Cylindrical Microshells Research Articles

On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

Since the multi-layered structures are widely used nowadays, and due to interesting applications of cylindrical shells, this study is dedicated to analyzing free vibrational behaviors of functionally graded saturated porous micro cylindrical shells with two nanocomposite skins. Based on Biot's assumptions, constitutive relations for the core are presented and effective properties of the skins are determined via the rule of mixture. A sinusoidal theory is used to capture the shear deformation effects, and to account for the scale effects, the modified couple stress theory is employed which suggests a material length-scale parameter for predicting the results in small-dimension. With the aid of extended form of Hamilton's principle for dynamic systems, differential equations of motion are extracted. Fourier series functions are used to obtain natural frequencies and after validating them, a set of parametric studies are carried out. The results show the significant effects of porosity and Skempton coefficient, pores placement patterns, CNTs addition and distribution patterns, temperature variations, material length-scale parameter and viscoelastic medium on the natural frequencies of the microstructure. The outcomes of this work could be used to design and manufacture more reliable micro cylindrical structures in thermo-dynamical environments.

Nonlinear dynamic response of functionally graded cylindrical microshells conveying steady viscous fluid

Nonlinear free and forced vibrations for functionally graded (FG) cylindrical microshells conveying steady viscous fluid are investigated based on the shear deformation shell and potential flow theory. The size effects are considered by modified couple stress theory. Steady viscous force produced by fluid are added to the inviscid and incompressible microshell-fluid coupled system using time-mean Navier-Stokes equations. Using Hamilton’s principle, the nonlinear partial differential equations are derived for microshell-fluid system. The reduced nonlinear ordinary differential equations are obtained based on static condensation method and Galerkin’s method. The critical flow velocity and natural frequency are here discussed by changing material composition and scale parameters. Moreover, the effects of axial load, scale parameter, fluid flow velocity and viscosity on nonlinear dynamic response are also investigated. Comparisons with corresponding inviscid case and previously literatures are also here discussed

Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller

The goal of the present research is an investigation of the smart control and wave propagation examination of a graphene nanoplatelets reinforced (GPLRC) cylindrical micro-shell covered with piezoelectric layers as the sensor and actuator (PLSA) in the framework of an analytical method. The stress and strain components are given based on the first-order shear deformable theory (FSDT), and for accessing the size effects, the nonlocal strain gradient theory is used for obtaining the correct results. The material properties of the GPLRC micro-shell are modeled via modified Halpin–Tsai and the rule of the mixture. The external voltage is applied to the sensor layer, and a Proportional-Derivative (PD) controller is used for sensor output control. The governing equations of the electrically micro-shell are derived via Hamilton’s principle. This work concludes that the PD controller, wave number, applied voltage, and weight fraction of graphene nanoplatelets (GPL) have a significant influence on the wave propagation of the GPLRC cylindrical micro-shell. The remarkable result is that consideration of the PD controller leads to expand the stable area and improve the dynamic behaviors of the smart system.

Enhancing vibration performance of a spinning smart nanocomposite reinforced microstructure conveying fluid flow

In this article, critical angular velocity, critical velocity of fluid flow and vibration control analysis of a rotating multi-hybrid nanocomposite reinforced (MHCR) cylindrical microshell covered with a piezoelectric layer as sensor and actuator (PLSA) are presented. The current non-classical model is capable of capturing the size dependency in the microshells using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. This structure is under conveying viscous fluid, and the related force is calculated by the modified formulation of Navier–Stokes. In addition, the current structure rotates around its axial direction. The Coriolis and centrifugal effects due to the rotation are considered. For semi-numerical method, the strains and stresses can be determined through via the first-order shear deformable theory (FSDT). For accessing to various mass densities, thermal expansion as well as Poisson ratio, the rule of mixture is applied, although a modified Halpin–Tsai theory is used for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a Proportional-Derivative (PD) controller has been utilized for controlling output of sensors. The boundary conditions are derived through governing equations of the MHCR cylindrical microshell using energy method known as Hamilton’s principle and finally are solved using generalized differential quadrature method (GDQM). The outcomes show that the angular velocity, velocity of fluid flow, external force, PD controller, external voltage and MHC’s weight fraction have a considerable impact on the amplitude, and vibration behavior of a spinning MHCR cylindrical shell conveying fluid flow.

