scholarly journals Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Baljeet Singh ◽  
Ritu Sindhu ◽  
Jagdish Singh
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Rotation Frequency ◽  
Frequency Equation ◽  
Governing Equations ◽  
Wave Solutions ◽  
Effects Of Rotation ◽  
Micropolar Material

A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

scholarly journals Propagation of Rayleigh Wave in a Thermoelastic Solid Half-Space with Microtemperatures

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Frequency Equation ◽  
Rayleigh Surface Wave ◽  
Governing Equations ◽  
Thermoelastic Medium ◽  
Wave Solutions ◽  
Special Cases ◽  
Thermoelastic Solid

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous thermoelastic solid half-space with microtemperatures. The governing equations of the thermoelastic medium with microtemperatures are solved for surface wave solutions. The particular solutions in the half-space are applied to the required boundary conditions at stress-free thermally insulated surface to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The non-dimensional speed of Rayleigh wave is computed numerically and presented graphically to reveal the dependence on the frequency and microtemperature constants.

scholarly journals Rotational Effects on Propagation of Rayleigh Wave in a Micropolar Piezoelectric Medium

2018 ◽  
Vol 48 (2) ◽  
pp. 93-105 ◽  
Author(s):  
Baljeet Singh ◽  
Ritu Sindhu
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Wave Speed ◽  
Propagation Speed ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Piezoelectric Medium ◽  
Effects Of Rotation ◽  
Radiation Conditions ◽  
Relevant Material

Abstract In this paper, the governing equations of a linear, homogeneous and transversely isotropic rotating micropolar piezoelectric medium are solved for surface wave solutions. The appropriate solutions satisfying the radiation conditions are obtained in a half-space. These solutions are applied to suitable boundary conditions at the free surface of the half-space. A frequency equation for Rayleigh wave is obtained for both charge free and electrically shorted cases. Using iteration method, the non-dimensional wave speed of Rayleigh wave is computed for relevant material constants modelling the medium. The effects of rotation, piezoelectricity, frequency and material parameters are observed graphically on the propagation speed.

scholarly journals Rayleigh-Type Waves in a Rotating Fiber-Reinforced Half Space under the Action of Magnetic Field, Gravity and Surface Stress

2021 ◽  
pp. 1-7
Author(s):  
Narottam Maity ◽  
◽  
S P Barik Barik ◽  
P K Chaudhuri ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Stress ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Frequency Equation ◽  
Complete Agreement ◽  
Fiber Reinforced ◽  
Electrically Conducting ◽  
Stress Rotation ◽  
Wave Velocity Equation

The aim of the present article is to analyze the propagation of Rayleigh waves in a rotating fiber-reinforced electrically conducting elastic solid medium under the influence of surface stress, magnetic field and gravity. The magnetic field is applied in such a direction that the problem can be considered as a two dimensional one. The wave velocity equation for Rayleigh waves has been obtained. In the absence of gravity field, surface stress, rotation and fiberreinforcement, the frequency equation is in complete agreement with the corresponding classical results. The effects on various subjects of interest are discussed and shown graphically. Comparisons are made with the corresponding results in absence of surface stress

Model study of explosion-generated Rayleigh waves in a half space

1964 ◽  
Vol 54 (2) ◽  
pp. 475-484
Author(s):  
I. N. Gupta ◽  
C. Kisslinger
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Radial Component ◽  
Two Dimensional ◽  
Source Depth ◽  
Dimensional Model ◽  
Retrograde Motion ◽  
Model Study ◽  
Two Dimensional Model

ABSTRACT The Rayleigh waves generated by an explosion on or in the interior of a two-dimensional model show that the source acts as a downward impulse when the shot is on or just below the surface, and as a buried source of compression for deeper shots. The seismograms are in agreement with established theory for the line source on or in a half-space. The source depth corresponding to the reversal of polarity of the Rayleigh wave is small, and appears to be equal to the radius of the zone of inelastic failure around the shot. The polarity reversal is a true indication of a change in the mechanism of Rayleigh wave generation, and is not related to the change from retrograde motion at the free surface to prograde motion in the interior associated with the change in sign of the radial component at depth.

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shishir Gupta ◽  
Rishi Dwivedi ◽  
Smita Smita ◽  
Rachaita Dutta
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Rayleigh Wave ◽  
Penetration Depth ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Rayleigh Surface Wave ◽  
Content Type

Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

scholarly journals Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the  Rayleigh wave H/V ratio.

RAYLEIGH‐WAVE MOTION IN AN ELASTIC HALF‐SPACE

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 97-101 ◽  
Author(s):  
W. A. Sorge
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Seismic Model

Measurements made on Rayleigh waves below the surface of a simulated elastic half‐space confirm in detail the behavior predicted by theory. These measurements, made by means of a two‐dimensional seismic model, show that the amplitude of the Rayleigh wave falls off rapidly with increasing depth.

scholarly journals Propagation of Rayleigh Wave in a Two-Temperature Generalized Thermoelastic Solid Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Special Cases ◽  
Temperature Parameter ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Two Temperature

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous two-temperature thermoelastic solid half-space in the context of Lord and Shulman theory of generalized thermoelasticity. The governing equations of a two-temperature generalized thermoelastic medium are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The speed of Rayleigh wave is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.

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.

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