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.

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.

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.

ELASTIC WAVES GENERATED BY HIGH-SPEED TRAINS

2001 ◽  
Vol 09 (03) ◽  
pp. 833-840 ◽  
Author(s):  
AUKE DITZEL ◽  
GERARD HERMAN ◽  
PAUL HÖLSCHER
Keyword(s):  
Rayleigh Wave ◽  
Efficient Method ◽  
Elastic Waves ◽  
High Speed ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Oscillatory Behavior ◽  
High Speed Trains ◽  
Train Speed ◽  
Rayleigh Wave Speed

High-speed trains can generate vibrations that propagate away from the track. We present an accurate and efficient method for computing the vibrations in an elastic half-space at both small and large distances from the track. The method takes possible oscillatory behavior of the train into account. We conclude that vibrations, generated by oscillating trains, can be observed at large distances from the track, even if the train speed is lower than the Rayleigh wave speed.

Response of an Elastic Half Space to a Decelerating Surface Point Load

1969 ◽  
Vol 36 (4) ◽  
pp. 819-826 ◽  
Author(s):  
K. I. Beitin
Keyword(s):  
Half Space ◽  
Poisson Ratio ◽  
Constant Load ◽  
Elastic Half Space ◽  
Point Load ◽  
Reciprocal Theorem ◽  
Surface Load ◽  
A Value ◽  
Mach Cones ◽  
Rayleigh Wave Speed

The displacement field on the surface of an elastic half space (Poisson ratio = 1/4), caused by the motion of a decelerating point surface load, is investigated by means of the dynamic Betti-Rayleigh reciprocal theorem. The load is applied impulsively and made to move rectilinearly at constant deceleration along the surface. The load speed varies from superseismic to a value less than the Rayleigh wave speed. The results show that significant differences exist between displacements obtained in this problem and those resulting from the usual assumption of constant load speed. The differences are primarily due to the presence of Mach cones which appear at superseismic load speeds and remain ahead of the initial wave fronts even after the speed becomes subseismic.

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1980-1987
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Half Space ◽  
Rotation Rate ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

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