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Surkay D Akbarov - One of the best experts on this subject based on the ideXlab platform.
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time harmonic dynamical stress field in a system comprising a pre stressed Orthotropic Layer and pre stressed Orthotropic half plane
Archive of Applied Mechanics, 2010Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:The time-harmonic dynamical stress field in a system comprising a pre-stressed Orthotropic Layer and Orthotropic half-plane is studied within the scope of the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in an initially stressed body. The main focus is on the influence of the mechanical properties of the constituent materials and the initial stresses present on the “resonance” values of the normal stress acting on the interface plane and on the “resonance” values of the frequency of the external point-located force. The numerical results are presented and discussed. In particular, it is shown that the values of the normal stress decrease with a decrease in the modulus of elasticity of the materials along the thickness of the covering Layer.
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dynamics of a system comprising an Orthotropic Layer and Orthotropic half plane under the action of an oscillating moving load
International Journal of Solids and Structures, 2009Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:This paper investigates the dynamic response to a time-harmonic oscillating moving load of a system comprising a covering Layer and half-plane, within the scope of the piecewise-homogeneous body model utilizing of the exact equations of the linear theory of elastodynamics. It is assumed that the materials of the Layer and half-plane are anisotropic (Orthotropic), and that the velocity of the line-located time-harmonic oscillating moving load is constant as it acts on the free face of the covering Layer. Our investigations were carried out for a two-dimensional problem (plane-strain state) under subsonic velocity for a moving load in complete and incomplete contact conditions. The corresponding numerical results were obtained for the stiffer Layer and soft half-plane system in which the modulus of elasticity of the covering Layer material (for the moving direction of the load) is greater than that of the half-plane material. Numerical results are presented and discussed for the critical velocity, displacement and stress distribution for various values of the problem parameters. In particular, it is established that the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the existence of the oscillation of the moving load causes two types of critical velocity to appear: one of which is less, but the other one is greater than that attained for the case where the mentioned oscillation is absent.
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dynamics of a system comprising a pre stressed Orthotropic Layer and pre stressed Orthotropic half plane under the action of a moving load
International Journal of Solids and Structures, 2008Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:This paper investigates the dynamic response to a moving load of a system comprising an initially stressed covering Layer and initially stressed half-plane, within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It was assumed that the materials of the Layer and half-plane are anisotropic (Orthotropic), and that the velocity of the line-located moving load is constant as it acts on the free face of the covering Layer. The investigations were made for a two-dimensional problem (plane-strain state) under subsonic velocity of the moving load for complete and incomplete contact conditions. Corresponding numerical results were obtained for the stiffer Layer and soft half-plane system in which the modulus of elasticity of the covering Layer material (for the moving direction of the load) is greater than that of the half-plane material, which was assumed to be isotropic. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it was established that, the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the initial stretching of the covering Layer causes to increase these values.
Lokenath Debnath - One of the best experts on this subject based on the ideXlab platform.
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on elastodynamical problem of interfacial griffith cracks in composite media
International Journal of Engineering Science, 2004Co-Authors: Subir Das, Bichitrananda Patra, Lokenath DebnathAbstract:The plane strain problem of determining stress intensity factors for two equal and parallel moving interfacial Griffith cracks in composite media consisting of an Orthotropic Layer bonded two dissimilar Orthotropic half planes is considered. The problem is reduced to solution of two pair of simultaneous singular integral equations containing Cauchy kernels. Expressions for stress intensity factor are obtained for the case of a general loading distribution.
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interaction between griffith cracks in a sandwiched Orthotropic Layer
Applied Mathematics Letters, 2003Co-Authors: Subir Das, Lokenath DebnathAbstract:A study is made of the interaction between three coplanar Griffith cracks which are located symmetrically in the midplane of an Orthotropic Layer of finite thickness 2h sandwiched between two identical Orthotropic half planes. The Fourier transform technique is used to reduce the elastostatic problem to a set of integral equations which have been solved by using the finite Hilbert transform and Cooke's results. Analytical expressions for the stress intensity factors at the tips of cracks are obtained for large values of h. Numerical results concerning the interaction effects are presented with physical significance. It is shown that interaction effects are either shielding or amplification depending on the location of cracks, spacing of crack-tips, and the thickness of the Layer. The stress magnification factors at the crack-tips are also calculated.
