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 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.

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.

Time after time: support for memory accounts of temporal preparation.

2019 ◽  
Author(s):  
Joe Butler ◽  
Samuel Ngabo ◽  
Marcus Missal
Keyword(s):  
Response Times ◽  
Reaction Times ◽  
Evidence Base ◽  
Higher Order ◽  
Order Effects ◽  
Previous Trial ◽  
Adaptive Responses ◽  
Temporal Preparation ◽  
Subsequent Trial ◽  
Higher Order Effects

Complex biological systems build up temporal expectations to facilitate adaptive responses to environmental events, in order to minimise costs associated with incorrect responses, and maximise the benefits of correct responses. In the lab, this is clearly demonstrated in tasks which show faster response times when the period between warning (S1) and target stimulus (S2) on the previous trial was short and slower when the previous trial foreperiod was long. The mechanisms driving such higher order effects in temporal preparation paradigms are still under debate, with key theories proposing that either i) the foreperiod leads to automatic modulation of the arousal system which influences responses on the subsequent trial, or ii) that exposure to a foreperiod results in the creation of a memory trace which is used to guide responses on the subsequent trial. Here we provide data which extends the evidence base for the memory accounts, by showing that previous foreperiod exposures are cumulative with reaction times shortening after repeated exposures; whilst also demonstrate that the higher order effects associated with a foreperiod remain active for several trials.

scholarly journals Responsible innovation, anticipation and responsiveness: case studies of algorithms in decision support in justice and security, and an exploration of potential, unintended, undesirable, higher-order effects

AI and Ethics ◽  
2021 ◽  
Author(s):  
Marc Steen ◽  
Tjerk Timan ◽  
Ibo van de Poel
Keyword(s):  
Decision Support ◽  
Case Studies ◽  
Personal Data ◽  
Higher Order ◽  
Popular Media ◽  
Responsible Innovation ◽  
Order Effects ◽  
Key Dimensions ◽  
Higher Order Effects

AbstractThe collection and use of personal data on citizens in the design and deployment of algorithms in the domain of justice and security is a sensitive topic. Values like fairness, autonomy, privacy, accuracy, transparency and property are at stake. Negative examples of algorithms that propagate or exacerbate biases, inequalities or injustices have received ample attention, both in academia and in popular media. To supplement this view, we will discuss two positive examples of Responsible Innovation (RI): the design and deployment of algorithms in decision support, with good intentions and careful approaches. We then explore potential, unintended, undesirable, higher-order effects of algorithms—effects that may occur despite good intentions and careful approaches. We do that by engaging with anticipation and responsiveness, two key dimensions of Responsible Innovation. We close the paper with proposing a framework and a series of tentative recommendations to promote anticipation and responsiveness in the design and deployment of algorithms in decision support in the domain of justice and security.

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.

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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