scholarly journals Mathematical Structure of Modal Interactions in a Spinning Disk-Stationary Load System

1992 ◽  
Vol 59 (2) ◽  
pp. 390-397 ◽  
Author(s):  
Jen-San Chen ◽  
D. B. Bogy
Keyword(s):  
Friction Force ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Mathematical Structure ◽  
Transverse Mass ◽  
Modal Interactions ◽  
Spinning Disk ◽  
Physical Insight ◽  
Insight Into

In a previous paper (Chen and Bogy, 1992) we studied the effects of various load parameters, such as friction force, transverse mass, damping, stiffness and the analogous pitching parameters, of a stationary load system in contact with the spinning disk on the natural frequencies and stability of the system when the original eigenvalues of interest are well separated. This paper is a follow-up investigation to deal with the situations in which two eigenvalues of the freely spinning disk are almost equal (degenerate) and strong modal interactions occur when the load parameters are introduced. After comparing an eigenfunction expansion with the finite element numerical results, we find that for each of the transverse and pitching load parameters, a properly chosen two-mode approximation can exhibit all the important features of the eigenvalue changes. Based on this two-mode approximation we study the mathematical structure of the eigenvalues in the neighborhood of degenerate points in the natural frequency-rotation speed plane. In the case of friction force, however, it is found that at least a four-mode approximation is required to reproduce the eigenvalue structure. The observations and analyses presented provide physical insight into the modal interactions induced by various load parameters in a spinning disk-stationary load system.

Effects of Load Parameters on the Natural Frequencies and Stability of a Flexible Spinning Disk With a Stationary Load System

1992 ◽  
Vol 59 (2S) ◽  
pp. S230-S235 ◽  
Author(s):  
Jen-San Chen ◽  
D. B. Bogy
Keyword(s):  
Friction Force ◽  
Centrifugal Force ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
Positive Definite ◽  
Transverse Mass ◽  
Gyroscopic System ◽  
Theoretical Understanding ◽  
Spinning Disk ◽  
Derivatives Of

The orthogonality properties among the eigenfunctions for a gyroscopic system are derived for a stiffness operator that is not positive definite. The derivatives of the eigenvalues with respect to certain parameters in the system are then obtained. The results are applied to a spinning disk in contact with a stationary load system, which contains such parameters as friction force, transverse mass, damping, stiffness, and the analogous pitching elements, to predict the effects of these parameters and the stiffening of the disk due to the centrifugal force on the natural frequencies and stability of the spinning disk. The results obtained provide a theoretical understanding for previously reported observations based on numerical solutions.

scholarly journals Characteristic Constraint Modes for Component Mode Synthesis

1999 ◽  
Author(s):  
Matthew P. Castanier ◽  
Yung-Chang Tan ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Cantilever Plate ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Physical Insight ◽  
Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

Thickness Expansions for Higher-Order Effects in Vibrating Cylindrical Shells

1993 ◽  
Vol 60 (2) ◽  
pp. 463-469 ◽  
Author(s):  
J. G. McDaniel ◽  
J. H. Ginsberg
Keyword(s):  
Natural Frequencies ◽  
Order Effects ◽  
Solid Cylinder ◽  
View Point ◽  
Spatial Coordinates ◽  
Physical Insight ◽  
Sinusoidal Functions ◽  
Limiting Case ◽  
Higher Order Effects ◽  
Insight Into

In the spirit of Mindlin and others who have used series expansions to express transverse dependences in thin bodies, the present work uses Ritz expansions in a variational formulation for cylindrical shell vibrations. By expanding displacements in spatial coordinates, integral expressions for strain and kinetic energy are converted to quadratic sums involving time-dependent generalized coordinates. Hamilton’s principle provides ordinary differential equations for these coordinates. This view-point yields physical insight into the mechanisms of energy storage and avoids the geometrically thin assumption inherent to many formulations. A set of Legendre polynomials multiplied by a radial factor represent the radial dependences of displacement components, while circumferential variations are represented by sinusoidal functions. Excellent agreement in natural frequencies is found between this approach and analytical solutions over the entire range of shell thicknesses, including the limiting case of a solid cylinder. Comparisons to several thin shell theories are given, leading to conclusions about the range of validity of these theories.

scholarly journals Design of a Novel Miniaturized Frequency Selective Surface Based on 2.5-Dimensional Jerusalem Cross for 5G Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Peng Zhao ◽  
Yihang Zhang ◽  
Rongrong Sun ◽  
Wen-Sheng Zhao ◽  
Yue Hu ◽  
...  
Keyword(s):  
Resonant Frequency ◽  
Equivalent Circuit ◽  
Equivalent Circuit Model ◽  
Frequency Selective Surface ◽  
Size Reduction ◽  
Two Dimensional ◽  
Physical Insight ◽  
Frequency Selective ◽  
Significant Size ◽  
Insight Into

A compact frequency selective surface (FSS) for 5G applications has been designed based on 2.5-dimensional Jerusalem cross. The proposed element consists of two main parts: the successive segments of the metal traces placed alternately on the two surfaces of the substrate and the vertical vias connecting traces. Compared with previous published two-dimensional miniaturized elements, the transmission curves indicate a significant size reduction (1/26 wavelengths at the resonant frequency) and exhibit good angular and polarization stabilities. Furthermore, a general equivalent circuit model is established to provide direct physical insight into the operating principle of this FSS. A prototype of the proposed FSS has been fabricated and measured, and the results validate this design.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Good Idea But Not Here! A Pilot Study of Swedish Tourism Stakeholders’ Perceptions of Halal Tourism

