The Experts below are selected from a list of 20022 Experts worldwide ranked by ideXlab platform
Pham Chi Vinh - One of the best experts on this subject based on the ideXlab platform.
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Rayleigh Waves with impedance boundary condition formula for the velocity existence and uniqueness
European Journal of Mechanics A-solids, 2017Co-Authors: Pham Chi Vinh, Nguyen Quynh XuanAbstract:Abstract The propagation of Rayleigh Waves in an isotropic elastic half-space with impedance boundary conditions was investigated recently by Godoy et al. [Wave Motion 49 (2012), 585–594]. The authors have proved the existence and uniqueness of the wave. However, they were not successful in obtaining an analytical exact formula for the wave velocity. The main purpose of this paper is to find such a formula. By using the complex function method, an analytical exact formula for the velocity of Rayleigh Waves has been derived. Furthermore, from the obtained formula, the existence and uniqueness of the wave has been established easily.
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Rayleigh Waves in an incompressible orthotropic half-space coated by a thin elastic layer
Archives of Mechanics, 2014Co-Authors: Pham Chi Vinh, Nguyen Thi Khanh Linh, Vu Thi Ngoc AnhAbstract:The present paper is concerned with the propagation of Rayleigh Waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The halfspace and the layer are both incompressible and they are in welded contact to each other. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method an approximate secular equation of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From it an approximate formula of third-order for the velocity of Rayleigh Waves is obtained and it is a good approximation. The obtained approximate secular equation and formula for the velocity will be useful in practical applications.
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Rayleigh Waves with impedance boundary conditions in anisotropic solids
Wave Motion, 2014Co-Authors: Pham Chi Vinh, Trinh Thi Thanh HueAbstract:Abstract The paper is concerned with the propagation of Rayleigh Waves in an elastic half-space with impedance boundary conditions. The half-space is assumed to be orthotropic and monoclinic with the symmetry plane x 3 = 0 . The main aim of the paper is to derive explicit secular equations of the wave. For the orthotropic case, the secular equation is obtained by employing the traditional approach. It is an irrational equation. From this equation, a new version of the secular equation for isotropic materials is derived. For the monoclinic case, the method of polarization vector is used for deriving the secular equation and it is an algebraic equation of eighth-order. When the impedance parameters vanish, this equation coincides with the secular equation of Rayleigh Waves with traction-free boundary conditions.
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Rayleigh Waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact
International Journal of Engineering Science, 2014Co-Authors: Pham Chi Vinh, Vu Thi Ngoc AnhAbstract:Abstract In the present paper, we are interested in the propagation of Rayleigh Waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main aim of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate secular equations of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From the secular equation obtained, an approximate formula of third-order for the Rayleigh wave velocity is derived and it is a good approximation.
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an approximate secular equation of generalized Rayleigh Waves in pre stressed compressible elastic solids
International Journal of Non-linear Mechanics, 2013Co-Authors: Pham Chi Vinh, Nguyen Thi Khanh LinhAbstract:Abstract The present paper is concerned with the propagation of Rayleigh Waves in a pre-stressed elastic half-space coated with a thin pre-stressed elastic layer. The half-space and the layer are assumed to be compressible and in welded contact with each other. By using the effective boundary condition method, an explicit third-order approximate secular equation of the wave has been derived that is valid for any pre-strains and for a general strain-energy function. When the pre-strains are absent, the secular equation obtained coincides with the one for the isotropic case. Numerical investigation shows that the approximate secular equation obtained is a good approximation. Since explicit dispersion relations are employed as theoretical bases for extracting pre-stresses from experimental data, the secular equation obtained will be useful in practical applications.
A M Abdalla - One of the best experts on this subject based on the ideXlab platform.
