The Problem on Dynamical Loading of Plane Elastic Regions With Irregular Boundaries

1998 ◽  
Vol 65 (2) ◽  
pp. 476-478
Author(s):  
N. Morozov ◽  
I. Sourovtsova

The study of the problem of wave propagation in elastic wedge meets considerable difficulties, which are intensified by the presence of waves of two types that interact with each other through boundary conditions. However, some special surface loading permits separation of the potentials in the boundary conditions, but even in this case the problem cannot be simply reduced to two acoustic ones. The reason for this is that the edge condition cannot be satisfied if the disturbances are limited to a single type (longitudinal or shear). In spite of this the problem, such a special boundary loading nevertheless turns out to be very similar to the acoustic one, which makes it possible to find a closed analytical solution by means of the modified Kostrov method (Kostrov, 1966) and the idea of extension of operators. A similar approach is used for the study of the general problem of loading of the body with several angles.

1969 ◽  
Vol 42 (1) ◽  
pp. 284-295 ◽  
Author(s):  
Allen L. Bell ◽  
David B. Peakall

The ampullate silk gland of the spider, Araneus sericatus, produces the silk fiber for the scaffolding of the web. The fine structure of the various parts of the gland is described. The distal portion of the duct consist of a tube of epithelial cells which appear to secrete a substance which forms the tunica intima of the duct wall. At the proximal end of the duct there is a region of secretory cells. The epithelium of the sac portion contains five morphologically distinct types of granules. The bulk of the synthesis of silk occurs in the tail of the gland, and in this region only a single type of secretory droplet is seen in the epithelium. Protein synthesis can be stimulated by the injection of 1 mg/kg acetylcholine into the body fluids. 10 min after injection, much of the protein stored in the cytoplasm of the epithelial cells has been secreted into the lumen. 20 min after stimulation, the ergastoplasmic sacs form large whorls in the cytoplasm. Protein, similar in electron-opacity to protein found in the lumen, begins to form in that portion of the cytoplasm which is enclosed by the whorls. The limiting membrane of these droplets is formed by ergastoplasmic membranes which lose their ribosomes. No Golgi material has been found in these cells. Protein appears to be manufactured in the cytoplasm of the tail cells in a form which is ready for secretion.


Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.


1972 ◽  
Vol 11 (3) ◽  
pp. 899-929
Author(s):  
L. H. BANNISTER

The structure of undischarged and discharged trichocysts has been examined in Paramecium caudatum, and their light-microscopic appearance compared with their fine-structural organization. In living specimens undischarged trichocysts appear to be of a single type with a unimodal variation in length about a mean of 3.7 µm. When fixed for electron microscopy or compressed beneath a coverslip many of the trichocysts expand within the cell, giving rise to a variety of different forms of lower phase density. Ultrastructurally the undischarged trichocyst consists of at least 10 different components: these include a mesh-like sheath surrounding the body of the organelle; an inner and an outer sheath enclosing the tip, the inner sheath being made up of 4 spiralling envelopes with a square net substructure, and the outer sheath being formed of a dense amorphous matrix containing longitudinal microtubules and scattered fine filaments; a boundary surface to the outer sheath; a membranous trichocyst sac the apical region of which is surrounded by a cylinder of microtubules joined to each other with dense material; and lastly, the crystalline matrix of the trichocyst body and tip. This crystalline appearance is apparently related to the presence of a loosely interwoven complex of fine filaments which form a highly regular pattern of unit structures repeating at 16-nm intervals. In extended trichocysts the 60-nm banding pattern of the body is also composed of fine filaments arranged in a different, elongated manner in 2 distinct and alternating patterns which are taken to be 2 views of the same structure. Measurements indicate that when trichocysts extend they elongate by a factor of from 6 to 8. It is proposed that the crystalline pattern of the unextended trichocyst body transforms into the extended form by a simple rearrangement of the constituent filaments accompanied by their elongation. Possible models of the undischarged and discharged states of organization are suggested.


1996 ◽  
Vol 40 (04) ◽  
pp. 269-277
Author(s):  
G. X. Wu ◽  
T. Miloh ◽  
G. Zilman

The problem of a hydrofoil moving near an interface of two fluids of different densities is analyzed. An iteration scheme is proposed which imposes the boundary conditions on the body surface and on the interface alternately. The numerical solution is obtained by using the linearized theory and a Glauert-type expansion for the vortex distribution. Results are provided for various cases with different densities and different speeds.


