pequeñas imperfecciones existentes en los álabes de un rótor de turbomaquinaria (conocidas como “mistuning”) pueden causar un aumento considerable de la amplitud de vibración de la respuesta forzada y, por el contrario, tienen típicamente un efecto beneficioso en el flameo del rótor. Para entender estos efectos se pueden llevar a cabo estudios numéricos del problema aeroelástico completo. Sin embargo, el cálculo de “mistuning” usando modelos de alta resolución es una tarea difícil de realizar, ya que los modelos necesarios para describir de manera precisa el componente de turbomáquina (por ejemplo rotor) tienen, necesariamente, un número muy elevado de grados de libertad, y, además, es necesario hacer un estudio estadístico para poder explorar apropiadamente las distribuciones posibles de “mistuning”, que tienen una naturaleza aleatoria. Diferentes modelos de orden reducido han sido desarrollados en los últimos años para superar este inconveniente. Uno de estos modelos, llamado “Asymptotic Mistuning Model (AMM)”, se deriva de la formulación completa usando técnicas de perturbaciones que se basan en que el “mistuning” es pequeño. El AMM retiene sólo los modos relevantes para describir el efecto del mistuning, y permite identificar los mecanismos clave involucrados en la amplificación de la respuesta forzada y en la estabilización del flameo. En este trabajo, el AMM se usa para estudiar el efecto del “mistuning” de la estructura y de la amortiguación sobre la amplitud de la respuesta forzada. Los resultados obtenidos son validados usando modelos simplificados del rotor y también otros de alta definición. Además, en el marco del proyecto europeo FP7 "Flutter-Free Turbomachinery Blades (FUTURE)", el AMM se aplica para diseñar distribuciones de “mistuning” intencional: (i) una que anula y (ii) otra que reduce a la mitad la amplitud del flameo de un rotor inestable; y las distribuciones obtenidas se validan experimentalmente. Por último, la capacidad de AMM para predecir el comportamiento de flameo de rotores con “mistuning” se comprueba usando resultados de CFD detallados. Abstract It is well known that the small imperfections of the individual blades in a turbomachinery rotor (known as “mistuning”) can cause a substantial increase of the forced response vibration amplitude, and it also typically results in an improvement of the flutter vibration characteristics of the rotor. The understanding of these phenomena can be attempted just by performing numerical simulations of the complete aeroelastic problem. However, the computation of mistuning cases using high fidelity models is a formidable task, because a detailed model of the whole rotor has to be considered, and a statistical study has to be carried out in order to properly explore the effect of the random mistuning distributions. Many reduced order models have been developed in recent years to overcome this barrier. One of these models, called the Asymptotic Mistuning Model (AMM), is systematically derived from the complete bladed disk formulation using a consistent perturbative procedure that exploits the smallness of mistuning to simplify the problem. The AMM retains only the essential system modes that are involved in the mistuning effect, and it allows to identify the key mechanisms of the amplification of the forced response amplitude and the flutter stabilization. In this work, AMM methodolgy is used to study the effect of structural and damping mistuning on the forced response vibration amplitude. The obtained results are verified using a one degree of freedom model of a rotor, and also high fidelity models of the complete rotor. The AMM is also applied, in the frame of the European FP7 project “Flutter-Free Turbomachinery Blades (FUTURE)”, to design two intentional mistuning patterns: (i) one to complete stabilize an unstable rotor, and (ii) other to approximately reduce by half its flutter amplitude. The designed patterns are validated experimentally. Finally, the ability of AMM to predict the flutter behavior of mistuned rotors is checked against numerical, high fidelity CFD results.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

One-sided asymptotic inferences for a proportion.

Two-sided asymptotic confidence intervals for an unknown proportion p have been the subject of a great deal of literature. Surprisingly, there are very few papers devoted, like this article, to the case of one tail, despite its great importance in practice and the fact that its behavior is usually different from that of the case with two tails. This paper evaluates 47 methods and concludes that (1) the optimal method is the classic Wilson method with a correction for continuity and (2) a simpler option, almost as good as the first, is the new adjusted Wald method (Wald's classic method applied to the data increased in the values proposed by Borkowf: adding a single imaginary failure or success).

