An Approximate Nonuniform Bending Theory and Its Application to the Swept-Plate Problem

1955 ◽  
Vol 22 (3) ◽  
pp. 383-388
Author(s):  
H. J. Plass
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Calculus Of Variations ◽  
Cross Section ◽  
Close Agreement ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Nonuniform Torsion

Abstract Differential equations and boundary conditions are derived, by means of the calculus of variations, for cylindrical bars in nonuniform bending. The resulting equations are used, together with similar nonuniform torsion equations, to obtain deflections and stresses in swept cantilever plates of uniform rectangular cross section. Comparisons are made with experimental results for plates with four different sweep angles. The theory predicts deflections quite close to those found experimentally. Stresses computed from the equations, however, are not in as close agreement. It is also noticed that the theory is less accurate for large sweep angles than for small ones.

The Investigation of the Kinetic Energy of Slug in a Horizontal Channel Using VOF Method

2018 ◽  
Author(s):  
Nariman Ashrafi ◽  
Mohammad Reza Ansari ◽  
Armin Chegini ◽  
Ali Sadeghi
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Vof Method ◽  
Experimental Results ◽  
Two Phase ◽  
Trapped Air ◽  
Helmholtz Condition

In this article, two-phase slug regime in a duct with rectangular cross-section is investigated numerically, using the volume of fluid (VOF) method. Equations of mass, momentum and advection of volume fraction are solved accompanying k-∈ realizable turbulence equations. To ensure the creditability, numerical results have been compared with experimental results using same geometry. With occurrence of instability in the entrance of duct, Kelvin-Helmholtz condition satisfies and with increasing instability, slug phenomenon occurs. With closing the cross-section of duct, slug causes pressure gradient in it. Trapped air behind a slug transfers the momentum and increases the kinetic energy of slug. In this research the kinetic energy of a slug is investigated.

Effect of Slenderness Ratio on the Natural Frequencies of Pre-Twisted Cantilever Beams of Uniform Rectangular Cross-Section

1971 ◽  
Vol 13 (1) ◽  
pp. 51-59 ◽  
Author(s):  
B. Dawson ◽  
N. G. Ghosh ◽  
W. Carnegie
Keyword(s):  
Differential Equations ◽  
Shear Deformation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Slenderness Ratio ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Rotary Inertia ◽  
Cantilever Beams

This paper is concerned with the vibrational characteristics of pre-twisted cantilever beams of uniform rectangular cross-section allowing for shear deformation and rotary inertia. A method of solution of the differential equations of motion allowing for shear deformation and rotary inertia is presented which is an extension of the method introduced by Dawson (1)§ for the solution of the differential equations of motion of pre-twisted beams neglecting shear and rotary inertia effects. The natural frequencies for the first five modes of vibration are obtained for beams of various breadth to depth ratios and lengths ranging from 3 to 20 in and pre-twist angle in the range 0–90°. The results are compared with those obtained by an alternative method (2), where available, and also to experimental results.

Condensation Phenomena in High Speed Flow of Steam—Experimental Apparatus

1973 ◽  
Vol 187 (1) ◽  
pp. 199-205 ◽  
Author(s):  
B. A. Campbell ◽  
F. Bakhtar
Keyword(s):  
Cross Section ◽  
Test Section ◽  
High Speed ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Theoretical Treatment ◽  
Wet Steam ◽  
High Speed Flow ◽  
Speed Flow ◽  
Experimental Apparatus

The paper describes a steam circuit for studies of nucleation and behaviour of wet steam. The test section is a duct of rectangular cross-section in which particular geometries are produced by fitting shaped profiles to its sides. To deliver steam to the test section, at required conditions, a turbine, cooler and superheater are included in the circuit. The experimental results presented are concerned with the variations of Wilson point as a function of pressure. Comparisons are made with the results of a theoretical treatment already published (1)‡ and agreement is shown to be good.

scholarly journals WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS

1972 ◽  
Vol 1 (13) ◽  
pp. 99 ◽  
Author(s):  
Charles K. Sollitt ◽  
Ralph H. Cross
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Cross Section ◽  
Wave Breaking ◽  
Wave Reflection ◽  
Rectangular Cross Section ◽  
Wave Component ◽  
Additional Consideration ◽  
Reflection And Transmission ◽  
Theoretical Results

A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

The Pressure Distribution in a Convergent-Divergent Steam Nozzle

1938 ◽  
Vol 138 (1) ◽  
pp. 229-266 ◽  
Author(s):  
A. M. Binnie ◽  
M.W. Woods
Keyword(s):  
Pressure Distribution ◽  
Cross Section ◽  
Cross Sections ◽  
Thermal Equilibrium ◽  
Close Agreement ◽  
Wilson Line ◽  
Rectangular Cross Section ◽  
Pressure Rise ◽  
Sharp Rise ◽  
Isentropic Expansion

