scholarly journals Discussion: “Influence Coefficients for Hemispherical Shells With Small Openings at the Vertex” (Galletly, G. D., 1955, ASME J. Appl. Mech., 22, pp. 20–24)

1955 ◽  
Vol 22 (3) ◽  
pp. 443
Author(s):  
W. R. Burrows ◽  
R. L. Graves ◽  
P. G. Stevens
Keyword(s):  
Influence Coefficients ◽  
Hemispherical Shells

Influence Coefficients for Hemispherical Shells With Small Openings at the Vertex

1955 ◽  
Vol 22 (1) ◽  
pp. 20-24
Author(s):  
G. D. Galletly
Keyword(s):  
Constant Thickness ◽  
Influence Coefficient ◽  
Circular Opening ◽  
Central Angle ◽  
Calculation Time ◽  
Numerical Example ◽  
Hemispherical Shell ◽  
Influence Coefficients ◽  
Hemispherical Shells

Abstract Three methods of obtaining the influence coefficients for a thin, constant-thickness, hemispherical shell with a circular opening at the vertex were investigated and utilized in a numerical example. Bearing in mind both accuracy and calculation time, it was concluded that when the total central angle subtended by the opening is less than approximately 30 deg, good results for the influence coefficient calculation will be obtained by using Method II in the text of the paper.

Influence Coefficients for Open-Crown Hemispheres

1960 ◽  
Vol 82 (1) ◽  
pp. 73-81 ◽  
Author(s):  
G. D. Galletly
Keyword(s):  
Central Angle ◽  
Intersection Problem ◽  
Influence Coefficients ◽  
Bending Load ◽  
Axis Of Symmetry ◽  
Hemispherical Shells ◽  
Interior Points

Stresses and deflections of hemispherical shells with nozzle openings lying on the axis of symmetry may be determined accurately and rapidly with the aid of the tables given in the paper. The tables give the influence coefficients (i.e., stresses and deflections obtained with unit applied loads) for the edge and interior points for various types of edge bending load. The radius-thickness ratios of the hemispherical shells considered varied from 15 to 250; the total central angle of the opening varied from twenty to one hundred degrees. An illustration of the utility of the coefficients is given by considering a hemisphere-cylinder intersection problem.

scholarly journals Environmental Behavior Spillover or Public Information Induction: Consumers’ Intention to Pay a Premium for Rice Grown with Green Manure as Crop Fertilizer

Foods ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1285
Author(s):  
Fuduo Li ◽  
Kangjie Zhang ◽  
Aibo Hao ◽  
Changbin Yin ◽  
Guosheng Wu
Keyword(s):  
Green Manure ◽  
Environmental Governance ◽  
Agricultural Sector ◽  
Environmental Behavior ◽  
Public Information ◽  
Chinese Consumers ◽  
Environmental Behaviors ◽  
Policy Makers ◽  
Influence Coefficients ◽  
Structural Research

Nowadays, there is a growing interest in pro-environmental foods produced by pro-environmental practices. However, consumers’ payment motivations towards such foods are currently poorly understood. This manuscript provided a critical investigation of Chinese consumers’ intention to pay a premium (ITPP) for rice grown with green manure as crop fertilizer (GMR). One focus was the establishment of an explanatory structural research framework that includes effects of environmental behavior spillover (EBS) and public information induction (PII); another focus was to analyze the impacts of the selected structural elements on ITPP by introducing education as a moderator. Results suggest that consumers’ ITPP can be largely influenced by PII, therefore, for GMR marketers and policy makers, measures should be developed to widen consumers’ access to public information related to GMR and to improve their capacity of screening effective information. EBS, when ITPP remains low, emerged as a pivotal predictor of consumers’ ITPP. This observation provides us with the enlightenment that breeding consumers’ daily environmental behaviors is highly valued to inspire their payment intention in the early stages of GMR market development. Another finding is that, with the introduction of the educational variable, the influence coefficients of EBS and PII on ITPP increased from 0.42 and 0.53 to 0.61 and 0.66, respectively, which means that it is possible to boost consumers’ payment intention by improving their educational attainment. This study contributes to the existing literature by providing empirical evidence for the GMR industrial upgrading strategy and have significant implications for the environmental governance of the agricultural sector.

scholarly journals Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter

2016 ◽  
Author(s):  
L. Salles ◽  
M. Vahdati
Keyword(s):  
Numerical Models ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Mode Shapes ◽  
Minimal Amount ◽  
Aeroelastic System ◽  
Cpu Time ◽  
Influence Coefficients ◽  
Non Linear ◽  
The Time Domain

