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Advances in Applied Mathematics and Mechanics 2023年第6期15卷 1655-1698页

作者： A.Mohammadpour S.Jafari Mehrabadi P.Yousefi H.Mohseni Monfared Department of Mechanical Engineering Islamic Azad UniversityArak Branch.ArakIran

Recently,the use of porous materials has grown widely in many structures,such as beams,plates,and shells.The characteristics of porous materials change in the thickness direction by different functions.This study has investigated the free vibration analysis of a sandwich porous elliptical micro-shell with a magneto-rheological fluid(MRF)core for the first time.Initially,we examined the displacement of the middle layer’s macro-and micro-components,using Love’s shell theory.Next,we used the modified couple stress theory(MCST)to obtain the strain and symmetrical curvature tensors for the three layers.The Hamilton’s principle was implemented to derive the equations of motion.We also used the Galerkin’s method to solve the equations of motion,resulting in a system of equations in the form of a linear eigenvalue problem.By solving the governing equations,we obtained the various natural frequencies and loss factors of the elliptical micro-shell,and compared them with the results in earlier studies.Lastly,we investigated the effects of thickness,porosity distribution pattern,aspect ratio,length scale parameter,and magnetic field intensity on the natural frequency and loss factor of the micro-shell.The data accuracy was validated by comparing them with those of reputable previous articles.

关键词： Elliptical micro shell free vibration magneto-rheological core modified couple stress theory sandwich porous material

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

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Defence Technology（防务技术） 2021年第1期17卷 119-134页

作者： Maryam Lori Dehsaraji Mohammad Arefi Abbas Loghman Department of Solid Mechanics Faculty of Mechanical EngineeringUniversity of KashanKashanIran

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

关键词： Thickness stretching effect Shear and normal deformation theory Vibration analysis Length scale parameter modified couple stress theory

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING modified couple stress theory

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Acta Mechanica Solida Sinica 2013年第4期26卷 427-440页

作者： Behrokh Abbasnejad Ghader Rezazadeh Rasool Shabani Mechanical Engineering Department Urmia University

Based on the modified couple stress theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.

关键词： MEMS FGM micro-beam stability pull-in voltage electrostatic pressure modified couple stress theory

A Size-Dependent Functionally Graded Higher Order Plate Analysis Based on modified couple stress theory and Moving Kriging Meshfree Method

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Computers, Materials & Continua 2018年第12期57卷 447-483页

作者： T.D.Tran Chien H.Thai H.Nguyen-Xuan Faculty of Construction&Electricity Ho Chi Minh City Open UniversityHo Chi Minh CityVietnam Division of Computational Mechanics Ton Duc Thang UniversityHo Chi Minh CityVietnam Faculty of Civil Engineering Ton Duc Thang UniversityHo Chi Minh CityVietnam Center for Interdisciplinary Research in Technology Ho Chi Minh City University of Technology(HUTECH)Ho Chi Minh CityVietnam Department of Physical Therapy Graduate Institute of Rehabilitation ScienceChina Medical UniversityTaichung40402Taiwan

A size-dependent computational approach for bending,free vibration and buckling analyses of isotropic and sandwich functionally graded(FG)microplates is in this study presented.We consider both shear deformation and small scale effects through the generalized higher order shear deformation theory and modified couple stress theory(MCST).The present model only retains a single material length scale parameter for capturing properly size effects.A rule of mixture is used to model material properties varying through the thickness of plates.The principle of virtual work is used to derive the discrete system equations which are approximated by moving Kriging interpolation(MKI)meshfree method.Numerical examples consider the inclusions of geometrical parameters,volume fraction,boundary conditions and material length scale parameter.Reliability and effectiveness of the present method are confirmed through numerical results.

关键词： modified couple stress theory isotropic and sandwich FGM plates moving Kriging meshfree method

A size-dependent composite laminated skew plate model based on a new modified couple stress theory

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Acta Mechanica Solida Sinica 2017年第1期30卷 75-86页

作者： Dan He Wanli Yang Wanji Chen Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation Shenyang Aerospace University

In this study, a size-dependent composite laminated skew Mindlin plate model is proposed based on a new modified couple stress theory. This plate model can be viewed as a simplified couple stress theory in engineering mechanics. Governing equations and related boundary conditions are derived based on the principle of minimum potential energy. The Rayleigh–Ritz method is employed to obtain the numerical solutions of the center deflections of simply supported plates with different ply orientations. Numerical results show that the normalized center deflections obtained by the proposed model are always smaller than those obtained by the classical one, i.e. the present model can capture the scale effects of microstructures. Moreover, a phenomenon reveals that the ply orientation would make a significant influence on the magnitude of scale effects of composite laminated plates at micro scale. Additionally, the present model of thick skew plate can be degenerated to the model of Kirchhoff plate based on the modified couple stress theory by adopting the assumptions in Bernoulli–Euler beam and material isotropy.