The paper describes experiments performed to determine the pressure distribution in a convergent-divergent steam nozzle of rectangular cross-section. By means of pressure tappings drilled along the axis, it was found that, in the course of its passage through the nozzle, initially superheated steam expanded continuously until condensation commenced, when a sharp rise of pressure (of the order of 1 lb. per sq. in.) occurred. Up to this point the observations were consistent with the predictions of Callendar's equation for the isentropic expansion of superheated and supersaturated steam: the friction loss was small as far as the throat of the nozzle, but in the divergent portion it was of appreciable magnitude. The Wilson line was determined after allowances for the effects of friction had been made. The pressure rise was also investigated in detail and was found to be accompanied by a decrease of velocity and an increase of total heat. At the peak of the rise, where continuous expansion recommenced, the steam was probably not in thermal equilibrium. Additional tappings were placed across the throat, where the pressure observations were in close agreement with the values demanded by Taylor's theory. This theory, which does not assume uniformity of conditions over cross-sections of the nozzle, is more accurate in the neighbourhood of the throat than the classical theory of Reynolds.

The Influence of Slip Boundary Conditions on Peristaltic Pumping in a Rectangular Channel

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
X. Mandviwalla ◽  
R. Archer
Keyword(s):  
Reynolds Number ◽  
Boundary Conditions ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Rectangular Channel ◽  
Slip Boundary Conditions ◽  
Long Wavelength ◽  
Slip Boundary ◽  
Peristaltic Pumping ◽  
Side Walls

The flow of an incompressible fluid is modeled in a channel of a rectangular cross section with two symmetric peristaltic waves propagating on the top and bottom. A low Reynolds number and a long wavelength are assumed. The effect on pumping of the inclusion of slip boundary conditions on the side walls is investigated.

Trapped modes in open channels

1991 ◽  
Vol 225 ◽  
pp. 153-175 ◽  
Author(s):  
D. V. Evans ◽  
C. M. Linton
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Cross Section ◽  
Water Wave ◽  
Rectangular Cross Section ◽  
Cutoff Frequency ◽  
Vertical Cylinder ◽  
Free Water ◽  
Constructive Method ◽  
Trapped Modes

Trapped or edge-wave modes are well-known in linear water-wave theory. They occur at discrete frequencies below a certain cutoff frequency and consist of local oscillations trapped near a long horizontal submerged body in finite or infinite depth or over a sloping beach. Less well known is the existence of trapped modes in certain problems in acoustics where the governing equation is the Helmholtz equation. Jones (1953) has proved the existence of such modes which correspond to point-eigenvalues of the spectrum of the differential operator satisfying certain boundary conditions in a semi-infinite region. In this paper we describe a constructive method for determining point-eigenvalues or trapped-mode frequencies in two specific problems in which the two-imensional Helmholtz equation is satisfied.The problems arise from a consideration of the fluid motion in a long narrow wave tank with a free water surface which contains a vertical cylinder of uniform horizontal cross-section extending throughout the water depth. Separation of the depth dependence results in Helmholtz's equation with Neumann boundary conditions. By seeking solutions which are antisymmetric with respect to the centreline of the channel, trapped modes are constructed for the case of a cylinder of rectangular cross-section placed symmetrically in the centre of the channel and also for the case of a symmetric rectangular indentation in the tank walls. These problems do not appear to be covered directly by Jones’ theory and whilst the method described provides convincing numerical evidence, it falls short of a rigorous existence proof. Extensions to other purely acoustic problems having no water-wave interpretation, including problems which are covered by the general theory of Jones, are also discussed.

Analysis of Buckling Column Spring With Pivoted Ends and Uniform Rectangular Cross Section

1961 ◽  
Vol 83 (1) ◽  
pp. 61-66
Author(s):  
Alexander Blake
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Strength Of Materials ◽  
Bending Stresses ◽  
Deflection Analysis ◽  
Uniform Cross Section

Design formulas and working charts are derived for predicting load-deflection characteristics and maximum bending stresses in initially straight buckling column springs, of uniform cross section, considered to be pin jointed at the supports. Load-deflection analysis is based on the study of a slender bar, compressed beyond critical buckling, made by Lagrange. Stresses are calculated using the elementary strength of materials theory. The predicted load-deflection curves for typical spring proportions are compared with the experimental results.

Collapse loads for thin cantilevers with rectangular holes along the centre-line

1976 ◽  
Vol 11 (2) ◽  
pp. 84-96 ◽  
Author(s):  
A S Ranshi ◽  
W Johnson ◽  
N R Chitkara
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Slip Line ◽  
Rectangular Cross Section ◽  
Local Buckling ◽  
Experimental Results ◽  
Line Field ◽  
Theoretical Results

Plane stress slip-line field solutions, which provide the modes of yielding and the corresponding yield loads, are presented for the plastic bending of end-loaded thin cantilevers of rectangular cross-section containing rectangular holes. The theoretical results obtained from these solutions are compared with some experimental results and those obtained from plane strain slip-line fields and lower bound estimates, all presented previously by the authors (1)‡. It is observed that the correlation of the experimental results was much better with the plane stress solutions than with either the plane strain or lower bound results. The effect of adjacent holes and possible lateral or local buckling on the ultimate strength of the cantilevers is also examined.

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