The aim of this paper is to study the effects of mistuning on fan flutter and to compare the prediction of two numerical models of different fidelity. The high fidelity model used here is a three-dimensional, whole assembly, time-accurate, viscous, finite-volume compressible flow solver. The Code used for this purpose is AU3D, written in Imperial College and validated for flutter computations over many years. To the best knowledge of authors, this is the first time such computations have been attempted. This is due to the fact that, such non-linear aeroelastic computations with mistuning require large amount of CPU time and cannot be performed routinely and consequently, faster (low fidelity) models are required for this task. Therefore, the second model used here is the aeroelastic fundamental mistuning model (FMM) and it based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from the time domain non-linear Code by shaking one blade in the datum (tuned) frequency and mode. Once the influence coefficients have been obtained, the computations of aero damping require minimal amount of CPU time and many different mistuning patterns can be studied. The objectives of this work are to: 1. Compare the results between the two models and establish the capabilities/limitations of aeroelastic FMM, 2. Check if the introduction of mistuning would bring the experimental and computed flutter boundaries closer, 3. Establish a relationship between mistuning and damping. A rig wide-chord fan blade, typical of modern civil designs, was used as the benchmark geometry for this study. All the flutter analyses carried out in this paper are with frequency mistuning, but the possible consequences of mistuned mode shapes are briefly discussed at the end of this paper. Only the first family of modes (1F, first flap) is considered in this work. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. For the mode shape mistuning computations, an FE analysis of the whole assembly different mass blades is performed. The results of this work clearly show the importance of mistuning on flutter. It also demonstrates that when using rig test data for aeroelastic validation of CFD codes, the amount mistuning present must be known. Finally, it should be noted that the aim of this paper is the study of mistuning and not steady/unsteady validation of a CFD code and therefore minimal aerodynamic data are presented.

Analysis of Mistuned Blade Vibrations Based on Normally Distributed Blade Individual Natural Frequencies

2015 ◽  
Author(s):  
Felix Figaschewsky ◽  
Arnold Kühhorn
Keyword(s):  
Probability Distribution ◽  
Development Process ◽  
Structural Model ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Lumped Mass ◽  
Mass Model ◽  
Influence Coefficients ◽  
Random Mistuning ◽  
Rotor Assembly

With increasing demands for reliability of modern turbomachinery blades the quantification of uncertainty and its impact on the designed product has become an important part of the development process. This paper aims to contribute to an improved approximation of expected vibration amplitudes of a mistuned rotor assembly under certain assumptions on the probability distribution of the blade’s natural frequencies. A previously widely used lumped mass model is employed to represent the vibrational behavior of a cyclic symmetric structure. Aerodynamic coupling of the blades is considered based on the concept of influence coefficients leading to individual damping of the traveling wave modes. The natural frequencies of individual rotor blades are assumed to be normal distributed and the required variance could be estimated due to experiences with the applied manufacturing process. Under these conditions it is possible to derive the probability distribution of the off-diagonal terms in the mistuned equations of motions, that are responsible for the coupling of different circumferential modes. Knowing these distributions recent limits on the maximum attainable mistuned vibration amplitude are improved. The improvement is achieved due to the fact, that the maximum amplification depends on the mistuning strength. This improved limit can be used in the development process, as it could partly replace probabilistic studies with surrogate models of reduced order. The obtained results are verified with numerical simulations of the underlying structural model with random mistuning patterns based on a normal distribution of individual blade frequencies.

Mistuning and Damping of a Radial Turbine Wheel. Part 1: Fundamental Analyses and Design of Intentional Mistuning Pattern

2021 ◽  
Author(s):  
Alex Nakos ◽  
Bernd Beirow ◽  
Arthur Zobel
Keyword(s):  
High Stress ◽  
Forced Response ◽  
Experimental Investigations ◽  
Detailed Knowledge ◽  
Turbine Wheel ◽  
Operation Conditions ◽  
Radial Turbine ◽  
Influence Coefficients ◽  
Modes Of Vibration ◽  
The Impact

Abstract The radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high stress levels compared to the tuned counterpart. Contrary, the use of intentional mistuning (IM) has proved to be an efficient measure to mitigate the forced response. Independently, the presence of aerodynamic damping is significant with respect to limit the forced response since structural damping ratios of integrally bladed rotors typically take extremely low values. Hence, a detailed knowledge of respective damping ratios would be desirable while developing a robust rotor design. For this, far-reaching experimental investigations are carried out to determine the damping of a comparative wheel within a wide pressure range by simulating operation conditions in a pressure tank. Reduced order models are built up for designing suitable intentional mistuning patterns by using the subset of nominal system modes (SNM) approach introduced by Yang and Griffin [1], which conveniently allows for accounting both differing mistuning patterns and the impact of aeroelastic interaction by means of aerodynamic influence coefficients (AIC). Further, finite element analyses are carried out in order to identify appropriate measures how to implement intentional mistuning patterns, which are featuring only two different blade designs. In detail, the impact of specific geometric modifications on blade natural frequencies is investigated.

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