Thermal buckling analysis of a functionally graded microshell based on higher-order shear deformation and modified couple stress theories

In this study, thermal buckling responses of a functionally graded (FG) cylindrical microshell are investigated. Material properties of the FG microshell are considered to be graded through the thickness based on a simple power-law distribution. The governing equations and associated boundary conditions are derived based on classical higher-order shear deformation theory. Size dependence of the FG microshell is properly characterized based on the modified couple stress theory (MCST). Two types of differential quadrature method (DQM) – polynomial based differential quadrature (PDQ) and Fourier expansion based differential quadrature (FDQ) – are adopted to transform the differential equations into algebraic equations. The standard eigenvalue equation in the whole computational domain is subsequently established to obtain critical buckling temperature. The present numerical technique shows very fast convergence speed and is validated by comparison with available data in the open literature. Parametric studies are provided to demonstrate the influences of the temperature distribution profile, edge boundary conditions, length scale parameter, length-to-radius ratio, FG power-law index on the critical buckling temperature. In addition, the values of critical thermal buckling loads predicted by classical and MCST models are compared.

Size-dependent stability analysis of a functionally graded cylindrical shell subjected to swirling annular flow including the fluid viscosity

In this paper, the stability and dynamics of a functionally graded materials (FGMs) cylindrical micro-shell subjected to swirling annular fluid through the annulus between the inner shell and the outer shell are firstly investigated. The fluid perturbation pressure related to the shell vibration is determined by the potential flow theory. The steady viscous forces are derived based on the fully developed turbulent flow. The shell motion equations are established on the basis of the Hamilton's principle along with the Donnell shell theory. To capture the size effect of micro-shell, the zero-level contour method is adopted to obtain the solutions of shell motion equations. First, the system subjected to an ideal annular flow is studied. The results show effects of the fluid rotation, material length-scale parameter, and material properties on the fluid-micro-shell system stability. Furthermore, the coupling effect of the fluid rotation and the material length-scale parameter on the dynamical stability of the system is evaluated. Second, the system subjected to a viscous annular flow is further studied. A more impressive result is observed that the fluid viscosity effect renders the system subjected to an annular flow more unstable, and the physical explanation for the phenomenon is presented.

Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment

By using differential quadrature method (DQM), forced vibrational behavior of a porous functionally graded (FG) cylindrical scale-dependent shell in thermal environment and under a moving point load having constant velocity has been researched. Within the micro-size shell, porosities exist with even or uneven distributions. Accordingly, the material properties of the micro-size shell rely on porosities and may be defined utilizing refined power-law functions. Strain gradients have been incorporated because of the existence of size effects at micro scale. Established governing equations based on first-order shell theory have been arranged in Laplace form. Next, time responses of the micro-size shell have been calculated accomplishing inverse Laplace transform technique together with differential quadrature method (DQM). It may be understood that forced vibrational behaviors of micro-size shells are dependent on the load speed, strain gradient factor, pore volume, material gradation and temperature variation.

Nonlinear resonance responses of size-dependent functionally graded cylindrical microshells with thermal effect and elastic medium

The nonlinear resonance responses of functionally graded (FG) cylindrical microshells with the elastic medium is investigated by considering thermal and scale effects. First, using the modified couple stress theory, the nonlinear dynamics model for FG microshell are established. Then the reduced nonlinear differential equations are derived by Galerkin’s method and static condensation. Finally, subharmonic, superharmonic and primary resonances of FG cylindrical microshells are analyzed by a perturbation method. In addition, the bifurcation characteristics of the nonlinear dynamic responses are investigated by some numerical examples. The effects of key parameters (modal damping, excitation frequency, foundation medium, scale parameter and thermal effect) on the nonlinear resonance responses are also discussed by numerical simulation.