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stress intensity factors around two co planar griffith cracks in an Orthotropic Layer sandwiched between two identical Orthotropic half planes
International Journal of Engineering Science, 2000Co-Authors: S Das, B Patra, Lokenath DebnathAbstract:Abstract An integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of two collinear Griffith cracks located in an Orthotropic elastic Layer of finite thickness 2 h sandwiched between two identical Orthotropic half planes. For large h analytical expressions for the stress intensity factors are determined up to the order h −4 . Graphical plots of the numerical results are also presented.
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stress intensity factors for an interfacial crack between an Orthotropic half plane bonded to a dissimilar Orthotropic Layer with a punch
Computers & Mathematics With Applications, 1998Co-Authors: S Das, Bichitrananda Patra, Lokenath DebnathAbstract:Abstract The plane strain problem of determining Stress Intensity Factors (SIF) for a moving interfacial Griffith crack between an elastic Orthotropic half-plane and a dissimilar Orthotropic Layer with a moving punch situated along the boundary of the Layer have been considered. The problem is reduced to the solution of three simultaneous singular integral equations with Cauchy-type singularities. Expressions for SIF for the case of a general loading are obtained. Numerical results for some particular cases are also presented graphically.
Nihat Ilhan - One of the best experts on this subject based on the ideXlab platform.
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time harmonic dynamical stress field in a system comprising a pre stressed Orthotropic Layer and pre stressed Orthotropic half plane
Archive of Applied Mechanics, 2010Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:The time-harmonic dynamical stress field in a system comprising a pre-stressed Orthotropic Layer and Orthotropic half-plane is studied within the scope of the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in an initially stressed body. The main focus is on the influence of the mechanical properties of the constituent materials and the initial stresses present on the “resonance” values of the normal stress acting on the interface plane and on the “resonance” values of the frequency of the external point-located force. The numerical results are presented and discussed. In particular, it is shown that the values of the normal stress decrease with a decrease in the modulus of elasticity of the materials along the thickness of the covering Layer.
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dynamics of a system comprising an Orthotropic Layer and Orthotropic half plane under the action of an oscillating moving load
International Journal of Solids and Structures, 2009Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:This paper investigates the dynamic response to a time-harmonic oscillating moving load of a system comprising a covering Layer and half-plane, within the scope of the piecewise-homogeneous body model utilizing of the exact equations of the linear theory of elastodynamics. It is assumed that the materials of the Layer and half-plane are anisotropic (Orthotropic), and that the velocity of the line-located time-harmonic oscillating moving load is constant as it acts on the free face of the covering Layer. Our investigations were carried out for a two-dimensional problem (plane-strain state) under subsonic velocity for a moving load in complete and incomplete contact conditions. The corresponding numerical results were obtained for the stiffer Layer and soft half-plane system in which the modulus of elasticity of the covering Layer material (for the moving direction of the load) is greater than that of the half-plane material. Numerical results are presented and discussed for the critical velocity, displacement and stress distribution for various values of the problem parameters. In particular, it is established that the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the existence of the oscillation of the moving load causes two types of critical velocity to appear: one of which is less, but the other one is greater than that attained for the case where the mentioned oscillation is absent.
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dynamics of a system comprising a pre stressed Orthotropic Layer and pre stressed Orthotropic half plane under the action of a moving load
International Journal of Solids and Structures, 2008Co-Authors: Surkay D Akbarov, Nihat IlhanAbstract:This paper investigates the dynamic response to a moving load of a system comprising an initially stressed covering Layer and initially stressed half-plane, within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It was assumed that the materials of the Layer and half-plane are anisotropic (Orthotropic), and that the velocity of the line-located moving load is constant as it acts on the free face of the covering Layer. The investigations were made for a two-dimensional problem (plane-strain state) under subsonic velocity of the moving load for complete and incomplete contact conditions. Corresponding numerical results were obtained for the stiffer Layer and soft half-plane system in which the modulus of elasticity of the covering Layer material (for the moving direction of the load) is greater than that of the half-plane material, which was assumed to be isotropic. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it was established that, the critical velocity of the moving load is controlled mainly with a Rayleigh wave speed of a half-plane material and the initial stretching of the covering Layer causes to increase these values.
Vu Thi Ngoc Anh - One of the best experts on this subject based on the ideXlab platform.