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propagation of Rayleigh Waves in a rotating orthotropic material elastic half space under initial stress and gravity
Journal of Mechanical Science and Technology, 2012Co-Authors: A M Abdalla, S M Abodahab, T A AlthamaliAbstract:This paper aims to investigate the influence of rotation, initial stress and gravity field on the propagation of Rayleigh Waves in a homogeneous orthotropic elastic medium. The government equations and Lame’s potentials are used to obtain the frequency equation which determines the velocity of Rayleigh Waves, including rotation, initial stress and gravity field, in a homogeneous, orthotropic elastic medium has been investigated. The numerical results analyzing the frequency equation are discussed and presented graphically. It is important to note that the Rayleigh wave velocity in an orthotropic elastic medium increases a considerable amount in comparison to the Rayleigh wave velocity in an isotropic material. The results indicate that the effects of rotation, initial stress and gravity field on Rayleigh wave velocity are very pronounced.
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propagation of Rayleigh Waves in generalized magneto thermoelastic orthotropic material under initial stress and gravity field
Applied Mathematical Modelling, 2011Co-Authors: A M Abdalla, S M Abodahab, H A H HammadAbstract:Abstract In this paper the influence of the gravity field, relaxation times and initial stress on propagation of Rayleigh Waves in an orthotropic magneto-thermoelastic solid medium has been investigated. The solution of the more general equations are obtained for thermoelastic coupling by Helmoltz’s theorem. The frequency equation which determines Rayleigh wave velocity have been obtained. Many special cases are investigated from the present problem. Numerical results analyzing the frequency equation are obtained and presented graphically. Relevant results of previous investigations are deduced as special cases from these results. The results indicate that the effect of initial stress, magnetic field and gravity field are very pronounced.
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on generalized magneto thermoelastic Rayleigh Waves in a granular medium under the influence of a gravity field and initial stress
Journal of Vibration and Control, 2011Co-Authors: A M Abdalla, S M Abodahab, H A H Hammad, S R MahmoudAbstract:In this paper, the influence of magnetic field, gravity field and initial stress on Rayleigh Waves propagation in a granular medium under incremental thermal stresses and relaxation times is studied. The frequency equation of Rayleigh Waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular medium. Some special cases are obtained from this study. Analytically, from the results obtained, one may illustrate that the effect of relaxation times, gravity field, initial stress and magnetic field on Rayleigh wave velocity are very pronounced. It is found that the frequency equation of Rayleigh Waves changes with respect to this friction. When the medium is an orthotropic and the magnetic field and friction coefficient vanish, the derived frequency equation reduces to that obtained by Abd-Alla and Ahmed. Relevant results from previous investigations are deduced as special cases of this study.
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influences of rotation magnetic field initial stress and gravity on Rayleigh Waves in a homogeneous orthotropic elastic half space
2010Co-Authors: A M Abdalla, S R Mahmoud, S M AbodahabAbstract:The aim of this paper is to investigate the influences of rotation, magnetic field, initial stress, and gravity field on Rayleigh Waves in a homogeneous orthotropic elastic medium. The government equations is solved by Lame’s potential and obtained the frequency equation which determines the velocity of Rayleigh Waves, including rotation, initial stress, gravity field, and magnetic field, in a homogeneous orthotropic elastic medium has been investigated. Numerical results analyzing the frequency equation are discussed and presented graphically. The results indicate that the effect of rotation, initial stress, magnetic field, and gravity field on Rayleigh wave velocity are very pronounced. Comparison are made with the results in the absence of rotation, initial stress, magnetic field and gravity field.
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Rayleigh Waves in a magnetoelastic half space of orthotropic material under influence of initial stress and gravity field
Applied Mathematics and Computation, 2004Co-Authors: A M Abdalla, H A H Hammad, S M AbodahabAbstract:In this paper, the frequency equation which determines the velocity of Rayleigh Waves, including initial stress, gravity field and magnetic field, in a homogeneous orthotropic elastic medium has been obtained. The theory of generalized surface Waves has firstly been developed and then it has been employed to investigate particular cases of Waves, viz. Rayleigh Waves under the influence of gravity field, initial stress and magnetic field. The frequency equation obtained is in agreement with the corresponding result obtained by Datta [Rev. Roumaine Sci. Tech. Ser. Mec. Appl. 31 (1986) 369], when the initial stress and magnetic field are neglected. Moreover, when the magnetic field is neglected, our result is in agreement with the corresponding result of Abd-Alla [Appl. Math. Comput. 99 (1999) 61]. Numerical results analyzing the frequency equation are discussed and presented graphically. The results indicate that the effect of orthotropy on such Waves is small and can be neglected, while the effect of initial stress, magnetic field and gravity field are very pronounced.