2021 ◽  
Vol 13 (5) ◽  
pp. 2646
Author(s):  
Saeid Abbasian
Keyword(s):  
Content Analysis ◽  
Pilot Study ◽  
Tourism Industry ◽  
Target Group ◽  
Exploratory Research ◽  
Swedish Study ◽  
Increased Risk ◽  
Insight Into

The following study is the first Swedish study on Halal tourism in Sweden. The purpose of this exploratory research is to get insight into the perception of Halal tourism in Sweden among representatives of tourism stakeholders. The overall methodology approach in this research is qualitative, consisting of 25 qualitative questionnaires, 21 short letters, four follow-up interviews, and a web observation, and content analysis was employed. The results indicate that there is a low knowledge of Halal tourism in Sweden including Swedish tourism industry. The concept is very challenging, and profits are low. It might result in problem scenarios such as detrimental effects on non-Halal tourism, cultural difficulties and increased risk of xenophobia, anti-Islamism, and tension in the society. There is low interest for Sweden among Muslim tourists as the interest and priority for Halal tourism is rather low from Swedish tourism industry. Despite Halal tourism’s importance internationally, these representatives are rather cautious and doubtful about promotion of Sweden towards this niche. Still, a majority seems to be positive to a lighter version of Muslim-friendly tourism with secular/moderate Muslims as a target group.

scholarly journals The spontaneous resolution of a vortex vein varix: case report

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Sara L Weidmayer ◽  
Hakan Demirci
Keyword(s):  
Case Report ◽  
Natural History ◽  
Extended Period ◽  
Spontaneous Resolution ◽  
Case Presentation ◽  
Clinical Resolution ◽  
History Of ◽  
Vortex Vein ◽  
Insight Into

Abstract Background The natural course of a vortex vein varix, though not well understood, has been known to remain stable. However, here we report a novel case of a vortex vein varix that resolved after an extended period of monitoring. Case presentation An asymptomatic 96-year-old Caucasian man was found to have a vortex vein varix. At his previous examination 13 months prior, his fundus was normal. At 13 months of observation, his vortex vein varix become clinically undetectable. Further follow-up confirmed continued absence of the varix. Conclusion This case demonstrates the development then clinical resolution of a vortex vein varix with no clear identifiable factors for its evolution. This case is novel and offers new insight into the natural history of some vortex vein varices, implicating venous congestion as an instigator and venous collateralization as its alleviator, suggesting that vortex vein varices are likely more common than previously reported since some may be temporary and under-identified.

scholarly journals The Implementation of Visual Comfort Evaluation in the Evidence-Based Design Process Using Lighting Simulation

2021 ◽  
Vol 11 (11) ◽  
pp. 4982
Author(s):  
Anahita Davoodi ◽  
Peter Johansson ◽  
Myriam Aries
Keyword(s):  
Performance Metrics ◽  
Analysis Data ◽  
Evidence Based ◽  
Visual Comfort ◽  
Simulation Tools ◽  
Post Occupancy Evaluation ◽  
Lighting Simulation ◽  
Insight Into

Validation of the EBD-SIM (evidence-based design-simulation) framework, a conceptual framework developed to integrate the use of lighting simulation in the EBD process, suggested that EBD’s post-occupancy evaluation (POE) should be conducted more frequently. A follow-up field study was designed for subjective–objective results implementation in the EBD process using lighting simulation tools. In this real-time case study, the visual comfort of the occupants was evaluated. The visual comfort analysis data were collected via simulations and questionnaires for subjective visual comfort perceptions. The follow-up study, conducted in June, confirmed the results of the original study, conducted in October, but additionally found correlations with annual performance metrics. This study shows that, at least for the variables related to daylight, a POE needs to be conducted at different times of the year to obtain a more comprehensive insight into the users’ perception of the lit environment.

Endwall Blockage in Axial Compressors

1999 ◽  
Vol 121 (3) ◽  
pp. 499-509 ◽  
Author(s):  
S. A. Khalid ◽  
A. S. Khalsa ◽  
I. A. Waitz ◽  
C. S. Tan ◽  
E. M. Greitzer ◽  
...  
Keyword(s):  
Tip Clearance ◽  
Design Parameters ◽  
Tip Clearance Flow ◽  
Axial Compressors ◽  
Clearance Flow ◽  
Flow Features ◽  
Physical Insight ◽  
Level Loading ◽  
Stagger Angle ◽  
Insight Into

This paper presents a new methodology for quantifying compressor endwall blockage and an approach, using this quantification, for defining the links between design parameters, flow conditions, and the growth of blockage due to tip clearance flow. Numerical simulations, measurements in a low-speed compressor, and measurements in a wind tunnel designed to simulate a compressor clearance flow are used to assess the approach. The analysis thus developed allows predictions of endwall blockage associated with variations in tip clearance, blade stagger angle, inlet boundary layer thickness, loading level, loading profile, solidity, and clearance jet total pressure. The estimates provided by this simplified method capture the trends in blockage with changes in design parameters to within 10 percent. More importantly, however, the method provides physical insight into, and thus guidance for control of, the flow features and phenomena responsible for compressor endwall blockage generation.

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