1943 ◽  
Vol 10 (2) ◽  
pp. A53-A61
Author(s):  
J. L. Meriam

Abstract The analysis of shells is an important subdivision of the general theory of elasticity, and its application is useful in the solution of engineering problems involving thin-walled structures. A common type of shell is one which possesses symmetry with respect to an axis of revolution. A theory for such shells has been developed by various investigators (1, 2, 3, 6) and applied to a few simple cases such as the cylindrical, spherical, and conical shapes. Boundary conditions, for the most part, have been simple static ones, and conditions of surface loading have been included in certain special cases. This paper extends the theory of axially symmetrical shells by including the body force of rotation about the axis and applies the results to the rotating conical shell. The analysis follows a pattern established by several investigators (1, 2, 3, 6) and for this reason is abbreviated to a considerable extent. Only where the inclusion of the body force makes elucidation advisable or where a slightly different method of approach is used are the steps presented in more detail.


1962 ◽  
Vol 52 (4) ◽  
pp. 807-822 ◽  
Author(s):  
John T. Kuo ◽  
John E. Nafe

abstract The problem of the Rayleigh wave propagation in a solid layer overlying a solid half space separated by a sinusoidal interface is investigated. The amplitude of the interface is assumed to be small in comparison to the average thickness of the layer or the wave length of the interface. Either by applying Rayleigh's approximate method or by perturbating the boundary conditions at the sinusoidal interface, plane wave solutions for the equations which satisfy the given boundary conditions are found to form a system of linear equations. These equations may be expressed in a determinant form. The period (or characteristic) equations for the first and second approximation of the wave number k are obtained. The phase and group velocities of Rayleigh waves in the present case depend upon both frequency and distance. At a given point on the surface, there is a local phase and local group velocity of Rayleigh waves that is independent of the direction of wave propagation.


Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.


2011 ◽  
Vol 1 (6) ◽  
pp. 20 ◽  
Author(s):  
G. E. Vincent

With a view to explaining the phenomena of sediment transport in the open sea, outside the wave breaking area, the author carried out a laboratory investigation of wave action on a horizontal bed. He puts forward a number of new results regarding : 1 - The state of turbulence near the bed and the stability of the oscillatory laminar boundary layer. 2 - The setting in notion of materials under the influence of wave alone. 3 - The entrapment current caused by wave action close to the bed. 4 - The transport of material under wave action only. 5 - The indirect action of wave on the bed. The main conclusions reached are as follows : 1/ - The results given by Kuon Li regarding the onset of turbulence within the oscillatory boundary layer overestimate the range of laminar conditions. Vo (maximum orbital velocity) and e (roughness) are the principle factors governing the transition. Test waves are either generally laminar, or are only slightly turbulent within the body of liquid, but they are, however, more often turbulent in the immediate neighbourhood of the bed. 2/ - The Investigation of conditions for the onset of grain movement of the bed material shows that the action of wave can be appreciable, even at depths of several tens of metres. A wave of 6 metres amplitude, with a total length of 120 metres, would be capable of putting a 0.3 mm sand grain into motion at a depth of 60 metres. 3/ - The experimental investigation, as well as the viscous fluid theory, shows the existence, close to the bed, of an entrainment current of liquid particles which always works In the direction of wave propagation. 4/ - In test flumes, this entrainment current forms part of a mass transport within the liquid, the vertical distribution of which varies with the characteristics of the fluid motion. On a horizontal bed, It generally gives rise to an effective sediment transport, in the direction of wave propagation, as the preponderant part of the liquid velocity component, near the bed. is in this direction. 5/ - Owing to the existence of the pass transport current and the onset of suspension of material above the bed, some sediment transport can exist out to sea. These results give an explanation of why, under the action of long and regular wave . material tends to be carried in the direction of the waves and build up on the beach whereas, under storm conditions, a strong resultant turbulence produces suspension and favours erosion of the beach. 6/ - On a sloping bed, transport towards the shore is counterbalanced by the effect of gravity, currents caused by winds from seaward and density currents set up in the wave break area so that finally material eroded from land surfaces are, In part, gradually carried away towards the open sea.


Sign in / Sign up

Export Citation Format

Share Document