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Rotating Variable-Thickness Inhomogeneous Cylinders: Part I—Analytical Elastic Solutions

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Applied mathematics 2010年第6期1卷 481-488页

作者： ashraf m. zenkour 不详

In this paper, an analytical solution for the rotation problem of an inhomogeneous hollow cylinder with variable thickness under plane strain assumption is developed. The present cylinder is made of a fiber-reinforced viscoelastic inhomogeneous orthotropic material. The thickness of the cylinder is taken as parabolic function in the radial direction. The elastic properties varies in the same manner as the thickness of the cylinder while the density varies according to an exponential law form. The inner and outer surfaces of the cylinder are considered to have combinations of free and clamped boundary conditions. Analytical solutions are given according to different types of the hollow cylinders. An extension of the present solutions to the viscoelastic ones and some applications are investigated in Part II.

关键词： Rotating Inhomogeneous Cylinders Orthotropic Variable Thickness and Density

Rotating Variable-Thickness Inhomogeneous Cylinders: Part II—Viscoelastic Solutions and Applications

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Applied mathematics 2010年第6期1卷 489-498页

作者： ashraf m. zenkour 不详

Analytical solutions for the rotating variable-thickness inhomogeneous, orthotropic, hollow cylinders under plane strain assumption are developed in Part I of this paper. The extensions of these solutions to the viscoelastic case are discussed here. The method of effective moduli and Illyushin's approximation method are used for this purpose. The rotating fiber-reinforced viscoelastic homogeneous isotropic hollow cylinders with uniform thickness are obtained as special cases of the studied problem. Numerical application examples are given for the dimensionless displacement of and stresses in the different cylinders. The influences of time, constitutive parameter and elastic properties on the stresses and displacement are investigated.

关键词： Rotating Viscoelastic Cylinder Orthotropic Variable Thickness and Density

THE EFFECT OF DUAL-PHASE-LAG mODEL ON REFLECTION OF THERmOELASTIC WAVES IN A SOLID HALF SPACE WITH VARIABLE mATERIAL PROPERTIES

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Acta mechanica Solida Sinica 2013年第6期26卷 659-670页

作者： A.m.zenkour D.S.mashat A.E.Abouelregal Department of mathematics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafr El-Sheikh 33516Egypt Department of mathematics Faculty of ScienceMansoura UniversityMansoura 35516Egypt Department of mathematics College of Science and ArtsUniversity of AljoufEl-QurayatSaudi Arabia

The present article represents an analysis of reflection of P-wave and SV-wave on the boundary of an isotropic and homogeneous generalized thermoelastic half-space when the boundary is stress-free as well as isothermal. The modulus of elasticity is taken as a linear function of reference temperature. The basic governing equations are applied under four theories of the generalized thermoelasticity： Lord-Shulman （L-S） theory with one relaxation time, Green-Naghdi （G-N） theory without energy dissipation and Tzou theory with dual-phase-lag （DPL）, as well as the coupled thermoelasticity （CTE） theory. It is shown that there exist three plane waves, namely, a thermal wave, a P-wave and an SV-wave. The reflection from an isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves. The amplitude ratios variations with the angle of incident are shown graphically. Also the effects of reference temperature of the modulus of elasticity and dual-phase lags on the reflection amplitude ratios are discussed numerically.

关键词： generalized thermoelasticity dual-phase-lag variable material properties reflection waves

Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical methods

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Engineering（科研） 2011年第4期3卷 422-430页

作者： ashraf m. zenkour Daoud S. mashat 不详

In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is available for the first disk while the exact analytical solution is not available for the second annular disk. Both exact and numerical results for stress function, stresses, strains and radial displacement will be investigated for the first annular disk of variable thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second rotating variable-thickness annular disk is investigated. Finally, the distributions of stress function, displacement, strains, and stresses will be presented. The appropriate comparisons and discussions are made at the same angular velocity.

关键词： Rotating Annular Disk Variable Thickness Runge-Kutta method

Thermal buckling analysis of ceramic-metal functionally graded plates

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Natural Science 2010年第9期2卷 968-978页

作者： ashraf m. zenkour Daoud S. mashat 不详

Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.

关键词： Thermal Buckling Non-Linear Strains Functionally Graded material Sinusoidal Plate

Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness

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Applied mathematics 2010年第5期1卷 430-437页

作者： ashraf m. zenkour Daoud S. mashat 不详

In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.

关键词： Rotating Annular Disk Solid Disk Finite Difference method

Two solutions for the BVP of a rotating variable-thickness solid disk

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Natural Science 2011年第2期3卷 145-153页

作者： ashraf m. zenkour Suzan A. Al-Ahmadi 不详

This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.

关键词： Rotating Solid Disk Variable Thickness Analytical method Finite Difference method

Analysis of wave propagation in a functionally graded nanobeam resting on visco-Pasternak＇s foundation

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Theoretical & Applied mechanics Letters 2017年第3期7卷 145-151页

作者： m. Arefi A.m. zenkour Department of Solid mechanic Faculty of Mechanical Engineering University of Kashan Kashan 87317-51167 Iron Department of mathematics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia Department of mathematics Faculty of Science Kafrelsheikh University Kafrelsheikh 33516 Egypt

Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak＇s foundation is studied in this paper. Timoshenko＇s beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton＇s principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.

关键词： wave propagation Timoshenko beam model Phase velocity Non-homogeneous index Visco-Pasternak's foundation

Analysis of Functionally Graded Piezoelectric Cylinders in a Hygrothermal Environment

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Advances in Applied mathematics and mechanics 2014年第2期6卷 233-246页

作者： m.N.m.Allam A.m.zenkour R.Tantawy Department of mathematics Faculty of ScienceMansoura UniversityMansoura 35516Egypt Department of mathematics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafr El-Sheikh 33516Egypt Department of mathematics Faculty of ScienceDamietta University34517Egypt

This paper presents an analytical solution for the interaction of electric potentials,electric displacement,elastic deformations,and describes hygrothermal effect responses in hollow and solid cylinders,subjected to mechanical load and electric *** solutions for displacement,stresses and electric potentials in functionally graded piezoelectric material are determined using the infinitesimal *** material properties coefficients of the present cylinder are assumed to be graded in the radial direction by a power law *** examples display the significant of influence of material *** is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the piezoelectric hollow and solid cylinders responses,which will be of particular importance in modern engineering designs.

关键词： Functionally graded piezoelectric material hygrothermal effect.