The Anticlastic Curvature of a Strip With Lateral Thickness Variation

1954 ◽  
Vol 21 (4) ◽  
pp. 351-358
Author(s):  
Y. C. Fung ◽  
W. H. Wittrick
Keyword(s):  
Cross Section ◽  
Large Deflection ◽  
Longitudinal Direction ◽  
Middle Surface ◽  
Thickness Variation ◽  
Double Wedge ◽  
Wedge Shape ◽  
The Cross ◽  
Anticlastic Curvature ◽  
Plates Of Variable Thickness

Abstract The large deflection equations of von Kármán have been extended to apply to plates of variable thickness with initial deviations of the middle surface from a plane. These are used to determine the distortion of the cross section of a strip with lateral thickness variation, when bent uniformly in the longitudinal direction. Numerical calculations are made for the case of a strip whose cross section is of double-wedge shape and it is shown that when the longitudinal curvature becomes large the distortion of the cross section is quite different from that of a strip of uniform thickness.

scholarly journals Quantum Eigenstates of Curved and Varying Cross-Sectional Waveguides

2020 ◽  
Vol 10 (20) ◽  
pp. 7240
Author(s):  
Jens Gravesen ◽  
Morten Willatzen
Keyword(s):  
Cross Section ◽  
Direct Access ◽  
Thickness Variation ◽  
Cross Sectional ◽  
Quantum Waveguide ◽  
Present Formalism ◽  
1D Model ◽  
The Cross ◽  
Waveguide Design ◽  
The Individual

A simple one-dimensional differential equation in the centerline coordinate of an arbitrarily curved quantum waveguide with a varying cross section is derived using a combination of differential geometry and perturbation theory. The model can tackle curved quantum waveguides with a cross-sectional shape and dimensions that vary along the axis. The present analysis generalizes previous models that are restricted to either straight waveguides with a varying cross-section or curved waveguides, where the shape and dimensions of the cross section are fixed. We carry out full 2D wave simulations on a number of complex waveguide geometries and demonstrate excellent agreement with the eigenstates and energies obtained using our present 1D model. It is shown that the computational benefit in using the present 1D model to calculate both 2D and 3D wave solutions is significant and allows for the fast optimization of complex quantum waveguide design. The derived 1D model renders direct access as to how quantum waveguide eigenstates depend on varying cross-sectional dimensions, the waveguide curvature, and rotation of the cross-sectional frame. In particular, a gauge transformation reveals that the individual effects of curvature, thickness variation, and frame rotation correspond to separate terms in a geometric potential only. Generalization of the present formalism to electromagnetics and acoustics, accounting appropriately for the relevant boundary conditions, is anticipated.

Hybridizing semianalytical and conventional finite-element schemes for simulations of electromagnetic borehole resistivity measurement

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. E17-E26 ◽  
Author(s):  
Jiefu Chen ◽  
Shubin Zeng
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Resistivity Measurement ◽  
Longitudinal Direction ◽  
Integration Scheme ◽  
The Cross ◽  
Semianalytical Method ◽  
Resistivity Logging ◽  
Finite Element Schemes

A semianalytical finite-element method (FEM) has been developed to simulate electromagnetic borehole resistivity measurements in a layered underground formation. A piecewise homogeneous structure is divided into several layers. Each layer is uniform in the longitudinal direction, and the distributions of geometry and material can be arbitrary on the transverse plane, or cross section, of the layer. To develop this semianalytical finite-element scheme, the standard functional corresponding to the vector wave equation is cast to a new form in the Hamiltonian system based on dual variables that are the transverse components of electric and magnetic fields on the cross section of the layer. The 2D finite elements are used to discretize the cross section, and a high-precision integration scheme based on the Riccati equations is used to exploit the longitudinal homogeneity in the layer. By transforming a 3D layered problem into a series of 2D problems, this semianalytical FEM can save a great amount of computational costs and meanwhile achieve a higher level of accuracy when compared with conventional finite-element schemes. The flexibility of this semianalytical method can be greatly increased by hybridization with conventional finite elements, and this strategy works well for layered structures with local inhomogeneities such as borehole washouts. Several tests, including near-bit resistivity measurement and wave propagation resistivity logging, verified the effectiveness of this semianalytical FEM.

