On the stability of liquid ridges

1999 ◽  
Vol 391 ◽  
pp. 293-318 ◽  
Author(s):  
R. VALÉRY ROY ◽  
LEONARD W. SCHWARTZ
Keyword(s):  
Contact Angle ◽  
Cross Section ◽  
Energy Functional ◽  
Liquid Region ◽  
Contact Lines ◽  
Property A ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Special Cases ◽  
The Stability

We consider the stability of a rectilinear liquid region whose boundary is composed of a solid cylindrical substrate of arbitrary shape and a free surface whose cross-section, in the absence of gravity, is a circular arc. The liquid–solid contact angle is a prescribed material property. A variational technique, using an energy functional, is developed that predicts the minimum wavelength for transverse instability under the action of capillarity. Conversely, certain configurations are absolutely stable and a simple stability criterion is derived. Stability is guaranteed if, for given substrate geometry and given contact angle, the unperturbed meniscus pressure is an increasing function of the liquid cross-sectional area. The analysis is applied to a variety of liquid/substrate configurations including (i) a liquid ridge with contact lines pinned to the sharp edges of a slot or groove, (ii) liquid ridges with free contact lines on flat and wedge-shaped substrates as well as substrates of circular or elliptical cross-section. Results are consistent with special cases previously treated including those that employ a slope-small-slope approximation.

scholarly journals HYDRAULICS AND SEDIMENTARY STABILITY OF COASTAL INLETS

1972 ◽  
Vol 1 (13) ◽  
pp. 38 ◽  
Author(s):  
M.P. O'Brien ◽  
R.G. Dean
Keyword(s):  
Cross Section ◽  
Stability Index ◽  
Hydraulic Loss ◽  
Cross Sectional ◽  
Equilibrium Relationship ◽  
Depositional Patterns ◽  
Storage Area ◽  
Loss Coefficients ◽  
The Stability ◽  
Coastal Inlets

A method is presented for investigating the stability of coastal inlets against closure due to transport and deposition of sand in the inlet cross-section. The method utilizes earlier contributions by: (1) Keulegan representing the hydraulics of inlets, (2) O'Brien which describes an equilibrium relationship between the cross-sectional area of an inlet and the bay tidal prism, and (3) Escoffier which relates to the stability of an inlet under changes in conditions which tend to close or enlarge an inlet. A "stability index" is defined which incorporates the buffer storage area available in the inlet cross-section, prior to the onset of closure and also includes the capability of the inlet to transport excess sand from its cross-section. In order to apply the method, geometric and hydraulic data representing the inlet are necessary; the minimum data required include a survey of the inlet throat cross-section and the lag between high (or low) water in the ocean and the following slack water in the inlet. In addition, it is necessary to conduct measurements or make assumptions concerning the minor and gradual hydraulic loss coefficients. Based on assumed depositional patterns in the inlet, the method is applied to five real inlets and the stability indices are presented.

scholarly journals Numerical simulation of cutting layer in internal corners milling

Mechanik ◽  
2019 ◽  
Vol 92 (7) ◽  
pp. 412-414
Author(s):  
Jan Burek ◽  
Rafał Flejszar ◽  
Barbara Jamuła
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
The Stability

The analytical and numerical model of the cross-section of the machined layer in the process of milling of concave rounding is presented. Simulation tests were carried out to determine the cross-sectional area of the cutting layer. A strategy has been developed that allows to increase the stability of the cross-section area of the cutting layer when the mill enters the inner corner area.

The Structure and Function of the Basement Membrane Muscle System in Amphiporus lactifloreus (Nemertea)

1952 ◽  
Vol s3-93 (21) ◽  
pp. 1-15
Author(s):  
J. B. COWEY
Keyword(s):  
Basement Membrane ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Minimum Length ◽  
Muscle Fibres ◽  
Body Volume ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Sectional Shape

