Effects of microstructure and liquid loading on velocity dispersion of leaky Rayleigh waves at liquid–solid interface

2018 ◽  
Vol 96 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Vikas Sharma ◽  
Satish Kumar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Liquid Layer ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Liquid Loading ◽  
Stress Theory ◽  
Leaky Rayleigh Waves

Inner atomic interactions at the micro scale produce new effects that cannot be accounted for by the classical theory of elasticity. To study the impact of the microstructures of the material, generalized continuum theories involving additional microstructural material parameters are preferred. One such microcontinuum theory involving an additional material parameter called internal characteristic length (l) is a consistent couple stress theory. The study of leaky Rayleigh waves generated at the interface of solid half-space with liquid layer is of great importance for quick scanning and imaging of large civil engineering structures. The problem of leaky Rayleigh waves propagating in elastic half-space under liquid loading has been studied in the context of this consistent couple stress theory. Dispersion equations are obtained by developing the mathematical model of the problem. Phase velocity of leaky Rayleigh waves is studied for three different values of characteristic length parameter (l), which is of the order of internal cell size of the material. Effects of thickness of liquid layer are also studied on the phase velocity profiles.

Rayleigh wave equations with couple stress: modeling and dispersion characteristic

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Yanqi Wu ◽  
Jianwei Ma
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Scale Effect ◽  
Linear Elasticity ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Homogeneous Half Space

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. In this work, we introduce one of the generalized continuum theories—couple stress theory—into solid earth geophysics to build a more practical model of underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple stress theory in homogeneous half- space and layered space. The results show that couple stress causes the dispersion of surface waves and shear waves even in homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to couple stress effect than body waves. Based on the phase-shifting method, it was determined that Rayleigh waves exhibit different dispersion characteristics in couple stress theory than in conventional elastic theory. For the fundamental mode, the dispersion curves tend to move to a lower frequency with an increase in characteristic length l. For the higher modes, the dispersion curves energy is stronger with a greater characteristic length l.

Transient Study of Couple Stress Effects in Compact Bone: Torsion

1981 ◽  
Vol 103 (4) ◽  
pp. 275-279 ◽  
Author(s):  
J. F. C. Yang ◽  
R. S. Lakes
Keyword(s):  
Couple Stress ◽  
Characteristic Length ◽  
Unit Area ◽  
Couple Stress Theory ◽  
Compact Bone ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Stress Effects ◽  
Apparent Stiffness ◽  
Transient Study

Couple stress theory, which admits an internal moment per unit area as well as the usual force per unit area, is a generalization of classical elasticity. Experimentally we have demonstrated the existence of couple stress by measuring the effect of size on apparent stiffness of compact bone in quasi-static torsion. From these measurements, we obtain the characteristic length for bone in couple stress theory.

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half-space

1974 ◽  
Vol 64 (2) ◽  
pp. 387-392
Author(s):  
M. Farshad ◽  
G. Ahmadi
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Material Parameters ◽  
Surface Wave Propagation

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.

Rayleigh waves obtained by the indeterminate couple-stress theory

2000 ◽  
Vol 19 (6) ◽  
pp. 929-947 ◽  
Author(s):  
Niels Saabye Ottosen ◽  
Matti Ristinmaa ◽  
Christer Ljung
Keyword(s):  
Rayleigh Waves ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory

An Embedded Elliptic Nano-Fiber in Anti-Plane Strain Couple Stress Elasticity

2008 ◽  
Author(s):  
Hossein M. Shodja ◽  
Hamed Haftbaradaran
Keyword(s):  
Size Effect ◽  
Isotropic Material ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Infinite Medium ◽  
Stress Theory ◽  
Couple Stress Elasticity ◽  
Nano Fiber ◽  
Continuum Theories

The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem.

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

2011 ◽  
Vol 3 (2) ◽  
pp. 219-238
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Thermoelastic Diffusion ◽  
Phase Velocity And Attenuation ◽  
And Diffusion ◽  
Complex Dispersion ◽  
Leaky Rayleigh Waves

AbstractThis paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

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