3i. On Waves Propagated along the Plane Surface of an Elastic Solid by John W. Strutt, Lord Rayleigh, D.C.L., F.R.S. [John William Strutt]

2007 ◽  
pp. 243-250
Keyword(s):  
Plane Surface ◽  
Elastic Solid

scholarly journals The torsion of a semi-infinite elastic solid by an elliptical stamp

1968 ◽  
Vol 9 (1) ◽  
pp. 36-45
Author(s):  
Mumtaz K. Kassir
Keyword(s):  
Field Equation ◽  
Classical Theory ◽  
Cross Sections ◽  
Plane Surface ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Circular Area

The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z ≧ 0) when a part of the boundary surface (z = 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11, and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.

scholarly journals The Reissner-Sagoci problem

1966 ◽  
Vol 7 (3) ◽  
pp. 136-144 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Plane Surface ◽  
Displacement Vector ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Cylindrical Coordinates ◽  
Circular Area ◽  
Image Position ◽  
Simple Equations

The statical Reissner-Sagoci problem [1, 2, 3] is that of determining the components of stress and displacement in the interior of the semi-infinite homogeneous isotropic elastic solid z ≧ 0 when a circular area (0 ≦ p ≦ a, z = 0) of the boundary surface is forced to rotate through an angle a about an axis which is normal to the undeformed plane surface of the medium. It is easily shown that, if we use cylindrical coordinates (p, φ, z), the displacement vector has only one non-vanishing component uφ (p, z), and the stress tensor has only two non-vanishing components, σρπ(p, z) and σπz(p, z). The stress-strain relations reduce to the two simple equationswhere μ is the shear modulus of the material. From these equations, it follows immediately that the equilibrium equationis satisfied provided that the function uπ(ρ, z) is a solution of the partial differential equationThe boundary conditions can be written in the formwhere, in the case in which we are most interested, f(p) = αρ. We also assume that, as r → ∞, uπ, σρπ and σπz all tend to zero.

Propagation of Elastic Waves at Micropolar Viscoelastic Solid/Fluid-Saturated Incompressible Porous Solid Interface

2018 ◽  
Vol 15 (08) ◽  
pp. 1850076 ◽  
Author(s):  
M. S. Barak ◽  
Vinod Kaliraman
Keyword(s):  
Half Space ◽  
Incident Wave ◽  
Plane Surface ◽  
Elastic Solid ◽  
Specific Model ◽  
Porous Solid ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Viscoelastic Solid ◽  
Micropolar Viscoelastic Solid

The present paper concerned with the reflection and transmission of plane wave from a plane surface separating a micropolar viscoelastic solid (MVES) half-space and a fluid-saturated (FS) incompressible porous solid half-space is studied. A longitudinal wave ([Formula: see text]-wave) or transverse wave (SV-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained with the help of boundary conditions at the interface. Then, these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with the angle of incidence of the incident wave. It is found that these amplitude ratios depend on the angle of incidence of the incident wave as well as on the properties of media. From the present investigation, a special case, when FS porous half-space reduces to empty porous solid and MVES half-space reduces to micropolar elastic solid, has also been deduced and discussed with the help of graphs.

scholarly journals Strongly anisotropic surface elasticity and antiplane surface waves

2019 ◽  
Vol 378 (2162) ◽  
pp. 20190100 ◽  
Author(s):  
V. A. Eremeyev
Keyword(s):  
Surface Waves ◽  
Plane Surface ◽  
Plane Waves ◽  
Surface Elasticity ◽  
Elastic Solid ◽  
Point Of View ◽  
Surface Strain ◽  
Elastic Membrane ◽  
Preferred Direction ◽  
Anisotropic Surface

Within the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic long flexible beams. Physically, the model was motivated by deformations of surface coatings consisting of aligned bar-like elements as in the case of hyperbolic metasurfaces. Using the least action variational principle, we derive the dynamic boundary conditions. The linearized boundary-value problem is also presented. In order to demonstrate the peculiarities of the problem, the dispersion relations for surface anti-plane waves are analysed. We have shown that the bending stiffness changes essentially the dispersion relation and conditions of anti-plane surface wave propagation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

The elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch

1945 ◽  
Vol 41 (1) ◽  
pp. 16-26 ◽  
Author(s):  
J. W. Harding ◽  
I. N. Sneddon
Keyword(s):  
Arbitrary Shape ◽  
Plane Surface ◽  
Elastic Solid ◽  
Integral Transforms ◽  
Senior Author ◽  
Rigid Punch ◽  
Elastic Stresses ◽  
Distribution Of Stress ◽  
Special Case ◽  
General Method

During the course of some investigations on the distribution of stress in an elastic solid it was noticed by the senior author that a systematic application of the method of integral transforms to the problem of the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch reduced the problem essentially to one of solving a pair of integral equations belonging to a class which has been studied by Titchmarsh and by Busbridge (4,5). This procedure allows one to obtain the solution for an arbitrary shape of punch by a general method which leads automatically to the solution and avoids the troublesome procedure, adopted by Love (2) in the case of a conical punch, of being obliged to guess appropriate combinations of solutions which will satisfy the prescribed boundary conditions in any special case. Moreover, it can easily be seen that an attempt to apply Love's method to more complicated shapes of punch will lead to considerable analytical difficulties.

Sign in / Sign up

Export Citation Format

Share Document