The body wall of A. lactifloreus has the following structure from the outside inwards. (i) A basement membrane of five to six layers immediately underlying the epithelium. Each layer consists of right-hand and left-hand geodesic fibres making a lattice, whose constituent parallelograms have a side length of from 5 to 6µ. The fibres are attached to one another where they cross; so there can be no slipping relative to one another. (ii) A layer of circular muscle-fibres running round the animal containing two systems of argyrophil fibres--one of fibres at intervals of 10µ. running parallel to the muscle-fibres and the other of fibres running radially through the layer from the basement membrane to the myoseptum. (iii) A myoseptum which is identical in structure with a single layer of the basement membrane (iv) A layer of longitudinal muscle, whose fibres are arranged in layers on each side of a series of longitudinal radial membranes. Membranes identical in structure with the basement membrane invest the nerve cords, the gut, the gonads, and the proboscis. The interrelations of argyrophil and muscle-fibres in the muscle layers is described and their functioning discussed. The system of inextensible geodesic fibres is analysed from a functional standpoint. The maximum volume enclosed by a cylindrical element (cross-section circular), of such a length that the geodesic makes one complete turn round it, varies with the value of the angle θ between the fibres and the longitudinal axis. When θ is 0° the volume is zero; it increases to a maximum when θ is 54° 44' and decreases again to zero when θ is 90°. The length of the element under these conditions varies from zero when θ is 90° to a maximum (the length of one turn of the geodesic) when θ is 0°. The body-volume of the worm is constant. Thus it has a maximum and minimum length when its cross-section is circular, and at any length between these values its cross-section becomes more or less elliptical. It is maximally elliptical when θ is 54° 44', i.e. when the volume the system could contain, at circular cross-section, is maximal. From measurements of the ratio of major to minor axes of this maximally elliptical cross-section, the maximum and minimum lengths of the worm relative to the relaxed length and values of θ at maximum and minimum length are calculated. The worm is actually unable to contract till its cross-section is circular; but measurements of its cross-sectional shape at the minimum length it can attain, permit calculation of the theoretical length and value of θ for this cross-sectional shape. Calculated values of length and the angle 6 agree well with the directly observed values.

scholarly journals A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory

2008 ◽  
Vol 15 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Jiao Sujuan ◽  
Li Jun ◽  
Hua Hongxing ◽  
Shen Rongying
Keyword(s):  
Cross Section ◽  
Spectral Element ◽  
Higher Order ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Coupled Equations ◽  
Aspect Ratios ◽  
Sectional Plane ◽  
The Cross ◽  
Element Matrix

The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

Dynamic Detection and Analysis of Raw Silk’s Flatness

2011 ◽  
Vol 175-176 ◽  
pp. 385-388
Author(s):  
Xin Zhang ◽  
Yi Quan Xu ◽  
Kai Meng ◽  
Qing Guan Chen
Keyword(s):  
Cross Section ◽  
Axial Length ◽  
Minor Axis ◽  
Cross Sectional Area ◽  
Elliptical Cross Section ◽  
Sectional Area ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Photoelectric Sensor ◽  
Dynamic Detection

The shape of most raw silk’s cross-section can be regarded as ellipse approximately. Axial length of the raw silk’s cross-section was detected and recorded dynamically by photoelectric sensor combined with the software of LabVIEW. Two photoelectric sensors were located orthogonally to measure axial lengths of the ellipse. The major and minor values can be considered as the major and minor axis values of the raw silk’s elliptical cross-section respectively. Thereby, the flatness and the area of raw silk’s cross-section can be calculated according to the values of major and minor axes. In addition, the raw silk’s evenness was characterized based on the variation of the cross-sectional area.

Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

1966 ◽  
Vol 33 (4) ◽  
pp. 881-887 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Thermoelastic Stress ◽  
Cross Sectional ◽  
Special Cases ◽  
End Conditions ◽  
Instantaneous Temperature ◽  
The Cross ◽  
Sectional Shape

It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ′αLΔT, where kδ and kδ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ′ = 1/8.