S M Abodahab - One of the best experts on this subject based on the ideXlab platform.
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propagation of Rayleigh Waves in modified couple stress generalized thermoelastic with a three phase lag model
Waves in Random and Complex Media, 2021Co-Authors: Rajesh Kumar, Shaloo Devi, S M AbodahabAbstract:The main aim of this article is to study the problem of propagation of Rayleigh Waves in a homogeneous isotropic modified couple stress generalized thermoelastic medium. The formulation of the prob...
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Rayleigh Waves at the boundary surface of modified couple stress generalized thermoelastic with mass diffusion
Advanced Composite Materials, 2018Co-Authors: Rajesh Kumar, S M Abodahab, Shaloo DeviAbstract:In this problem, we have studied propagation of Rayleigh Waves in an homogeneous isotropic modified couple stress generalized thermoelastic with mass diffusion solid half space in the context of Lord–Shulman (L-S), Green–Lindsay (G-L) theories of thermoelasticity. Secular equations are derived mathematically by using appropriate boundary conditions. The values of determinant of secular equation, Rayleigh wave velocity and attenuation coefficient with respect to angular velocity for different values of wave number and relaxation times in the absence and presence of mass diffusion, are computed numerically. The numerical simulated results are depicted graphically for copper material.
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effect of rotation on Rayleigh Waves in magneto thermoelastic transversely isotropic medium with thermal relaxation times
Journal of Electromagnetic Waves and Applications, 2017Co-Authors: S M Abodahab, Siddhartha BiswasAbstract:AbstractThe present article deals with the propagation of Rayleigh surface Waves in homogeneous transversely isotropic medium. Effect of rotation on Rayleigh Waves in thermoelastic half-space is studied under the purview of the three-phase-lag model in presence of magnetic field. The normal mode analysis is used to obtain the expressions for the displacement components, stresses, and temperature distribution. The frequency equations in the closed form are derived and the path of particles during Rayleigh wave propagation is found elliptical. In order to illustrate the analytical developments, the numerical solution is carried out and the computer-simulated results in respect of Rayleigh wave velocity, attenuation coefficient, and specific loss are presented graphically.
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mathematical model for Rayleigh Waves in microstretch thermoelastic medium with microtemperatures
Journal of Applied Science and Engineering, 2017Co-Authors: Arvind Kumar, Rajesh Kumar, S M AbodahabAbstract:ABSTRACT This paper is concerned with the study of propagation of Rayleigh Waves in a homogeneous isotropic microstretch-thermoelastic solid half-space with microtemperatures in the context of theory of thermoelasticity. The medium is subjected to stress free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases are also deduced from the present investigation.
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propagation of Rayleigh Waves in a rotating orthotropic material elastic half space under initial stress and gravity
Journal of Mechanical Science and Technology, 2012Co-Authors: A M Abdalla, S M Abodahab, T A AlthamaliAbstract:This paper aims to investigate the influence of rotation, initial stress and gravity field on the propagation of Rayleigh Waves in a homogeneous orthotropic elastic medium. The government equations and Lame’s potentials are used to obtain the frequency equation which determines the velocity of Rayleigh Waves, including rotation, initial stress and gravity field, in a homogeneous, orthotropic elastic medium has been investigated. The numerical results analyzing the frequency equation are discussed and presented graphically. It is important to note that the Rayleigh wave velocity in an orthotropic elastic medium increases a considerable amount in comparison to the Rayleigh wave velocity in an isotropic material. The results indicate that the effects of rotation, initial stress and gravity field on Rayleigh wave velocity are very pronounced.
Vu Thi Ngoc Anh - One of the best experts on this subject based on the ideXlab platform.
