Cylindrical Nanoshell Research Articles

Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell

In this article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques.

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

Postbuckling analysis of axially loaded nanoscaled shells embedded in elastic foundations based on Ru's surface elasticity theory

The nonlinear buckling and postbuckling characteristics of cylindrical nanoshells embedded in elastic foundations are investigated based on a strain-consistent elastic shell model including the both surface tension and the induced residual stress. For this purpose, in contrast to the previous models on the basis of the Gurtin-Murdoch elasticity theory, a new non-classical shell model based on Ru's surface elasticity theory is developed in which the non-strain displacement gradient terms are eliminated from the surface stress-strain relations. Using the virtual work's principle, the governing differential equations incorporating surface effects are derived. After that, the size-dependent governing equations are deduced to a boundary layer type problem which is subsequently solved through employing a two-stepped singular perturbation technique. It is revealed that because the edge supports of nanoshells are movable, before applying the axial compression, surface effects lead to an initial shortening due to induced residual strains, but the terms related to the residual strain and initial surface tension vanish in the size-dependent nonlinear governing equations. As a result, it is observed that before applying the axial compressive load, the surface effects cause an initial end-shortening for very thin nanoshells and these effects quickly diminish by increasing the shell thickness.Communicated by Krzysztof Kamil Żur

Magneto-mechanical coupling characteristic analysis of a magnetic energy nanoharvester with surface effect

In the current work, a nonlinear magnetoelectric (ME) coupling model is developed to investigate the working performance of a magnetic energy nanoharvester, which is composed of a magneto-electro-elastic (MEE) laminated cylindrical nanoshell array when the circuit is connected either in series or in parallel. The analytical results indicate that the performance of nanoharvester exhibits obvious size-dependent phenomenon, including the resonant frequency, output electrical power density, efficiency and so forth, which is only attributed to the surface effect. Based on this, a critical thickness, distinguishing micro-scale from macro-scale, is proposed, below which the size-dependent effect must be included during mechanical analysis. On the other hand, it is demonstrated that the output electrical power, as an important performance index, can be improved evidently and tuned artificially via the pre-stress and matched magnetic field, which may provide us opportunity to control the harvester in nano-scale. The current work is essential and crucial for the physical phenomenon explanations and experimental design of the MEE nanodevices, especially in the extremely complex magnetic and pre-stress field environments.

Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory

In this paper, influence of modified strain gradient theory (MSGT) on buckling, free and forced vibration characteristics of the composite cylindrical nanoshell reinforced with graphene nanoplatelet (GPL) in thermal environment is investigated. The material properties of piece-wise functionally graded graphene-reinforced composites GPLRC are assumed to be graded in the thickness direction of a cylindrical nanoshell and are estimated through a nanomechanical model. The results show that GPL distribution pattern, three length scale parameters, number of layers and GPL weight function have important role on resonance frequencies, buckling load, relative frequency and dynamic deflections of the GPLRC cylindrical nanoshell.

Non-classical Natural Frequency Analysis of Piezoelectric Cylindrical Nano-shell with Surface Energy Effects

Non-classical Natural Frequency Analysis of Piezoelectric Cylindrical Nano-shell with Surface Energy Effects

Nonlinear Thermo-Electro-Mechanical Vibration of Functionally Graded Piezoelectric Nanoshells on Winkler–Pasternak Foundations Via Nonlocal Donnell’s Nonlinear Shell Theory

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell’s nonlinear shell theory. The Hamilton’s principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin’s method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation.

Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton’s principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors.

Nonlinear vibration of magnetoelectroelastic nanoscale shells embedded in elastic media in thermoelectromagnetic fields

This study investigates the nonlinear vibration of magnetoelectroelastic composite cylindrical nanoshells embedded in elastic media for the first time. The small-size effect and thermoelectromagnetic loadings are considered. Based on the nonlocal elasticity theory and Donnell’s nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived using Hamilton’s principle. Then, the Galerkin method is utilized to transform the governing equations into a nonlinear ordinary differential equation and subsequently the method of multiple scales is employed to obtain an approximate analytical solution to nonlinear frequency response. The present results are verified by the comparison with the published ones in the literature. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external magnetic potential, the external electric potential, the temperature change, and the elastic media on the nonlinear vibration characteristics of magnetoelectroelastic composite nanoshells.

Pre- and post-buckling analysis of FG cylindrical nanoshells in thermal environment considering the surface stress effect

An analytical approach is developed to study the pre- and post-buckling responses of circular cylindrical nanoscale shells subjected to lateral and axial loads as well as thermal environment. The effect of surface free energy as one of the key nanoscale effects is considered in the context of Gurtin-Murdoch surface elasticity theory. The nanoshell is made of functionally graded materials (FGMs) whose properties are calculated using power-law functions. The basic formulation is derived according to the classical shell theory together with the von-Karman nonlinear relations. Moreover, the physical neutral plane position is taken into consideration. Using the Ritz energy method, an analytical approach is also proposed to solve the problem. Comprehensive numerical results are presented to investigate the behavior of nanoshell under lateral pressure and axial load in thermal environment, in pre- and post-buckling domains. The influences of various parameters including the surface stress, FGM gradient index, temperature and geometrical parameters on the non-linear critical axial stress/lateral pressure are illustrated.

Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets

Due to a rapid development of process manufacturing, composite materials with graphene-reinforcement have obtained so much commercially notices in the promoted engineering applications. With this regard, the critical voltage and frequency characteristics of a graphene nanoplatelets (GNP) composite cylindrical nanoshell coupled with the piezoelectric actuator (PIAC) are investigated. The material properties of piece-wise graphene-reinforced composites (GNPRCs) are assumed to be graded through the thickness direction of a cylindrical nanoshell and are estimated based on a nanomechanical model. For the first time, the current study is considering the effects of the piezoelectric layer, GNPRC and size-effects on the natural frequency and critical voltage of the GNPRC cylindrical nanoshell coupled with PIAC. The governing equations and boundary conditions have been developed using minimum potential energy, and have been solved with the aid of generalized differential quadrature (GDQM). In addition, because of the piezoelectric layer, Maxwell's equation is derived. The results show that piezoelectric layer, GNP distribution pattern, length scale parameter and GNP weight function, play important roles on the natural frequency and critical voltage of the GNP cylindrical nanoshell coupled with PIAC. The results of the current study are useful suggestions for the design of materials science, micro-electro-mechanical systems and nanoelectromechanical systems such as nanoactuators and nanosensors.

Vibration analysis of a high-speed rotating GPLRC nanostructure coupled with a piezoelectric actuator

In this article, the vibration characteristics of high-speed rotating graphene-nanoplatelets (GNP)-reinforced composite cylindrical nanoshell coupled with a piezoelectric actuator (PIAC) are investigated. This composite nanostructure rotates around the axial direction, and the Coriolis and centrifugal effects are considered in the formulation. The material properties of piecewise graphene-reinforced composites (GNPRCs) are assumed to be graded in the thickness direction of the cylindrical nanoshell and estimated through a nanomechanical model. In the current study, the effects of angular velocity, piezoelectric layer, GNPRC and size-effects on the frequency of the spinning GNPRC cylindrical nanoshell coupled with PIAC are studied for the first time. The governing equations and boundary conditions are developed using the minimum potential energy and solved with the aid of generalized differential quadrature (GDQM). In addition, due to existence of piezoelectric layer, Maxwell’s equation is derived. The results show that angular velocity, piezoelectric layer, GNP distribution pattern, length scale parameter and GNP weight function play an important role in the vibrational characteristics of the spinning GNP cylindrical nanoshell coupled with PIAC. The results of the current study are useful for design of materials science, micro-electro-mechanical systems and nanoelectromechanical systems such as nanoactuators and nanosensors.

Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation

• Nonlinear dynamics, vibration and stability analysis of cylindrical nanoshell resonator is studied. • Electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model are used. • The effects of different parameters on nonlinear frequency response and stability analysis are investigated. • Effects of electrostatic and harmonic excitation on nonlinear frequency response and stability analysis are studied. In this paper, nonlinear dynamics, vibration and stability analysis of piezo-visco medium nanoshell resonator (PVM-NSR) based on functionally graded (FG) cylindrical nanoshell integrated with two piezoelectric layers subjected to visco-pasternak medium, electrostatic and harmonic excitations is investigated. Nonclassical method of the electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model as well as Hamilton's principle, the assumed mode method combined with Lagrange–Euler's are considered. Complex averaging method combined with arc-length continuation is used to achieve a numerical solution for the steady state vibrations of the system. The stability analysis of the steady state response is performed. The parametric studies such as the effects of different boundary conditions, different geometric ratios, structural parameters, electrostatic and harmonic excitation on the nonlinear frequency response and stability analysis are studied. The results indicate that near the natural frequency of the nanoshell, it will lead to resonance and will have large motion amplitude and near the resonant frequency, the nanoshell shows a softening type of nonlinear behavior, and the nanoshell bandwidth increases due to nonlinear factors. In this range, nanoshell has three different ranges of motion, of which two are stable and the other unstable, and so the jump phenomenon and saddle-node bifurcation are visible in the behavior of the system. Also piezoelectric voltage influences on static deformation and resonant frequency but has no significant effect on nonlinear behavior and bandwidth and also system very sensitive to the damping coefficient and due to decrease of nano shell stiffness, natural frequency decreases. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system's instability, nonlinear behavior and bandwidth.

Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects

In current study, nonlinear dynamics and stability analysis of piezoelectric nanoresonator (PENR) based on cylindrical nanoshell is investigated using the Gurtin–Murdoch surface/interface (S/I) theory. The piezoelectric nanoresonator is simultaneously subjected to direct voltage DC and alternating voltage AC. For this analysis, Hamilton′s principles, the assumed mode method combined with Lagrange–Euler′s are used for the governing equations and boundary conditions. Complex averaging method combined with arc-length continuation is used to achieve the effect electrostatic and piezoelectric voltages and other parameters on pull-in voltage, nonlinear frequency response and stability region of the piezoelectric nanoresonator. It is found that the mentioned parameters can effectively change the flexural rigidity of the system which in turn affects the pull-in instability regime and nonlinear frequency response. The obtained results show that, by changing the surface/interface densities for nanoresonator (NR) and PENR and as a result, increasing or decreasing the system stiffness, the natural frequency can be lower or greater than the case of without S/I effects. Also near the natural frequency of the nanoshell, softening or hardening types of nonlinear behavior, the jump phenomenon and saddle-node bifurcation are presented. The effect of different parameters on nonlinear dynamics and stability analysis of piezoelectric nanoresonator (PENR) is also examined.

Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension

In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell.

Radial postbuckling of nanoscaled shells embedded in elastic foundations based on Ru's surface stress elasticity theory

In this article, the nonlinear buckling and postbuckling response of cylindrical nanoshells under radial compressive load is investigated on the basis of a new surface elasticity theory. To this point, in contrast to the previous models based on the Gurtin-Murdoch elasticity theory, a new non-classical shell model based on the Ru's surface elasticity theory is developed in which the non-strain displacement gradient terms are eliminated from the surface stress-strain relations. The non-classical governing equations are derived using the principle of virtual work. Then they are deduced to boundary layer-type equations including simultaneously the nonlinear prebuckling deformations and the large postbuckling deflections. By using a singular perturbation technique, the new size-dependent problem is solved. It is indicated that due to the immovable edge supports and in the absence of the hydrostatic pressure, surface effects lead to an initial shortening caused by the induced residual strains. Additionally, the residual strain and initial surface tension terms vanish in the size-dependent nonlinear governing equations. Moreover, it is observed that this initial shortening diminishes quickly for thicker nanoshells.

Wave propagation in functionally graded cylindrical nanoshells based on nonlocal Flügge shell theory

In the present work, wave propagation characteristics of circular cylindrical nanoshells made of functionally graded materials are investigated. Material properties of the nanoshells are graded in the thickness direction according to the power-law distribution. The Flugge shell theory together with the nonlocal elasticity theory is employed to model the present system. The wave dispersion relations with respect to the wave number in the longitudinal and circumferential directions are derived. In addition, a parametric study is carried out to highlight the influences of the power-law exponent, the wave number, the nonlocal parameter and the radius-to-thickness ratio. The results indicate that these parameters have a significant effect on the wave propagation characteristics of functionally graded material (FGM) cylindrical nanoshells.

Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshell

In this paper, vibration analysis of double-walled piezo-viscoelastic cylindrical nanoshell integrated with piezoelectric layers is investigated using Gurtin–Murdoch surface/interface theory and Donnell's theory. Three parameters namely, shear modulus, damp coefficient, and Winkler modulus are used for simulation of visco-Pasternak model. Hamilton's principle is used for deriving the governing equations and boundary conditions and also the assumed mode method is used for changing the partial differential equations into ordinary differential equation. The effects of the surface energy, length and thickness of nanoshell and piezoelectric layer, boundary condition, van der Waals force, and visco-Pasternak effects on the undamped and damped natural frequencies of piezo-viscoelastic cylindrical nanoshell is studied. Also, the results show that on considering surface effects in the nanoscale system without considering the surface density, the maximum frequency will be obtained and this case will be considered as the critical state of the system. As a result, controlling the frequency of the system in this case is essential and it is quite clear that considering the effects of the surface energy will have a remarkable effect on the natural frequency of the piezo-viscoelastic nanoshell.

Nonlinear free vibration of piezoelectric cylindrical nanoshells

The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on a viscoelastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell’s nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton’s principle. Then, the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temper-ature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.

Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell

In this article, wave propagation characteristics of a size-dependent graphene nanoplatelet (GNP) reinforced composite cylindrical nanoshell coupled with piezoelectric actuator (PIAC) and surrounded with viscoelastic foundation is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT) which is an accurate theory employing exact length scale parameter and nonlocal constant. The governing equations of the GNP composite cylindrical nanoshell coupled with PIAC have been evolved using Hamilton’s principle and solved with assistance of the analytical method. For the first time in the current study, wave propagation electrical behavior of a GNP composite cylindrical nanoshell coupled with PIAC based on NSGT is examined. The results show that, by decreasing the PIAC thickness, extremum values of phase velocity occur in the lower values of the wave number. Another important result is that, by increasing GPL%, the effects of PIAC thickness on the phase velocity decrease. Finally, influence of PIAC thickness, wave number, applied voltage, and different GPL distribution patterns on phase velocity is investigated using mentioned continuum mechanics theory. Useful suggestion of this research is that for designing of a nanostructure coupled with PIAC attention should be given to PIAC thickness and applied voltage, simultaneously. The outputs of the current study can be used in the structural health monitoring and ultrasonic inspection techniques.