On the stability of flow in an elliptic pipe which is nearly circular

1994 ◽  
Vol 281 ◽  
pp. 357-369 ◽  
Author(s):  
A. Davey ◽  
H. Salwen
Keyword(s):  
Cross Section ◽  
Specific Problem ◽  
Sectional Area ◽  
Leading Order ◽  
Straight Pipe ◽  
Cross Sectional ◽  
Double Eigenvalue ◽  
Circular Problem ◽  
Qualitative Structure ◽  
The Stability

In an earlier paper (Davey 1978) the first author investigated the linear stability of flow in a straight pipe whose cross-section was an ellipse, of small ellipticity e, by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. That paper contained some serious errors which we correct herein. We show analytically that for the most important mode n = 1, for which the circular problem has a double eigenvalue c0 as the ‘swirl’ can be in either direction, the ellipticity splits the double eigenvalue into two separate eigenvalues c0 ± e2c12, to leading order, when the cross-sectional area of the pipe is kept fixed. The imaginary part of c12 is non-zero and so the ellipticity always makes the flow less stable. This specific problem is generic to a much wider class of fluid dynamical problems which are made less stable when the symmetry group of the dynamical system is reduced from S1 to Z2.In the Appendix, P. G. Drazin describes simply the qualitative structure of this problem, and other problems with the same symmetries, without technical detail.

A New Method of Measuring the Cross-Sectional Area of Connective Tissue Structures

1988 ◽  
Vol 110 (2) ◽  
pp. 104-109 ◽  
Author(s):  
N. G. Shrive ◽  
T. C. Lam ◽  
E. Damson ◽  
C. B. Frank
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Connective Tissues ◽  
Maximum Width ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
The Cross

There appears to be no generally accepted method of measuring in-situ the cross-sectional area of connective tissues, particularly small ones, before mechanical testing. An instrument has therefore been devised to measure the cross-sectional area of one such tissue, the rabbit medial collateral ligament, directly and nondestructively. However, the methodology is general and could be applied to other tissues with appropriate changes in detail. The concept employed in the instrument is to measure the thickness of the tissue as a function of position along the width of the tissue. The plot obtained of thickness versus width position is integrated to provide the cross-sectional area. This area is accurate to within 5 percent, depending mainly on alignment of the instrument and pre-load of the ligament. Results on the mid-substance of the rabbit medial collateral ligaments are repeatable and reproducible. Values of maximum width and thickness are less variable than those obtained with a vernier caliper. The measured area is considerably less than that estimated assuming rectangular cross-section and slightly less than that estimated on the assumption of elliptical cross-section.

scholarly journals Saint-Venant’s torsion of thin-walled nonhomogeneous open elliptical cross section

2021 ◽  
Vol 11 (5) ◽  
pp. 151-158
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel ◽  
Attila Baksa ◽  
Dávid Gönczi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Elliptical Cross Section ◽  
Curvilinear Coordinates ◽  
Torsion Problem ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Thin Walled ◽  
The One

This paper deals with the Saint-Venant’s torsion of thin-walled isotropic nonhomogeneous open elliptical cross section whose shear modulus depends on the one of the curvilinear coordinates which define the cross-sectional area of the beam. The approximate solution of torsion problem is obtained by variational method. The usual simplification assumptions are used to solve the uniform torsion problem of bars with thin-walled elliptical cross-sections. An example illustrates the application of the derived formulae of shearing stress and torsional rigidity.

Experimental and Numerical Analysis of Titanium Microtube Elliptical Flaring

2010 ◽  
Author(s):  
Weichao Wu ◽  
Ying Huang ◽  
Rajiv Malhotra ◽  
Yongjun Wang ◽  
Jian Cao
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Fem Simulation ◽  
Circular Cross Section ◽  
Forming Process ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Tube Flaring ◽  
Sectional Shape ◽  
The Relationship

Traditional tube flaring processes focuses on expanding one end of the tube without changing its cross-sectional shape. This paper presents a new two-step tube flaring process for expanding one end of a titanium alloy microtube while simultaneously changing its cross-sectional shape from circular to elliptical. Experiments were performed to investigate and verify this process. Furthermore, an analytical model was developed to analyze the forming process and investigate the relationship between punch feed and maximum plastic strain during the flaring process. The analysis shows that the two-step flaring process used is effective in expanding the circular cross section to an elliptical cross section without failure. It is also shown that the developed analytical model can predict the fracture of the tube end during the flaring process approximately. Finally, a FEM simulation was performed to further investigate the two-step flaring process.

Sign in / Sign up

Export Citation Format

Share Document