A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer continuum problem

This article analyzes critical voltage and frequency information of functionally graded graphene nanoplatelets-reinforced composite (FG-GPLRC) porous cylindrical microshell embedded in piezoelectric layer, subjected to temperature gradient. The current non-classical model is capable of capturing the size dependency in the microshells by using only one material length scale parameter; moreover, the mathematical formulation of microshells based on the classical model can be recovered from the present model by neglecting the material length scale parameter. To satisfy temperature boundary conditions, the Fourier series solution is extracted. In addition, for the first time, thermal conductivity coefficients regarding each GPL’s distribution pattern are presented. The thermally equations are solved via Heun’s differential equation. The mechanical properties of FG-GPLRC layer are estimated based on modified Halpin–Tsai micromechanics and rule of mixtures. Hamilton’s principle is utilized to develop governing equations of motion and boundary conditions. Finally, an analytical solution is carried out based on Navier method to obtain critical voltage and frequency in the case of simply supported shell, whereas a semi-analytical solution is proposed based on differential quadrature method (DQM) for other boundary conditions. The results show that piezoelectric layer, graphene nanoplatelets’ (GPLs) distribution pattern, porosity distribution, difference gradient thermal, length scale parameter and GPL weight function play important roles on the natural frequency and critical voltage of the GPL porous cylindrical microshell coupled with piezoelectric actuator. The results of the current study are useful suggestions for the design of materials science, micro-electromechanical systems and nano-electromechanical systems such as nano-actuators and nano-sensors.

Active vibration control responses of a smart microshell reinforced with graphene nanoplatelets and subjected to external force

Smart control and dynamic investigation of a graphene nanoplatelets composite (GPLRC) cylindrical microshell surrounded by a piezoelectric layer as actuator and sensor based on a numerical solution method called generalized differential quadrature method are presented for the first time. The current structure is under an external load. The strains and stresses can be determined through via the first-order shear deformable theory. For accessing to various mass densities, thermal expansion as well as Poisson ratio, the rule of mixture is applied, although, a modified Halpin–Tsai theory is used for obtaining the module of elasticity. The external voltage is applied to the sensor layer, while a proportional-derivative (PD) controller has been utilized for controlling output of sensor. GPLRC’s boundary conditions are derived through governing equations of the cylindrical microshell using energy method known as Hamilton’s principle. The outcomes show that the PD controller, viscoelastic foundation, slenderness factor (L/R), external voltage, and GPL’s weight fraction have a considerable impact on the amplitude, and vibration behavior of a smart GPLRC cylindrical microshell. As an applicable result in related industries, the parameter and consideration of the PD controller have a positive effect on the static and dynamic behaviors of the microstructure subjected to external load.

Free vibration and instability analysis of a viscoelastic micro-shell conveying viscous fluid based on modified couple stress theory in thermal environment

Modeling of viscoelastic behavior can be useful to accurate study of micro-shell vibration. In this study, influence of viscoelastic coefficient and material length scale parameter on frequency of a cylindrical micro-shell with/without conveying fluid are investigated. Considering trapezoidal shape factor via Kirchhoff-Love’s hypotheses and modified couple stress theory (MCST), governing equations of motion are derived using Hamilton’s principle. Viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The novelty of the current study is the consideration of viscoelastic effect, trapezoidal shape factor and size effect based on shell theory as well as influence of conveying viscous fluid on the frequency of micro-shells in thermal environment using MCST. Equations of motion are solved using Fourier series expansion along the axial and circumferential coordinates with Navier procedure as an analytical solution of frequency for a simply-supported micro-shell. As a numerical solution, considering conveying fluid with changing temperature, generalized differential quadrature (GDQ) method along the axial direction for different boundary conditions are utilized. Influences of length-to-mid-radius, thickness-to-mid-radius, length-to-thickness ratio and the number of the mode shapes of the micro-shell on the natural frequencies are examined. Considering fluid flow, effects of length-to-outer-radius, viscoelastic coefficient, fluid viscosity, Knudsen number with the effect of slip/no-slip boundary condition and temperature changes on critical flow velocity versus fundamental frequency of the micro-shell are investigated. Numerical results reveal that structural damping effect of viscoelastic coefficients and damping effect of fluid flow on frequency of the linear vibration are more significant to detect the stability domain of the micro-shell.

