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Sanjay Kumar Mohanty - One of the best experts on this subject based on the ideXlab platform.
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Time-dependent wave motion with undulated bottom
Acta Mechanica, 2020Co-Authors: Sanjay Kumar MohantyAbstract:In the present manuscript, the time-dependent capillary gravity wave motion in the presence of a current and an undulated permeable bottom is analyzed. The spectral method is used to simulate the time-dependent surface elevation. Also, the Laplace–Fourier Transform method is used to obtain the integral form of the surface elevation, and the asymptotic form of the associated highly oscillatory integral is derived using the method of stationary phase. The reflection and transmission coefficients due to the small bottom undulation are obtained using the perturbation method and the Fourier Transform method and also alternatively using Green’s function technique and Green’s identity. The nature of wave energy propagation obtained from plane capillary gravity wave motion is verified through time domain simulation and using the spectral method. It is found that, in the case of co-propagating waves, the wave energy propagates faster and also the surface profiles in terms of wave packets move faster for larger values of the Froude number. Also, the maximum value of the reflection and transmission coefficients decreases due to increasing values of the Froude number. For the sinusoidal bottom topography, the Bragg resonance occurs if the ratio of the wave numbers of the wave and the rippled bed is one by two.
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Time dependent wave motion in a permeable bed
Meccanica, 2020Co-Authors: Sanjay Kumar Mohanty, Manjari SidharthAbstract:The present study deals with the transient flexural gravity wave motion associated with floating elastic plate in the presence of permeable bottom. Integral form of the floating plate deflection is obtained analytically using Laplace–Fourier Transform method and the asymptotic solution is derived for large time using stationary phase method. Also, using fast Fourier Transform method the time domain simulation of floating plate deflection is obtained. The effect of current, compressive force and porosity parameter on phase and group velocities and floating plate deflection are analyzed. It is observed that in the absence of current, due to the presence of porosity parameter there exist two points where there is a situation of no wave propagation. It is also observed that the current and compressive force have significant effect on transient flexural gravity wave motion whereas the porosity parameter has small impact on the gravity wave motion associated with floating elastic plate. The properties of the roots of the dispersion relation associated with the flexural gravity wave motion in the presence of permeable bed are discussed analytically and numerically.
Manjari Sidharth - One of the best experts on this subject based on the ideXlab platform.
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Time dependent wave motion in a permeable bed
Meccanica, 2020Co-Authors: Sanjay Kumar Mohanty, Manjari SidharthAbstract:The present study deals with the transient flexural gravity wave motion associated with floating elastic plate in the presence of permeable bottom. Integral form of the floating plate deflection is obtained analytically using Laplace–Fourier Transform method and the asymptotic solution is derived for large time using stationary phase method. Also, using fast Fourier Transform method the time domain simulation of floating plate deflection is obtained. The effect of current, compressive force and porosity parameter on phase and group velocities and floating plate deflection are analyzed. It is observed that in the absence of current, due to the presence of porosity parameter there exist two points where there is a situation of no wave propagation. It is also observed that the current and compressive force have significant effect on transient flexural gravity wave motion whereas the porosity parameter has small impact on the gravity wave motion associated with floating elastic plate. The properties of the roots of the dispersion relation associated with the flexural gravity wave motion in the presence of permeable bed are discussed analytically and numerically.
Salah Naili - One of the best experts on this subject based on the ideXlab platform.
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ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids a spectral finite element study
Computer Methods in Biomechanics and Biomedical Engineering, 2013Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace–Fourier Transform, the vibroacoustic problem may be Transformed into the frequency–wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.
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Simulation of wave propagation in anisotropic poroelastic bone plate immersed in fluid
2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This paper deals with modeling of the ultrasound axial transmission technique for in vivo cortical long bone which is known as being a anisotropic solid medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic medium using the Biots theory. We develop a hybrid spectral/finite element formulation to obtain the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed two fluid halfspaces. The numerical method is based on a combined Laplace-Fourier Transform which solves the problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performances of the proposed approach. A preliminary study on the FAS (First Arrived Signal) velocities computed by using equivalent elastic and poroelastic models will be presented.
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Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.
International Journal for Numerical Methods in Biomedical Engineering, 2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:SUMMARY This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace–Fourier Transform, which allows to obtain a reduced dimension problem in the frequency–wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented.Copyright © 2012 John Wiley & Sons, Ltd.
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Simulation of transient ultrasonic wave propagation in fluid-loaded heterogeneous cortical bone
Vietnam Journal of Mechanics, 2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. The proposed method is based on a combined Laplace-Fourier Transform which substitutes a problem defined by partial differential equations into a system of differential equations established in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performance of the proposed approach. Keywords: Spectral finite element, transient wave, ultrasound, anisotropic, vibroacoustic, cortical bone, axial transmission.
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Simulation of transient ultrasonic wave propagation in fluid-loaded heterogeneous cortical bone
Vietnam Journal of Mechanics, 2011Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. The proposed method is based on a combined Laplace-Fourier Transform which substitutes a problem defined by partial differential equations into a system of differential equations established in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid half-spaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performance of the proposed approach.