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Rayleigh Waves in an incompressible orthotropic half-space coated by a thin elastic layer
Archives of Mechanics, 2014Co-Authors: Pham Chi Vinh, Nguyen Thi Khanh Linh, Vu Thi Ngoc AnhAbstract:The present paper is concerned with the propagation of Rayleigh Waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The halfspace and the layer are both incompressible and they are in welded contact to each other. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method an approximate secular equation of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From it an approximate formula of third-order for the velocity of Rayleigh Waves is obtained and it is a good approximation. The obtained approximate secular equation and formula for the velocity will be useful in practical applications.
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Rayleigh Waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact
International Journal of Engineering Science, 2014Co-Authors: Pham Chi Vinh, Vu Thi Ngoc AnhAbstract:Abstract In the present paper, we are interested in the propagation of Rayleigh Waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main aim of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate secular equations of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From the secular equation obtained, an approximate formula of third-order for the Rayleigh wave velocity is derived and it is a good approximation.
S R Mahmoud - One of the best experts on this subject based on the ideXlab platform.
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Influence of rotation and generalized magneto-thermoelastic on Rayleigh Waves in a granular medium under effect of initial stress and gravity field
Meccanica, 2012Co-Authors: S R MahmoudAbstract:Influence of rotation, relaxation times, magnetic field, initial stress and gravity field on attenuation coefficient (Imaginary part of frequency equation root) and Rayleigh Waves velocity (the real part of frequency equation root) in an elastic half-space of granular medium is studied. The analytical solution is obtained by using Lame’s potential techniques. The numerical calculations are carried out for the frequency equation of Rayleigh Waves velocity. The results are displayed graphically. Some results of previous investigations are deduced as special cases from this study.
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Effect of Rotation, Gravity Field and Initial Stress on Generalized Magneto-Thermoelastic Rayleigh Waves in a Granular Medium
2011Co-Authors: S R MahmoudAbstract:In the present paper, the effect of rotation, magnetic field, initial stress and gravity field on Rayleigh Waves velocity in an elastic half-space of granular medium is investigated. The solution of the problem is obtained by using Lame's potential techniques. The frequency equation of Rayleigh Waves in the form of a determinant containing a term involving the coefficient of friction of a granular medium is obtained. The numerical calculations are carried out for the frequency equation of Ralyeigh Waves velocity. The results are displayed graphically to illustrate the effect of rotation, relaxation times, magnetic and gravity fields and initial stress on Rayleigh wave velocity are very pronounced. Relevant results of previous investigations are deduced as special cases from this study.
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on generalized magneto thermoelastic Rayleigh Waves in a granular medium under the influence of a gravity field and initial stress
Journal of Vibration and Control, 2011Co-Authors: A M Abdalla, S M Abodahab, H A H Hammad, S R MahmoudAbstract:In this paper, the influence of magnetic field, gravity field and initial stress on Rayleigh Waves propagation in a granular medium under incremental thermal stresses and relaxation times is studied. The frequency equation of Rayleigh Waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular medium. Some special cases are obtained from this study. Analytically, from the results obtained, one may illustrate that the effect of relaxation times, gravity field, initial stress and magnetic field on Rayleigh wave velocity are very pronounced. It is found that the frequency equation of Rayleigh Waves changes with respect to this friction. When the medium is an orthotropic and the magnetic field and friction coefficient vanish, the derived frequency equation reduces to that obtained by Abd-Alla and Ahmed. Relevant results from previous investigations are deduced as special cases of this study.
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influences of rotation magnetic field initial stress and gravity on Rayleigh Waves in a homogeneous orthotropic elastic half space
2010Co-Authors: A M Abdalla, S R Mahmoud, S M AbodahabAbstract:The aim of this paper is to investigate the influences of rotation, magnetic field, initial stress, and gravity field on Rayleigh Waves in a homogeneous orthotropic elastic medium. The government equations is solved by Lame’s potential and obtained the frequency equation which determines the velocity of Rayleigh Waves, including rotation, initial stress, gravity field, and magnetic field, in a homogeneous orthotropic elastic medium has been investigated. Numerical results analyzing the frequency equation are discussed and presented graphically. The results indicate that the effect of rotation, initial stress, magnetic field, and gravity field on Rayleigh wave velocity are very pronounced. Comparison are made with the results in the absence of rotation, initial stress, magnetic field and gravity field.