关键词： modified couple stress theory Composite laminated plates Scale effects Ply orientation Rayleigh-Ritz method

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

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Applied Mathematics and Mechanics(English Edition) 2015年第12期36卷 1555-1568页

作者： Junhua ZHU Renhuai LIU Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory China Electronic Product Reliability and Environmental Testing Research Institute Institute of Applied Mechanics Jinan University

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.

关键词： stepped cantilever beam pull-in voltage modified couple stress theory radio frequency （RF） micro electro-mechanical system （MEMS） switch analytical solution,sensitivity analysis

VIBRATION ANALYSIS OF MICROSCALE PLATES BASED ON modified couple stress theory

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Acta Mechanica Solida Sinica 2010年第5期23卷 386-393页

作者： Li Yin Department of Mechanics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment Wuhan 430074 China

A non-classical Kirchhoff plate model is developed for the dynamic analysis of microscale plates based on the modified couple stress theory in which an internal material length scale parameter is included. Unlike the classical Kirchhoff plate model, the newly developed model can capture the size effect of microscale plates. Two boundary value problems of rectangular micro- plates are solved and the size effect on the lowest two natural frequencies is investigated. It is shown that the natural frequencies of the microscale plates predicted by the current model are size-dependent when the plate thickness is comparable to the material length scale parameter.

关键词： microscale plate vibration natural frequency modified couple stress theory size effect

Application of modified couple stress theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 23-42页

作者： Mir Masoud Seyyed Fakhrabadi School ofMechanical Engineering College of EngineeringUniversity of TehranTehranIran

The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method.Due to the less accuracy of the classical elasticity theorems,the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes.Both of the static and dynamic behaviors under static DC and step DC voltages are discussed.The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.

关键词： Carbon nanotubes modified couple stress theory homotopy perturbation method electrostatic actuation

modified couple stress and thickness-stretching included formulation of a sandwich micro shell subjected to electro-magnetic load resting on elastic foundation

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Defence Technology（防务技术） 2022年第11期18卷 1935-1944页

作者： Jun Song Didi Wu Mohammad Arefi School of Energy Engineering Huanghuai UniversityZhumadian463000HenanChina Henan Key Laboratory of Smart Lighting Huanghuai UniversityZhumadian463000HenanChina School of Culture and Communication Zhumadian463000HenanChina Faculty of Mechanical Engineering Department of Solid MechanicsUniversity of KashanKashan87317-51167Iran Department of Engineering and Architecture University of ParmaParco Area delle Scienze 181/A43124ParmaItaly

This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal deformable model.modified-couple-stress-theory(MCST)is used for accounting small-scaledependency.The numerical results are derived using an analytical method.The effect of small scale parameter in micro scale,initial electric and magnetic potentials and foundation parameters is studied on the electromagnetoelastic bending results.It is confirmed an enhancing in stiffness of small scale shell with an increase in micro length scale parameter.

关键词： Electromagnetoelastic bending analysis Curved shell Thickness stretching formulation modified couple stress theory

Dynamic modeling of preloaded size-dependent nano-crystalline nano-structures

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Applied Mathematics and Mechanics(English Edition) 2017年第12期38卷 1753-1772页

作者： F.EBRAHIMI M.R.BARATI Department of Mechanical Engineering Faculty of EngineeringImam Khomeini International University Aerospace Engineering Department and Center of Excellence in Computational Aerospace Amirkabir University of Technology

The vibration behavior of size-dependent nano-crystalline nano-beams is investigated based on nonlocal, couple stress and surface elasticity theories. A nano- crystalline nano-beam is composed of three phases which are nano-grains, nano-voids, and interface. Nano-voids or porosities inside the material have a stiffness-softening impact on the nano-beam. A Eringen＇s nonlocal elasticity theory is applied in the analysis of nano-crystalline nano-beams for the first time. Residual surface stresses which are usually neglected in modeling nano-crystalline nano-beams are incorporated into nonlocal elasticity to better understand the physics of the problem. Also, a modified couple stress theory is used to capture rigid rotations of grains. Applying a differential transform method （DTM） satisfying various boundary conditions, the governing equations obtained from the Hamilton＇s principle are solved. Reliability of the proposed approach is verified by comparing the obtained results with those provided in the literature. The effects of the nonlocal parameter, surface effect, couple stress, grain size, porosities, and interface thickness on the vibration characteristics of nano-crystalline nano-beams are explored.

关键词： surface effect free vibration nano-crystalline nano-beam nonlocal elasticity modified couple stress theory