Propagation of Rayleigh waves in an incompressible rotating orthotropic elastic solid half-space with impedance boundary conditions

2017 ◽  
Vol 26 (3-4) ◽  
pp. 73-78 ◽  
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Wave Speed ◽  
Secular Equation ◽  
Tangential Displacement ◽  
Rayleigh Surface Wave ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Dimensional Wave

AbstractIn this paper, the governing equations of an incompressible rotating orthotropic elastic medium are formulated and are solved to obtain Rayleigh surface wave solutions in a particular half-space. The surface of half-space is subjected to impedance boundary conditions, in which normal and tangential stresses are proportional to frequency times normal and tangential displacement components, respectively. A secular equation for Rayleigh surface wave is obtained. With the help of MATLAB, the secular equation is solved numerically to obtain non-dimensional wave speed. The dependence of non-dimensional wave speed on non-dimensional material constant, rotation parameter and impedance parameters is shown graphically.

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.

The Effect of Rotation on Propagation of Rayleigh Wave in an Incompressible Monoclinic Elastic Solid

2020 ◽  
Vol 36 (4) ◽  
pp. 485-495
Author(s):  
Baljinder Kaur ◽  
Baljeet Singh
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Half Space ◽  
Secular Equation ◽  
Elastic Solid ◽  
Elastic Materials ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Impedance Parameters

ABSTRACTIn this paper, the Rayleigh wave propagation is investigated in rotating half-space of incompressible monoclinic elastic materials which are subjected to the impedance boundary conditions. In particular, the explicit secular equation of the Rayleigh wave is obtained. The main objective of this paper is to illustrate the dependence of dimensionless speed of Rayleigh wave on rotation, anisotropy and impedance parameters. An algorithm in MATLAB software is developed to solve the secular equation of Rayleigh wave. The speed of Rayleigh wave is plotted against rotation, anisotropy and impedance parameters.

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.

Rayleigh waves in an incompressible fibre-reinforced elastic solid with impedance boundary conditions

2015 ◽  
Vol 24 (5-6) ◽  
pp. 183-186 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Wave Speed ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Radiation Condition ◽  
Equation Of Motion ◽  
Scalar Function ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

AbstractIn the present paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function. The general solution of the equation of motion is obtained, which satisfies the required radiation condition. The appropriate impedance boundary conditions are also satisfied by the solution to obtain the required explicit secular equation for the Rayleigh wave speed. The numerical values of non-dimensional speed of a Rayleigh wave are obtained with the application of Iteration method. The dependence of the non-dimensional wave speed on non-dimensional material parameter and impedance parameters is shown graphically.

scholarly journals Reflection of Plane Waves from Surface of a Generalized Thermo-Viscoelastic Porous Solid Half-Space with Impedance Boundary Conditions

2020 ◽  
Vol 22 (4) ◽  
pp. 1483-1496
Author(s):  
Baljeet Singh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Impedance Boundary ◽  
Reflected Waves ◽  
Material Parameters ◽  
Impedance Boundary Conditions ◽  
Impedance Parameter

AbstractA phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x–z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

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