Viscoelastic dynamics and static responses of a graphene nanoplatelets-reinforced composite cylindrical microshell

In this study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with assistance of the generalized differential quadrature method (GDQM). Besides, for the validation of the results, the results of the current model are compared to the results acquired from analytical method. The results show that, viscoelastic foundation, patterns of GPL distribution, nonlocal parameter, length scale parameter, layers’ numbers, boundary condition as well as GPL weight function have considerable impact on the stability of the GPLRC cylindrical microshell. Another significant result is that; for C-F B.Cs, at the higher value of the parameter, the influence of the on the dimensionless buckling load of the structure is much more remarkable in comparison with the lower one which in results section is investigated in detail. The results of the present investigation would be informative for design and fabrication of the microactuators and microsensors.

A unified modified couple stress model for size-dependent free vibrations of FG cylindrical microshells based on high-order shear deformation theory

The aim of present work is to propose a unified modified couple stress-based shear deformable shell model that has capability of analyzing size-dependent free vibrations of functionally graded (FG) cylindrical microshells. In the current model, the classical strain tensors and curvature tensor components are given within the framework of a unified high-order shear deformation theory. The trapezoidal shape factor is taken into account for achieving reasonable stress resultants over thickness and makes the proposed model more accurate for thick shell structures. Various classical boundary conditions of the cylindrical microshells are considered using the admissible functions of the displacements containing a beam modal function. The governing equations associated with free vibrations of microshells are derived using a standard Lagrange method. A few comparisons are conducted and verify that the results from the current model coincide favorably to the ones from three-dimensional elasticity solutions. The comparisons also prove that the proposed model has a sufficient capability of dealing with free vibration problems of the thick functionally graded cylindrical microshells. To the end, the size-dependent free vibrations of an FG cylindrical microshell are investigated. As new results, natural frequencies of the FG microshells with various boundary conditions are tabulated, and the effects of some important parameters on vibration characteristics of FG microshells are discussed.

Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency

The dynamic characteristics of functionally graded (FG) metal foam cylindrical micro-scale shells in contact with a moving load will be analyzed thorough this paper accounting for strain-gradient size-dependency. In the material structure of a metal foam, pores can diffuse uniformly or non-uniformly. Based upon Laplace transform, the dynamical governing equations of the first-order micro-shell model can be established in a new domain. In order to go back into the time domain, an inverse Laplace transform will be required. Thus, on can express the time response or dynamic deflection of the micro-shell under moving load. In the presented results, it is easy to see the prominence of strain-gradient size-dependency, load velocity and pore dispersions in the dynamic behavior of metal foam micro-shells.

Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load

Forced vibration of a porous functionally graded (FG) cylindrical microshell due to a moving point load with constant velocity is studied for the first time. Through the thickness of microshell, there are even-type or uneven-type porosities. Therefore, material properties of the microshell become porosity-dependent and are described via modified power-law function. For micro-scale shells, small size effects due to non-uniform strain field can be considered via strain gradient theory (SGT). At first, the governing equations of the microshell are converted to new equations in Laplace domain. Then, time response of the microshell will be obtained implementing inverse Laplace transform technique. It will be demonstrated that forced vibration characteristics of a FG microshell rely on the velocity of moving load, strain gradients, porosity percentage, material/porosity distribution and its geometry.

Material length scale and nonlocal effects on the wave propagation of composite laminated cylindrical micro/nanoshells

Wave propagation in composite laminated cylindrical microshell was investigated by accounting for simultaneous effects of two influential parameters resulting from the nonlocal and strain gradient effects. The thin shell model was used for modeling the composite laminated cylindrical microshell, and the nonlocal strain gradient theory was employed as well. Classical governing equations were derived from Hamilton’s principle. The results demonstrate that the rigidity of the composite laminated cylindrical microshell in the strain gradient theory is more than that in the classical theory and less than that in the nonlocal theory. Moreover, the effect of fiber angle in layers on phase velocity of the composite laminated cylindrical microshell was investigated, demonstrating that the size parameter, the composite laminated cylindrical microshell thickness, and the circumferential wave number have considerable effects on the phase velocity of the composite laminated cylindrical microshell.

