Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic half-space

2021 ◽  
pp. 030932472110012
Author(s):  
AM Abd-Alla ◽  
SM Abo-Dahab ◽  
SM Ahmed ◽  
MM Rashid
Keyword(s):  
Magnetic Field ◽  
Surface Wave ◽  
Surface Waves ◽  
Wave Speed ◽  
Nonlocal Parameter ◽  
Mode Analysis ◽  
Rayleigh Surface Wave ◽  
Coupled Equations ◽  
Rayleigh Surface Waves ◽  
Dimensional Wave

This work is concerned with the propagation of surface waves is considered in an isotropic elastic homogeneous nonlocal generalized thermoelastic solid medium in the presence of a magnetic field and voids. The normal mode analysis and Lame’s potential theory are used to solve the resulting non-dimensional coupled equations. Dispersion relation for Rayleigh surface wave are derived for both thermally insulated and isothermal surfaces. The non-dimensional wave speed of Rayleigh surface wave is computed for a specific material. The non-dimensional wave speed of Rayleigh surface waves are found to be influenced by the presence of voids, magnetic field, thermal field, and elastic nonlocal parameter. For a particular model, the effect of magnetic field, void parameters, thermal parameter, and nonlocality has been studied numerically on the Rayleigh surface waves. All the computed results obtained have been depicted graphically and explained.

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.

scholarly journals ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

2011 ◽  
Vol 03 (04) ◽  
pp. 633-665 ◽  
Author(s):  
P. SAXENA ◽  
R. W. OGDEN
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Sagittal Plane ◽  
Isotropic Energy ◽  
Surface Wave Propagation ◽  
Homogeneous Strain

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

Steady State Motion and Surface Waves

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Surface Waves ◽  
Existence And Uniqueness ◽  
Wave Speed ◽  
Wave Theory ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Steady State Motion ◽  
Anisotropic Elastic

The Stroh formalism for two-dimensional elastostatics can be extended to elastodynamics when the problem is a steady state motion. Most of the identities in Chapters 6 and 7 remain applicable. The Barnett-Lothe tensors S, H, L now depend on the speed υ of the steady state motion. However S(υ), H(υ), L(υ) are no longer tensors because they do not obey the laws of tensor transformation when υ≠0. Depending on the problems the speed υ may not be prescribed arbitrarily. This is particularly the case for surface waves in a half-space where υ is the surface wave speed. The problem of the existence and uniqueness of a surface wave speed in anisotropic materials is the crux of surface wave theory. It is a subject that has been extensively studied since the pioneer work of Stroh (1962). Excellent expositions on surface waves for anisotropic elastic materials have been given by Farnell (1970), Chadwick and Smith (1977), Barnett and Lothe (1985), and more recently, by Chadwick (1989d).

Magneto-acoustic surface waves on current sheets

1994 ◽  
Vol 51 (2) ◽  
pp. 221-232 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Surface Wave ◽  
Surface Waves ◽  
Constant Amplitude ◽  
Current Sheets ◽  
Change Of Direction ◽  
Acoustic Surface Waves ◽  
Resonance Damping ◽  
Arbitrary Change ◽  
The Magnetic Field

The theory of linear magneto-acoustic surface waves is investigated for current sheets across which the magnetic field has an arbitrary change of direction: in the first place discontinuously, and in the second place via a narrow transition region in which the magnetic field rotates with constant amplitude, so that the gas pressure remains constant. It is found that the effect of non-zero pressure is to eliminate the surface wave for certain angles of propagation and to allow the existence of an additional, slower, surface wave for other angles of propagation. The resonance damping of the surface waves when the current sheet is of small non-zero width is considered, and it is found that Alfvénresonance damping always occurs, as well as (for high β and certain angles of propagation) compressive- or cusp-resonance damping.