Mridula Kanoria - One of the best experts on this subject based on the ideXlab platform.
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Propagation of thermal waves in a functionally graded thick plate
Mathematics and Mechanics of Solids, 2015Co-Authors: Abhik Sur, Mridula KanoriaAbstract:The aim of the present contribution is concerned with the interactions of thermoelastic displacements, temperatures and stresses for the three-phase-lag and Green–Naghdi heat equations in a functionally graded transversely isotropic plate subjected to a spatially varying heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The governing equations for displacement and temperature fields are obtained in the Laplace–Fourier Transform domain by applying Laplace and Fourier Transform techniques. The inversion of double Transform has been done numerically. The numerical inversion of Laplace Transform is done by using a method based on the Fourier Series expansion technique. The solution to the analogous problem for isotropic material is obtained by taking suitable nonhomogeneity parameters. A comparative study between isotropic material and transversely isotropic material is als...
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Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces
Applied Mathematics and Mechanics, 2011Co-Authors: M. Islam, Sadek Hossain Mallik, Mridula KanoriaAbstract:This paper deals with a two-dimensional (2D) problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier Transform domain by applying the Laplace and Fourier Transforms. The inversion of the double Transform is done numerically. Numerical inversion of the Laplace Transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium (Mg), and the results are presented graphically. The results for an isotropic material (Cu) are obtained numerically and presented graphically to be compared with those of a transversely isotropic material (Mg). The effect of the body forces is also studied.
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Study of Dynamical Response in a Two-Dimensional Transversely Isotropic Thick Plate Due to Heat Source
Journal of Thermal Stresses, 2011Co-Authors: M. Islam, Mridula KanoriaAbstract:This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of three-phase-lag thermoelastic model, GN model II (TEWOED) and GN model III (TEWED). The governing equations for displacement and temperature fields are obtained in Laplace–Fourier Transform domain by applying Laplace and Fourier Transform techniques. The inversion of double Transform has been done numerically. The numerical inversion of Laplace Transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and a comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) are presented graphically. The results for an isotropic material (Cu) have been deduced numerically an...
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A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source
European Journal of Mechanics - A Solids, 2008Co-Authors: Sadek Hossain Mallik, Mridula KanoriaAbstract:Abstract This paper deals with a two dimensional problem for a transversely isotropic thick plate having heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in Laplace–Fourier Transform domain by applying Laplace and Fourier Transform techniques. The inversion of double Transform has been done numerically. The numerical inversion of Laplace Transform is done by using a method based on Fourier Series expansion technique. Numerical computations have been done for magnesium (Mg) and the results are presented graphically. The results for an isotropic material (Cu) have been deduced numerically and presented graphically to compare with those of transversely isotropic material (Mg).
Vuhieu Nguyen - One of the best experts on this subject based on the ideXlab platform.
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ultrasonic wave propagation in viscoelastic cortical bone plate coupled with fluids a spectral finite element study
Computer Methods in Biomechanics and Biomedical Engineering, 2013Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally graded anisotropic material coupled with fluids. The viscous effects are taken into account. The geometrical configuration mimics the one of axial transmission technique used for evaluating the bone quality. We present a numerical procedure adapted for this purpose which is based on the spectral finite element method (FEM). By using a combined Laplace–Fourier Transform, the vibroacoustic problem may be Transformed into the frequency–wavenumber domain in which, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analysed using FEM. Several numerical tests are presented showing very good performance of the proposed approach. We present some results to study the influence of the frequency on the first arriving signal velocity in (visco)elastic bone plate.
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Simulation of wave propagation in anisotropic poroelastic bone plate immersed in fluid
2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This paper deals with modeling of the ultrasound axial transmission technique for in vivo cortical long bone which is known as being a anisotropic solid medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic medium using the Biots theory. We develop a hybrid spectral/finite element formulation to obtain the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed two fluid halfspaces. The numerical method is based on a combined Laplace-Fourier Transform which solves the problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performances of the proposed approach. A preliminary study on the FAS (First Arrived Signal) velocities computed by using equivalent elastic and poroelastic models will be presented.
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Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.
International Journal for Numerical Methods in Biomedical Engineering, 2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:SUMMARY This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace–Fourier Transform, which allows to obtain a reduced dimension problem in the frequency–wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented.Copyright © 2012 John Wiley & Sons, Ltd.
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Simulation of transient ultrasonic wave propagation in fluid-loaded heterogeneous cortical bone
Vietnam Journal of Mechanics, 2012Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. The proposed method is based on a combined Laplace-Fourier Transform which substitutes a problem defined by partial differential equations into a system of differential equations established in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performance of the proposed approach. Keywords: Spectral finite element, transient wave, ultrasound, anisotropic, vibroacoustic, cortical bone, axial transmission.
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Simulation of transient ultrasonic wave propagation in fluid-loaded heterogeneous cortical bone
Vietnam Journal of Mechanics, 2011Co-Authors: Vuhieu Nguyen, Salah NailiAbstract:This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. The proposed method is based on a combined Laplace-Fourier Transform which substitutes a problem defined by partial differential equations into a system of differential equations established in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid half-spaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performance of the proposed approach.
