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.

scholarly journals SOLITARY WAVE TRANSMISSION THROUGH POROUS BREAKWATERS

1988 ◽  
Vol 1 (21) ◽  
pp. 80 ◽  
Author(s):  
C. Vidal ◽  
M.A. Losada ◽  
R. Medina ◽  
J. Rubio
Keyword(s):  
Wave Reflection ◽  
Large Range ◽  
Rectangular Cross Section ◽  
Equivalent Linearization ◽  
Governing Equations ◽  
Empirical Theory ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Semi Empirical ◽  
Theoretical Results

A semi-empirical theory is formulated to predict wave reflection and transmission at a porous breakwater of rectangular cross section for normally incident solitary waves. The solution is based on the linearized form of the governing equations and on equivalent linearization of the friction loss in the porous structure. Experimental results of transmission coefficients are presented for a large range of incident wave amplitudes, with several gravel sizes, water depths and breakwater geometries. Experimental and theoretical results are compared and evaluated; the comparison shows satisfactory agreement for the transmission coefficient.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

Wave Propagation Analysis of an Axially Strained, Rotating Timoshenko Shaft: Part II

1997 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Boundary Conditions ◽  
Wave Reflection ◽  
Axial Strain ◽  
Free Vibration Analysis ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Propagation Analysis ◽  
Geometric Discontinuities ◽  
Bernoulli Models ◽  
Incident Waves

Abstract In this paper, the wave reflection and transmission characteristics of an axially strained, rotating Timoshenko shaft under general support and boundary conditions, and with geometric discontinuities are examined. As a continuation to Part I of this paper (Kang and Tan, 1997), the wave reflection and transmission at point supports with finite translational and rotational constraints are further discussed. The reflection and transmission matrices for incident waves upon general supports and geometric discontinuities are derived. These matrices are combined, with the aid of the transfer matrix method, to provide a concise and systematic approach for the free vibration analysis of multi-span rotating shafts with general boundary conditions. Results on the wave reflection and transmission coefficients are presented for both the Timoshenko and the Euler-Bernoulli models to investigate the effects of the axial strain, shaft rotation speed, shear and rotary inertia.

scholarly journals Reflection and Transmission of Acoustic Waves through the Layer of Multifractional Bubbly Liquid

2018 ◽  
Vol 148 ◽  
pp. 15001
Author(s):  
Damir Anvarovich Gubaidullin ◽  
Ramil Nakipovich Gafiyatov
Keyword(s):  
Acoustic Waves ◽  
Wave Reflection ◽  
Water Model ◽  
Bubbly Liquid ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Multilayer Medium ◽  
Bubble Layer ◽  
The Mathematical Model ◽  
Theoretical Results

The mathematical model that determines reflection and transmission of acoustic wave through a medium containing multifractioanl bubbly liquid is presented. For the water-water with bubbles-water model the wave reflection and transmission coefficients are calculated. The influence of the bubble layer thickness on the investigated coefficients is shown. The theory compared with the experiment. It is shown that the theoretical results describe and explain well the available experimental data. It is revealed that the special dispersion and dissipative properties of the layer of bubbly liquid can significantly influence on the reflection and transmission of acoustic waves in multilayer medium

scholarly journals On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading

1902 ◽  
Vol 70 (459-466) ◽  
pp. 491-496
Keyword(s):  
Approximate Solution ◽  
Special Reference ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Equilibrium ◽  
Elastic Solid ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Applied Stresses

The paper investigates the elastic equilibrium of a long bar of rectangular cross-section in those cases where the problem may be treated as one of two dimensions, namely:— ( a .) When the strain being in the plane of xy , the elastic solid extends indefinitely in the direction of the applied stresses over the bounding planes y = ± b , x = ± a being the same for any two sections parallel to the plane of xy . We then have a strictly two-dimensional strain.

In-Plane Vibrations of Thick Circular Rings With T or I Cross Sections

1979 ◽  
Vol 46 (2) ◽  
pp. 470-472
Author(s):  
H. Lecoanet ◽  
J. Piranda
Keyword(s):  
Experimental Data ◽  
Eigenvalue Problem ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Rings ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with the problem of eigenfrequencies and eigenvectors for rings whose cross section may be decomposed in basic rectangular cross sections. The solution is derived from a solution of the in-plane eigenvalue problem for rectangular cross-section thick rings. A good agreement between theoretical results and experimental data is obtained.

An Experimental and Analytical Study of Close-Contact Melting

1986 ◽  
Vol 108 (4) ◽  
pp. 894-899 ◽  
Author(s):  
M. K. Moallemi ◽  
B. W. Webb ◽  
R. Viskanta
Keyword(s):  
Approximate Solution ◽  
Surface Temperature ◽  
Cross Section ◽  
Analytical Study ◽  
Close Contact ◽  
Rectangular Cross Section ◽  
Melting Rate ◽  
Contact Melting ◽  
Series Of Experiments ◽  
Convection Dominated

Close-contact melting was investigated by performing a series of experiments in which blocks of solid n-octadecane (with circular or rectangular cross section) were melted by a horizontal planar heat source at constant surface temperature. Close contact between the source and the solid prevailed throughout the experiments by permitting the uncontained solid to descend under its own weight while squeezing the melt out of the gap separating it from the source. The velocity of the solid was measured and is reported as a function of the instantaneous weight of the solid. Effects of the surface temperature of the source and radius of the solid on its temporal velocity are also reported. A closed-form approximate solution is developed for the motion of solid and predictions are compared with the experimental data. The results for the solid velocity are correlated in terms of the governing parameters of the problem as revealed by the approximate solution. Compared with natural convection-dominated melting from below (solid confined and contained in a rectangular cavity) close contact gives rise to approximately a sevenfold increase in the melting rate of the solid.

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.

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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