On the Response of an Elastic Half-Space to a Moving Blast Wave

1960 ◽  
Vol 27 (4) ◽  
pp. 710-716 ◽  
Author(s):  
J. W. Miles
Keyword(s):  
Half Space ◽  
Blast Wave ◽  
Asymptotic Approximation ◽  
Constant Velocity ◽  
Wave Speed ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Variable Pressure ◽  
Formal Integral ◽  
Rayleigh Wave Speed

A formal integral transform solution is obtained for the response of an elastic half-space to a radially symmetric pressure signature of variable pressure and variable velocity. An asymptotic approximation to this solution is developed and expressed in terms of the known solution for the response of a half-space to a two-dimensional pulse moving with constant velocity plus a correction that is important only if the blast-wave speed directly above the point of observation is close to the Rayleigh-wave speed.

Impedance of Strip-Traveling Waves on an Elastic Half Space: Asymptotic Solution

1974 ◽  
Vol 41 (2) ◽  
pp. 412-416
Author(s):  
S. H. Crandall ◽  
A. K. Nigam
Keyword(s):  
Asymptotic Solution ◽  
Rayleigh Wave ◽  
Half Space ◽  
Traveling Wave ◽  
Load Distribution ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Surface Load ◽  
Shear Wave Speed ◽  
Rayleigh Wave Speed

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

Elastic Half Space under Axisymmetric Surface Loading and Influence of Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 129-133
Author(s):  
Jintara Lawongkerd ◽  
Toan Minh Le ◽  
Suraparb Keawsawasvong ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Half Space ◽  
Integral Transform ◽  
Couple Stress Theory ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Small Scale ◽  
Internal Length ◽  
Stress Theory ◽  
Axisymmetric Surface ◽  
Small Scale Effect

This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

Dynamic Response of a Rigid Foundation Subjected to a Distance Blast

2012 ◽  
Author(s):  
Deji Ojetola ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Integral Transform ◽  
Numerical Technique ◽  
Formal Solution ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Rigid Foundation ◽  
Transform Method

Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.

scholarly journals Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150800 ◽  
Author(s):  
R. Chebakov ◽  
J. Kaplunov ◽  
G. A. Rogerson
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Elastic Half Space ◽  
Interior Solution ◽  
Homogeneous Half Space ◽  
Classical Boundary ◽  
Non Local ◽  
Rayleigh Wave Speed

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the ‘local’ problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Surface Displacement of a Convective Elastic Half-Space Under an Arbitrarily Distributed Fast-Moving Heat Source

1965 ◽  
Vol 87 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. F. Ling ◽  
V. C. Mow
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Fast Moving ◽  
Constant Velocity ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Two Dimensional ◽  
Moving Heat Source ◽  
Thermoelasticity Theory

A solution of the normal displacement of the elastic half-space under an arbitrarily distributed fast-moving heat source of constant velocity within the two-dimensional quasi-static, uncoupled thermoelasticity theory is presented. The surface of the half-space is allowed to dissipate heat by convection. Moreover, an example associated with the problem of elastohydrodynamics is given.

scholarly journals On Propagation of Rayleigh Type Surface Wave in Five Different Theories of Thermoelasticity

2019 ◽  
Vol 24 (3) ◽  
pp. 661-673 ◽  
Author(s):  
B. Singh ◽  
S. Verma
Keyword(s):  
Relaxation Time ◽  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Wave Speed ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Governing Equations ◽  
Particular Solutions ◽  
Rayleigh Wave Speed

Abstract The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.

Low Velocity Impact of an Elastic Plate Resting on Sand

1988 ◽  
Vol 55 (4) ◽  
pp. 887-894 ◽  
Author(s):  
H. L. Chen ◽  
W. Lin ◽  
L. M. Keer ◽  
S. P. Shah
Keyword(s):  
Half Space ◽  
Wave Speed ◽  
Impact Load ◽  
Radial Strain ◽  
Elastic Half Space ◽  
Low Velocity Impact ◽  
Target Plate ◽  
Low Velocity ◽  
Soil Response ◽  
Velocity Impact

This article describes the measurement and analysis of plate and soil response under low velocity impact. A free-drop impact system was developed to generate the dynamic loading on the plate free surface. The radial strain of the target plate, the longitudinal wave speed and the acceleration of the sand were measured. The measured wave speed data were then used to evaluate the elastic constants of the sand. An analysis based on linear elastodynamics was developed for transient waves on a thin plate resting on an elastic half space. The contact stresses and the normal displacements of the plate were taken as unknown functions. The contact between the plate and the half space were assumed frictionless. The experimental results of the radial strain at the bottom of the target plate and the acceleration of the sand beneath the center of the target plate were compared with the analytical solution. The arrival time, the duration, and the magnitude have good correlation between the analysis and experiment. The overall results appear good and provide an understanding of the transmission of impact load through the plate, the interaction between the plate and the sand, and the propagation of the load into the sand.

Transient Response of an Elastic Half Space Subjected to a Reciprocating Antiplane Shear Load

1976 ◽  
Vol 43 (4) ◽  
pp. 625-629 ◽  
Author(s):  
K. Watanabe
Keyword(s):  
Analytical Solution ◽  
Wave Front ◽  
Half Space ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Trigonometric Function ◽  
Antiplane Shear ◽  
Maximum Speed ◽  
Shear Load ◽  
Sh Wave

In this paper we consider a problem of the response of an elastic half space subjected to an antiplane shear load. The load is suddenly applied and thereafter moves in an interval reciprocally as a trigonometric function of time. An analytical solution for the displacement is obtained in terms of single integration. It is shown that the discontinuity in the displacement occurs only for the case that the initial (maximum) speed of the load is greater than the speed of SH-wave. In this case the displacement has a finite jump on the leading wave front and a logarithmic discontinuity immediately behind the wave front which emanates from a point where the load speed comes up with SH-wave speed. Numerical calculations are carried out for several cases of the initial (maximum) speed of the load and are shown graphically.

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