An Acoustoelastic Theory for Surface Waves in Anisotropic Media

1987 ◽  
Vol 54 (1) ◽  
pp. 127-135 ◽  
Author(s):  
G. Thomas Mase ◽  
G. C. Johnson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Wave Speed ◽  
Transversely Isotropic ◽  
Wave Speeds ◽  
Local Rotation ◽  
Copper Single Crystals ◽  
Cubic Function

A theory for surface waves in an anisotropic material is developed in the framework of acoustoelasticity in which the material’s strain energy density is taken to be a cubic function in the strain. In order to relate the surface wave speeds to the applied stress, a configuration is introduced in which the effect of the local rotation is removed. The development shows that the surface wave speed can be determined from the eigenvalues of a particular real symmetric 2×2 matrix. Numerical results are given for uniaxial loading applied to aluminum and copper single crystals and to an ideal transversely isotropic aggregate of aluminum.

SURFACE WAVES ALONG AN AXIALLY MAGNETIZED PLASMA COLUMN: I. SYMMETRIC MODES

1967 ◽  
Vol 45 (9) ◽  
pp. 2889-2911 ◽  
Author(s):  
G. L. Yip ◽  
S. R. Seshadri
Keyword(s):  
Magnetic Field ◽  
Surface Wave ◽  
Resonant Frequency ◽  
Surface Waves ◽  
Infinite Number ◽  
Applied Magnetic Field ◽  
Cold Plasma ◽  
Magnetized Plasma ◽  
Wave Power ◽  
Point Electric Dipole

The characteristics of surface waves excited by an axially oriented point electric dipole situated along the axis of an infinitely long; and axially magnetized column of uniform cold plasma are investigated. The surface waves are found to be slow waves and exist only below the upper hybrid resonant frequency. In the gyromagnetic and plasma resonance regions, the existence of an infinite number of discrete modes is noted. The dispersion curves are presented for different values of the strength of the applied magnetic field and the column radius. Also, the power transported by the surface waves is evaluated and is found to become infinite in the two resonance frequency regions. A technique for the removal of this singularity in the surface wave power is indicated.

scholarly journals Surface waves guided by topography in an anisotropic elastic half-space

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120371 ◽  
Author(s):  
Y. B. Fu ◽  
G. A. Rogerson ◽  
W. F. Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Simple Eigenvalue ◽  
Plane Shear ◽  
Number Of Factors ◽  
Present Context ◽  
Anisotropic Elastic

We consider the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topography-guided surface waves). Our aim is to investigate how such a weak inhomogeneity modifies the surface-wave speed slightly. We first recover previously known results for isotropic materials and then present additional results for a generally anisotropic elastic half-space assuming only one plane of material symmetry. It is shown that a topography-guided surface wave in the present context may or may not propagate depending on a number of factors. In particular, they cannot propagate if the original two-dimensional surface wave on a flat half-space is supersonic with respect to the speed of anti-plane shear waves. For the case when a topography-guided surface wave may exist, the existence and computation of wave speed correction is reduced to the solution of a simple eigenvalue problem whose properties are previously well understood. As a by-product of our analysis, we deduce that there exists at least one topography-guided surface wave on an isotropic elastic half-space, and that it is unique when the geometric inhomogeneity has sufficiently small amplitude.

scholarly journals Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

2021 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Rayleigh Wave ◽  
Wave Speed ◽  
Transverse Isotropy ◽  
Nonlocal Parameter ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Nonlocal Elasticity Theory ◽  
Governing Equations

In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medium is assumed rotating about an axis perpendicular to the plane. The transverse isotropy axis is taken perpendicular to the surface. The specialized governing equations are first applied to derive a velocity equation for homogeneous plane wave. The specialized governing equations along with traction free boundary conditions are also applied to derive the secular equation governing the wave speed of Rayleigh wave.  The speeds of plane wave and Rayleigh wave are computed and illustrated graphically to observe the effects of nonlocality, rotation, anisotropy, frequency and propagation direction. It is noticed from the theory and numerical results that the speeds of both plane wave and Rayleigh wave decrease sharply with an increase in nonlocal parameter or rotation parameter. The speeds of plane wave and Rayleigh wave increase logarithmically with anisotropy material parameter. The feasible ranges of nonlocality, rotation or anisotropy parameters for the existence of plane wave or Rayleigh surface wave are determined for a given wave speed when the values of other parameters are fixed.

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