Vibration analysis of fluid-conveying multi-scale hybrid nanocomposite shells with respect to agglomeration of nanofillers

The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution.The consistent material is considered to be made from an initial matrix strengthened via both macro-and nano-scale reinforcements.The influence of nanofillers’agglomeration,generated due to the high surface to volume ratio in nanostructures,is included by implementing Eshelby-Mori-Tanaka homogenization scheme.Afterwards,the equivalent material properties of the carbon nanotube reinforced(CNTR)nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture.On the other hand,the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders.A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work.Next,the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions.Presenting a set of illustrations,effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.

A Semi-analytical Method for Vibrational and Buckling Analysis of Functionally Graded Nanobeams Considering the Physical Neutral Axis Position

In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.

Buckling analysis of embedded graphene oxide powder-reinforced nanocomposite shells

In this study,the buckling analysis of a Graphene oxide powder reinforced(GOPR)nanocomposite shell is investigated.The effective material properties of the nanocomposite are estimated through Halpin-Tsai micromechanical scheme.Three distribution types of GOPs are considered,namely uniform,X and O.Also,a first-order shear deformation shell theory is incorporated with the principle of virtual work to derive the governing differential equations of the problem.The governing equations are solved via Galerkin’s method,which is a powerful analytical method for static and dynamic problems.Comparison study is performed to verify the present formulation with those of previous data.New results for the buckling load of GOPR nanocomposite shells are presented regarding for different values of circumferential wave number.Besides,the influences of weight fraction of nanofillers,length and radius to thickness ratios and elastic foundation on the critical buckling loads of GOP-reinforced nanocomposite shells are explored.

Agglomeration Effects on Static Stability Analysis of Multi-Scale Hybrid Nanocomposite Plates

We propose a multiscale approach to study the influence of carbon nanotubes’agglomeration on the stability of hybrid nanocomposite plates.The hybrid nanocomposite consists of both macro-and nano-scale reinforcing fibers dispersed in a polymer matrix.The equivalent material properties are calculated by coupling the Eshelby-Mori-Tanaka model with the rule of mixture accounting for effects of CNTs inside the generated clusters.Furthermore,an energy based approach is implemented to obtain the governing equations of the problem utilizing a refined higher-order plate theorem.Subsequently,the derived equations are solved by Galerkin’s analytical method to predict the critical buckling load.The influence of various boundary conditions is studied as well.After validation,a set of numerical examples are presented to explain how each variant can affect the plate’s natural frequency.

基于传统板理论的智能圆形FGM薄板自由振动研究

基于传统板理论(CPT)对圆形功能梯度(FG)薄板的自由振动性能进行分析。这种板具有2个由压电(PZT4)材料构成的均布驱动器。对FG底层板的材料特性进行假定,考虑了材料体积分数的能量分布,将材料沿厚度方向进行分级,并采用二次方程模拟沿压电覆层厚度方向分布的电势场。采用运动微分方程来模拟板的固定端边界条件。介绍了详细的数学推导过程,并采用数值分析来研究FG板的梯度变化对结构自由振动的影响。其分析结果得到了三维有限元分析结果的证实。

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

In the present work,thermo-electro-mechanical buckling behavior of functionally graded piezoelectric(FGP)nanobeams is investi-gated based on higher-order shear deformation beam theory.The FGP nanobeam is subjected to four types of thermal loading including uniform,linear,and sinusoidal temperature rise as well as heat conduction through the beam thickness.Thermo-electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model.To consider the influences of small-scale sizes,Eringen’s nonlocal elasticity theory is adopted.Applying Hamilton’s princi-ple,the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Navier-type analytical solution.The significance of various parameters,such as thermal loadings,external electric voltage,power-law index,nonlocal parameter,and slenderness ratio on thermal buck-ling response of size-dependent FGP nanobeams is investigated.

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

This work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic func-tionally graded(METE-FG)nanoplates in thermal environments based on a refined trigonometric plate theory.Temperature field has uniform,linear,and nonlinear distributions across the thick-ness.Nonlinear thermal loadings are considered as heat conduc-tion(HC)and sinusoidal temperature rise(STR).A power law function is applied to govern the gradation of material properties through the nanoplate thickness.Considering coupling impacts between magneto,electro,thermo-mechanical loadings,the equa-tions of motion,and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived.The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier’s method.Moreover,the accuracy of the present formulation is examined by comparing the obtained results with published ones.Furthermore,the effects played by the magneto-electrical field,various temperature rises,nonlocality,power law index,side-to-thickness ratio,and aspect ratio on the critical buckling tempera-ture response are all investigated and reported.

Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory

This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.

Effect of temperature on pull-in voltage and nonlinear vibration behavior of nanoplate-based NEMS under hydrostatic and electrostatic actuations

This paper deals with the study of the temperature effect on the nonlinear vibration behavior of nanoplate-based nano electromechanical systems（NEMS） subjected to hydrostatic and electrostatic actuations. Using Eringen＇s nonlocal elasticity and Gurtin–Murdoch theory, the nonlocal plate model is derived through Hamilton＇s principle. The governing equation which is extremely nonlinear due to the geometrical nonlinearity and electrostatic attraction forces is solved numerically using the differential quadrature method（DQM）. The accuracy of the present method is veriied by comparing the obtained results with the experimental data and those in the literature and very good agreement is obtained. Finally a comprehensive study is carried out to determine the inluence of temperature on the nonlinear vibration characteristics of NEMS made of two different materials including aluminum（Al）and silicon（Si） and some conclusions are drawn.

Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

In this paper,the thermal effects on the buckling of functionally graded（FG） nanobeams subjected to various types of thermal loading including uniform,linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory.The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form.The governing equations are derived through Hamilton＇s principle and solved analytically.Comparison examples are performed to verify the present results.Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index,nonlocal parameter,slenderness ratio and thermal loading in detail.