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explicit transfer matrix for an incompressible Orthotropic elastic Layer and applications
Zeitschrift für Angewandte Mathematik und Physik, 2021Co-Authors: Vu Thi Ngoc Anh, Pham Chi Vinh, N T K Linh, L T ThangAbstract:In this paper, we establish transfer matrix for an incompressible Orthotropic elastic Layer. It is explicit and expressed compactly in terms of square brackets. This transfer matrix is a very convenient tool for solving various problems of wave propagation in Layered elastic media including incompressible Orthotropic Layers. To prove this point, we apply it to investigate the reflection of SV-waves from an incompressible Orthotropic Layer overlying an incompressible Orthotropic half-spaces and the propagation of Lamb waves in a composite plate consisting of two incompressible Orthotropic Layers. By using the obtained transfer matrix along with the effective boundary condition technique, we reduce the reflection of SV-waves from the Layer to the reflection of SV-waves from the surface of half-space. The necessary and sufficient conditions for one or two reflected waves to exist have been established, and formulas for the reflection coefficients have been derived. Unlike the previously obtained formulas, the formulas derived in the present paper for the reflection coefficients are totally explicit. Employing the obtained transfer matrix, we arrive immediately at explicit dispersion equation of Lamb waves. Based on the obtained dispersion equation, it is shown numerically that for a two-Layered plate with high-contrast material properties of the Layers, the cutoff frequency of the first harmonic is close to zero. That means the low-frequency vibration spectrum of strongly inhomogeneous two-Layered plates involves not only the fundamental bending mode, but also the first harmonic.
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on a technique for deriving the explicit secular equation of rayleigh waves in an Orthotropic half space coated by an Orthotropic Layer
Waves in Random and Complex Media, 2016Co-Authors: Pham Chi Vinh, Vu Thi Ngoc Anh, Nguyen Thi Khanh LinhAbstract:The secular equation of Rayleigh propagating in an Orthotropic half-space coated by an Orthotropic Layer has been obtained by Sotiropolous [Sotiropolous, D. A. (1999), The e®ect of anisotropy on guided elastic waves in a Layered half-space, Mechanics of Materials 31, 215–233] and by Sotiropolous & Tougelidis [Sotiropolous, D. A. and Tougelidis, G. (1998), Guided elastic waves in Orthotropic surface Layer, Ultrasonics 36, 371–374]. However, it is not totally explicit and some misprints have occurred in this secular equation in both papers. This secular equation was derived by expanding directly a six-order determinant originated from the traction-free conditions at the top surface of the Layer and the continuity of displacements and stresses through the interface between the Layer and the half-space. Since the expansion of this six-order determinant was not shown in both two papers, it has been difficult to readers to recognize these misprints. This paper presents a technique that provides a totally explic...
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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 Das - One of the best experts on this subject based on the ideXlab platform.
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interaction between line cracks in an Orthotropic Layer
International Journal of Mathematics and Mathematical Sciences, 2002Co-Authors: S DasAbstract:We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an Orthotropic Layer of finite thickness 2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips are obtained for large h. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the Layer.
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stress intensity factors around two co planar griffith cracks in an Orthotropic Layer sandwiched between two identical Orthotropic half planes
International Journal of Engineering Science, 2000Co-Authors: S Das, B Patra, Lokenath DebnathAbstract:Abstract An integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of two collinear Griffith cracks located in an Orthotropic elastic Layer of finite thickness 2 h sandwiched between two identical Orthotropic half planes. For large h analytical expressions for the stress intensity factors are determined up to the order h −4 . Graphical plots of the numerical results are also presented.
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stress intensity factors for an interfacial crack between an Orthotropic half plane bonded to a dissimilar Orthotropic Layer with a punch
Computers & Mathematics With Applications, 1998Co-Authors: S Das, Bichitrananda Patra, Lokenath DebnathAbstract:Abstract The plane strain problem of determining Stress Intensity Factors (SIF) for a moving interfacial Griffith crack between an elastic Orthotropic half-plane and a dissimilar Orthotropic Layer with a moving punch situated along the boundary of the Layer have been considered. The problem is reduced to the solution of three simultaneous singular integral equations with Cauchy-type singularities. Expressions for SIF for the case of a general loading are obtained. Numerical results for some particular cases are also presented graphically.