Tunnel magnetoresistance in GaMnAs: going beyond Jullière formula

The relation between tunnel magnetoresistance (TMR) and spin polarization is explored for GaMnAs∕GaAlAs∕GaMnAs structures where the carriers experience strong spin–orbit interactions. TMR is calculated using the Landauer approach. The materials are described in the 6 band k⋅p model which includes spin–orbit interaction. Ferromagnetism is described in the virtual crystal mean field approximations. Our results indicate that TMR is a function of spin polarization and barrier thickness. As a result of the stong spin–orbit interactions, TMR also depends on the the angle between current flow direction and the electrode magnetization. These results compromise the validity of Julliere formula.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Geometry of Dirac Operators

Thesis (Master, Mathematics & Statistics) -- Queen's University, 2016-07-04 20:27:20.386

A partial success of trade cooperation within the ‘16+1’ formula: the case of food exports to China. OSW COMMENTARY #189, 2015-10-29

When in 2012 China approached the countries of Central and Eastern Europe (CEE) with a proposal of cooperation in the ‘16+1’ formula, it declared it was willing to meet the needs of CEE countries. Beijing had been aware of the political importance of the problem of trade deficit (which has been ongoing for years) and launched cooperation with the governments of 16 CEE countries to boost imports from these states. The years 2011–2014 brought an improvement in the balance of trade between China and: Hungary, Latvia, the Czech Republic, Romania, Bulgaria and Croatia. The remaining ten CEE countries recorded an increase in their trade deficits. Changes in CEE countries’ balance of trade with China resulted only slightly from political actions. Instead, they were due to the macroeconomic situation and to a deterioration of the debt crisis in the EU which, for example, caused a decline in the import of Chinese goods in some of these countries. Multilateral trade cooperation was successfully developed in the entire region only in the agricultural and food production sector – the area of greatest interest to China. The pace of bilateral cooperation with specific countries varied, with the fastest being Poland, Latvia, Romania, Hungary and Bulgaria. Actions by governments of CEE countries resulted in Chinese market opening up to hundreds of local companies which, in turn, translated into an increase in the volume of foodstuffs sold by ‘the 16’ to China from US$ 137 million in 2011 to US$ 400 million in 2014. The success achieved in the agricultural and food production sector has demonstrated the effectiveness of trade cooperation in the ‘16+1’ formula. It is, however, insufficient to generate a significant improvement of the trade balance. At present, the sector’s share in the total volume of goods sold to China by CEE states is a mere 3.7%, and any reduction of the trade deficit would require long-term and more comprehensive solutions still to be implemented by the governments of individual CEE states.

China’s foreign direct investments within the ‘16+1’ cooperation formula: strategy, institutions, results. OSW Commentary Number 191|27.11.2015

The ‘16+1’ formula of cooperation between the countries of Central and Eastern Europe (CEE) and China was launched in 2012. One of its priorities involved increasing the inflow of China’s foreign direct investments (FDI) to the region. China has been interested in carrying out investments which are likely to help Chinese companies gain competitive advantage in areas such as advanced technologies, recognizable brands and distribution channels. The following sectors were identified as areas of priority importance in CEE: construction and modernisation of transport infrastructure, including motorways; development of the network of railways, airports and sea ports; energy, in particular renewable sources of energy and nuclear energy; companies trading in commodities; the food production sector. China’s strategy mainly involves purchasing existing companies, preceded by cherry picking the most favourable candidates for investment, rather than making large greenfield investments.

Sediment and organic matter properties, and molecular formula from sampling locations in the Northern Black Sea

Remineralization of organic matter in reactive marine sediments releases nutrients and dissolved organic matter (DOM) into the ocean. Here we focused on the molecular-level characterization of DOM by high-resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) in sediment pore waters and bottom waters from contrasting redox regimes in the northern Black Sea with particular emphasis on nitrogen-bearing compounds to derive an improved understanding of the molecular transformations involved in nitrogen release. The number of nitrogen-bearing molecules is generally higher in pore waters than in bottom waters. This suggests intensified degradation of nitrogen-bearing precursor molecules such as proteins in anoxic sediments: No significant difference was observed between sediments deposited under oxic vs anoxic conditions (average O/C ratios of 0.55) suggesting that the different organic matter quality induced by contrasting redox conditions does not impact protein diagenesis in the subseafloor. Compounds in the pore waters were on average larger, less oxygenated, and had a higher number of unsaturations. Applying a mathematical model, we could show that the assemblages of nitrogen-bearing molecular formulas are potential products of proteinaceous material that was transformed by the following reactions: (a) hydrolysis and deamination, both reducing the molecular size and nitrogen content of the products and intermediates; (b) oxidation and hydration of the intermediates; and (c) methylation and dehydration.

The expanding soybean meal market : how changes in feeding practices and growth of the formula feed industry have affected demand /

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