Influence of three-parameter viscoelastic medium on vibration behavior of a cylindrical nonhomogeneous microshell in thermal environment: An exact solution

ABSTRACTIn this article, the free vibration behavior of a functionally graded (FG) size-dependent microshell surrounded by viscoelastic foundation subjected to various thermal loading conditions is analytically studied. The material properties of the cylindrical FG microshell are supposed to be temperature dependent and vary continuously along the thickness direction according to the modified rule of mixtures. The size-dependent FG microshell is analyzed based on the modified couple stress theory. The analytical modeling is developed using the first-order shear deformation theory and the equations of motion are derived by the principle of minimum total potential energy. Then the governing equations for the free vibration behavior of a simply supported FG cylindrical microshell subjected to thermal loading are solved using the Navier procedure. The effects of some important parameters, such as material length scale parameter, stiffness and damping of the visco-Pasternak foundation, temperature changes, axial and circumferential wave number, and length of the microshell on the natural frequency are investigated and discussed.

Size dependent analysis of wave propagation in functionally graded composite cylindrical microshell reinforced by carbon nanotube

In this study, wave propagation in functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical microshell is investigated by taking into consideration nonlocal constant and material length scale parameter. For this purpose, FG-CNTRC cylindrical microshell is modeled using shear deformable shell theory as well as nonlocal strain gradient theory. The classical governing equations are extracted using Hamilton’s principle. Carbon nanotubes are distributed in UD and FG-X shapes in FG-CNTRC cylindrical microshells. The results demonstrate that the rigidity of FG-CNTRC cylindrical microshell is higher in the strain gradient theory and lower in the nonlocal theory compared to that in the classical theory. In addition, the effect of manner of distribution of carbon nanotubes in the FG-CNTRC cylindrical microshell as well as the effect of volume fraction of the carbon nanotubes on the phase velocity of the FG-CNTRC cylindrical microshell is investigated. The results demonstrate that the effects of nonlocal constant and material length scale parameter, thickness, and wavenumber on the phase velocity of FG-CNTRC cylindrical microshell are considerable.

Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter

In this article, the influences of various temperature distributions on the vibration analysis of temperature-dependent rotating cylindrical functionally graded (FG) microshells are investigated using the modified couple stress theory (MCST) in a thermal environment. MCST is applied to this model which is practical in the design and analysis of micro actuators and micro sensors. The modeled cylindrical FG microshell, its equations of motion and boundary conditions are derived by Hamilton’s principle and the first-order shear deformation theory (FSDT). For the first time, in the present study, the functionally graded lengthscale parameter changing along the thickness has been considered in temperature-dependent rotating cylindrical FG microshells. The accuracy of the presented model is verified with previous studies and also with those obtained by the Navier analytical method. The novelty of the current study is the consideration of rotation, various temperature distributions and size effect as well as satisfying various boundary conditions implemented on the proposed model using MCST. The generalized differential quadrature method (GDQM) is applied to discretize the equations of motion. In this study the simply supported conditions have been applied to edges $\theta = 0,2\pi$ and various boundary conditions have been studied in $x=0,L$ . Finally, the effects of various geometrical and material parameters on natural frequencies are studied.

Buckling analysis of functionally graded sandwich cylindrical micro/nanoshells based on the couple stress theory

Buckling of functionally graded sandwich cylindrical microshell under axial load is investigated. For this purpose, Donnell shell theory as well as material length scale parameter as considered by the couple stress theory is used, and equations of motion of the functionally graded sandwich cylindrical microshell along with boundary conditions are developed using Hamilton’s principle. Finally, dimensionless critical buckling load is determined for three functionally graded sandwich cylindrical microshells using the Navier procedure. Results of the new model are compared with the classical theory. The results indicate that the rigidity of the functionally graded sandwich cylindrical microshell in the couple stress theory is higher than that in the classical theory, which leads to increased dimensionless critical buckling load. Besides, the effect of material length scale parameter on dimensionless critical buckling load of the functionally graded sandwich cylindrical microshell in different wavenumbers is considerable.