scholarly journals Elastic Buckling Behaviour of a Four-Lobed Cross Section Cylindrical Shell with Variable Thickness under Non-Uniform Axial Loads

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Mousa Khalifa Ahmed
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Transfer Matrix ◽  
Cross Section ◽  
Variable Thickness ◽  
Nonlinear Differential Equations ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Thickness Variation ◽  
Matrix Differential

The static buckling of a cylindrical shell of a four-lobed cross section of variable thickness subjected to non-uniform circumferentially compressive loads is investigated based on the thin-shell theory. Modal displacements of the shell can be described by trigonometric functions, and Fourier's approach is used to separate the variables. The governing equations of the shell are reduced to eight first-order differential equations with variable coefficients in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the nonlinear differential equations of the cylindrical shells by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The transfer matrix approach is used to get the critical buckling loads and the buckling deformations for symmetrical and antisymmetrical shells. Computed results indicate the sensitivity of the critical loads and corresponding buckling modes to the thickness variation of cross section and the radius variation at lobed corners of the shell.

scholarly journals Relationships between the Macrostructure Features and Acoustic Parameters of Resonance Spruce for Piano Soundboards

2021 ◽  
Vol 11 (4) ◽  
pp. 1749
Author(s):  
Ginevra Manzo ◽  
Jan Tippner ◽  
Petr Zatloukal
Keyword(s):  
Sound Velocity ◽  
Cross Section ◽  
Acoustic Radiation ◽  
Longitudinal Direction ◽  
Acoustic Properties ◽  
Mode Shapes ◽  
Strong Correlations ◽  
Acoustic Parameters ◽  
Radiation Coefficient ◽  
The Cross

An experimental examination of the relationship between the macrostructure characteristics and the acoustic properties of Norway spruce was performed. The macrostructure features were found to comprise the density (ρ), percentage of latewood (%LW), slope of grain (α), and angle the annual rings in a cross section (β). The main acoustic parameters of the research were the sound velocity, dynamic Young’s modulus, acoustic impedance (Z), and radiation coefficient (R). The acoustic properties for both the cross section and the longitudinal direction were calculated. Non-destructive evaluation (NDE) is the appropriate approach to define acoustic properties. Ultrasonic direct transmission and a transitory excitation method were used to calculate and compare the acoustic properties. A modal analysis was performed to predict the frequency range that corresponded to the different mode shapes. There were no significant differences between the two methods, yet an 80% reduction of the velocity, Z and R was identified between the longitudinal direction and the cross section. The equations used to define acoustic radiation according to the latewood component were defined, and strong correlations between the macrostructure and acoustic parameters were confirmed. A tight relationship was observed between the reduction of sound velocity and material density exceeding 440 kg m−3.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Energy Distribution in Electron Beams

1972 ◽  
Vol 30 ◽  
pp. 568-569
Author(s):  
Tamotsu Ohno
Keyword(s):  
Electron Beam ◽  
Energy Distribution ◽  
Cross Section ◽  
Integral Curve ◽  
Electron Beams ◽  
Electron Gun ◽  
Angular Divergence ◽  
Apparent Increase ◽  
Integral Width ◽  
The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

Research in the cross-section of community psychology and global climate change: A call for action

2009 ◽  
Author(s):  
Marci Culley ◽  
Holly Angelique ◽  
Courte Voorhees ◽  
Brian John Bishop ◽  
Peta Louise Dzidic ◽  
...  
Keyword(s):  
Climate Change ◽  
Cross Section ◽  
Global Climate Change ◽  
Community Psychology ◽  
Global Climate ◽  
The Cross

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

Seasonality in the Cross-Section of Stock Returns

CFA Digest ◽  
2008 ◽  
Vol 38 (3) ◽  
pp. 55-56
Author(s):  
Kathryn Dixon Jost
Keyword(s):  
Stock Returns ◽  
Cross Section ◽  
The Cross
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