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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

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变厚度非均匀粘弹性复合圆柱体的旋转应力

应用数学和力学 2011年第4期32卷 483-496页

作者： a.m.任库尔黄锋(译) 张禄坤(校) 阿卜杜勒阿齐兹国王大学理学院数学系 80203邮箱吉达21589沙特阿拉伯卡夫拉一谢赫大学理学院数学系卡夫拉-谢赫35516埃及不详

在平面应变的假设下,给出了两个复合弹性圆柱体旋转时的解析解.外柱是由厚度按公式变化的正交各向异性材料所组成,它包裹着一个等厚度纤维增强粘弹性均匀各向同性的实心圆柱体.外圆柱体的厚度和弹性性质按半径方向的幂函数变化.应用边... 详细信息

在平面应变的假设下,给出了两个复合弹性圆柱体旋转时的解析解.外柱是由厚度按公式变化的正交各向异性材料所组成,它包裹着一个等厚度纤维增强粘弹性均匀各向同性的实心圆柱体.外圆柱体的厚度和弹性性质按半径方向的幂函数变化.应用边界和连续条件,确定复合圆柱体旋转时的径向位移和应力,应用等效模量和Illyushin逼近法,得到问题的粘弹性解.讨论了各向异性、厚度变化、本构参数以及时间参数,对径向位移和应力的影响.

关键词：旋转的复合圆柱体正交各向异性非均匀性变厚度纤维增强的粘弹性核心体

Bending of orthotropic plates resting on Pasternak's foundations using mixed shear deformation theory

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Acta.m.chanica Sinica 2011年第6期27卷 956-962页

作者： a.m.zenkour Department of mathematics Faculty of Science King AbdulAziz University Department of mathematics Faculty of Science Kafrelsheikh University

The mixed first-order shear deformation plate theory（mFPT） is employed to study the bending response of simply-supported orthotropic *** present plate is subjected to a.m.chanical load and resting on Pasternak＇s model or Winkler＇s model of elastic foundation or without any elastic *** examples are presented to verify the accuracy of the present *** results for deflection and stresses are *** proposed mFPT is shown simplely to implement and capable of giving satisfactory results for shear deformable plates under static loads and resting on two-parameter elastic *** results presented here show that the characteristics of deflection and stresses are significantly influenced by the elastic foundation stiffness,plate aspect ratio and side-to-thickness ratio.

关键词： mixed theory Bending Rectangular plates Pasternak's model

Stresses in rotating heterogeneous viscoelastic composite cylinders with variable thickness

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Applied mathematics and mechanics(English Edition) 2011年第4期32卷 507-520页

作者： a.m.zenkour Department of mathematics Faculty of ScienceKing AbdulAziz University Department of mathematics Faculty of ScienceKafrelsheikh University

An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material. It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions, the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin＇s approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness variation, constitutive, time parameters on the radial displacement, and stresses are investigated.

关键词： rotating composite cylinder orthotropic heterogeneous variable-thickness fiber-reinforced viscoelastic core

BENDING RESPONSES OF AN EXPONENTIALLY GRADED SImPLY-SUPPORTED ELASTIC/VISCOELASTIC/ELASTIC SANDWICH PLATE

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Acta.m.chanica Solida Sinica 2011年第3期24卷 250-261页

作者： a.m.zenkour Department of mathematics Faculty of ScienceKing AbdulAziz University Department of mathematics Faculty of ScienceKafr El-Sheikh University

The bending response for exponentially graded composite （EGC） sandwich plates is investigated. The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories. Four types of sand- wich plates are considered taking into account the symmetry of the plate and the thickness of each layer. The effective moduli and Illyushin＇s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates. Then numerical results for deflections and stresses are presented and the effects due to time parameter, aspect ratio, side-to-thickness ratio and constitutive parameter are investigated.

关键词： symmetric sandwich plates viscoelasticity EGC sinusoidal plate theory

The effect of fractional thermoelasticity on a two-dimensional problem of a.m.de I crack in a rotating fiber-reinforced thermoelastic medium

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Chinese Physics B 2013年第10期22卷 575-582页

作者： a.m.d E.Abouelregal Ashraf m.zenkour Department of mathematics Faculty of ScienceMansoura University Department of mathematics Faculty of ScienceKing Abdulaziz University Department of mathematics College of Science and ArtsUniversity of Aljouf Department of mathematics Faculty of ScienceKafrelsheikh University

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a.m.de-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.

关键词： fiber-reinforced mode-I crack fractional order thermoelasticity theory rotating medium norma.m.de analysis

Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation

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Applied mathematics and mechanics(English Edition) 2020年第8期41卷 1269-1286页

作者： a.m.zenkour H.D.EL-SHAHRANY Department of mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt Department of mathematics Faculty of ScienceBisha UniversityBisha 61922Saudi Arabia

The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is *** constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration *** formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam ***’s principle is utilized to give the equations of motion and then to describe the vibration of the current *** on Navier’s approach,the solution of the dynamic system is *** effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.

关键词： vibration suppression laminated composite beam magnetostrictive material visco-Pasternak’s foundation

Thermoelastic diffusion problem for a half-space due to a refined dual-phase-lag Green-Naghdi model

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Journal of Ocean Engineering and Science 2020年第3期5卷 214-222页

作者： Ashraf m.zenkour Department of mathematics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt

The thermoelastic diffusion problem of an isotropic half-space is *** Green-Naghdi model with and without energy dissipation is *** multi single/dual-phase-lag models are presented to investigate the thermoelastic diffusion behavior of the *** simple Green-Naghdi type Ⅱ and Ⅲ and their modified models are all examined *** exact solution of thermodiffusion governing equations has been obtained considering the initial and boundary *** validity of results is acceptable by comparing all *** results are reported to help other investigators in their future comparisons.

关键词： Green–NaghdiⅡ Ⅲ Thermodiffusion Chemical potential Dual-phase-lag

Thermodynamical Bending of FGm Sandwich Plates Resting on Pasternak’s Elastic Foundations

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Advances in Applied mathematics and mechanics 2015年第1期7卷 116-134页

作者： moha.m.d Sobhy Ashraf m.zenkour Department of mathematics Faculty of ScienceKing Faisal UniversityP.O.Box 400Hufof 31982Saudi Arabia Department of mathematics Faculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh 33516Egypt

The analysis of thermoelastic deformations of a simply supported functionally graded material(FGm)sandwich plates subjected to a time ha.m.nic sinusoidal temperature field on the top surface and varying through-the-thickness is illustrated in this *** FGm sandwich plates are assumed to be made of three layers and resting on Pasternak’s elastic *** volume fractions of the constituents of the upper and lower layers and,hence,the effective material properties of them are assumed to vary in the thickness direction only whereas the core layer is still *** in-plane sinusoidal variations of the displacements and the temperature that identically satisfy the boundary conditions at the edges,the governing equations of motion are solved analytically by using various shear deformation theories as well as the classical *** influences of the time parameter,power law index,temperature exponent,top-to-bottom surface temperature ratio,side-to-thickness ratio and the foundation parameters on the dynamic bending are investigated.

关键词： FGm sandwich plates dynamic bending elastic foundations thermal load