Cylindrical Nanoshell Research Articles

Vibration analysis of size-dependent bimorph functionally graded piezoelectric cylindrical shell based on nonlocal strain gradient theory

Functionally graded piezoelectric materials (FGPMs) have emerged as promising candidates for electronic nanodevices. In this paper, a study on dynamic response of a bimorph FGP cylindrical nanoshell based on nonlocal strain gradient theory is presented. The material properties are assumed to be variable across thickness direction according to power law distribution. The electric potential is considered to be quadratic through thickness direction. The governing equations and boundary conditions are obtained on the basis of first-order shear deformation theory using Hamilton’s principle. As case study, free vibration of simply supported bimorph FGP cylindrical nanoshell is studied and the influences of different parameters on natural frequency are illustrated. The results obtained provide detailed insights into dynamic response of bimorph FGP cylindrical nanoshell and provide evidence for its size dependency especially by increase in thickness and decrease in length, which is an important conclusion for obtaining appropriate functionality in sensors and actuators.

Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory

Wave propagation in viscoelastic single walled carbon nanotubes is investigated by accounting for the simultaneous effects of the nonlocal constant and the material length scale parameter. To this end, thin shell theory is used to model the viscoelastic single walled carbon nanotubes, and the nonlocal strain gradient theory is used to account for the effects of the nonlocal constant and the material length scale parameter. The Kelvin–Voigt model is used to model the viscoelastic property, and the governing equations are derived through Hamilton’s principle. The viscoelastic single walled carbon nanotube medium is modeled as visco-Pasternak. The results demonstrate that viscoelastic single walled carbon nanotube rigidity is higher in the strain gradient theory and lower in the nonlocal theory in comparison to that in the classical theory. Also, the size effects, nanotube radius, circumferential wavenumber, nanotube damping coefficient, and foundation damping coefficient exert considerable effects on viscoelastic single walled carbon nanotube phase velocity.

Buckling of bimorph functionally graded piezoelectric cylindrical nanoshell

Functionally graded piezoelectric materials are of interest for a wide variety of nanotechnological applications. Buckling of functionally graded piezoelectric nanotubes, as ubiquitous event, recently attracted increasing interest. Also, in this article, the buckling response of bimorph functionally graded piezoelectric cylindrical nanoshells attended to lateral pressure is investigated on the basis of nonlocal strain gradient theory. The formulation developed on the basis of the first-order shear deformation theory with von Kármán kinematic nonlinearity. The material properties are considered to vary across thickness direction according to power law distribution. The electric potential is considered to be quadratic through thickness direction. Due to bifurcation analysis, the prebuckling deformation is initially investigated; then, in the case of simply supported edge condition, the buckling response of a bimorph functionally graded piezoelectric nanotube is studied and the influences of various parameters on buckling pressure are illustrated.

Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures

Combining Goldenveizer-Novozhilov shell theory, thin plate theory and electro-elastic surface theory, the size-dependent vibration of nano-sized piezoelectric double-shell structures under simply supported boundary condition is presented, and the surface energy effect on the natural frequencies is discussed. The displacement components of the cylindrical nano-shells and annular nano-plates are expanded as the superposition of standard Fourier series based on Hamilton's principle. The total stresses with consideration of surface energy effect are derived, and the total energy function is obtained by using Rayleigh-Ritz energy method. The free vibration equation is solved, and the natural frequency is analyzed. In numerical examples, it is found that the surface elastic constant, piezoelectric constant and surface residual stress show different effects on the natural frequencies. The effect of surface piezoelectric constant is the maximum. The effect of dimensions of the double-shell under different surface material properties is also examined.

Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells

Abstract The present study deals with the size-dependent nonlinear buckling and postbuckling characteristics of magneto-electro-elastic cylindrical composite nanoshells incorporating simultaneously the both of hardening-stiffness and softening-stiffness size effects. To accomplish this purpose, the nonlocal strain gradient elasticity theory is applied to the classical shell theory. Via the virtual work's principle, the size-dependent governing differential equations are constructed including the coupling terms between the axial mechanical compressive load, external magnetic potential and external electrical potential. The nonlinear prebuckling deformations and the large postbuckling deflections are taken into consideration based upon the boundary layer theory of shell buckling. Finally, an improved perturbation technique is employed to achieve explicit analytical expressions for nonlocal strain gradient stability curves of magneto-electro-elastic nanoshells under various surface electric and magnetic voltages. It is seen that a positive electric potential and a negative magnetic potential cause to increase both of the nonlocality and strain gradient size dependencies in the nonlinear instability behavior of axially loaded magneto-electro-elastic composite nanoshells, while a negative electric potential and a positive magnetic potential play an opposite role.

An efficient size-dependent shear deformable shell model and molecular dynamics simulation for axial instability analysis of silicon nanoshells

Understanding the size-dependent behavior of structures at nanoscale is essential in order to have an effective design of nanosystems. In the current investigation, the surface elasticity theory is extended to study the nonlinear buckling and postbuckling response of axially loaded silicon cylindrical naoshells. Thereby, an efficient size-dependent shear deformable shell model is developed including the size effect of surface free energy. A boundary layer theory of shell buckling in conjunction with a perturbation-based solution methodology is employed to predict the size dependency in the buckling loads and postbuckling behavior of silicon nanoshells having various thicknesses. After that, on the basis of the Tersoff empirical potential, a molecular dynamics (MD) simulation is performed for a silicon cylindrical nanoshell with thickness of four times of silicon lattice constant, the critical buckling load and critical shortening of which are extracted and compared with those of the developed non-classical shell model. It is demonstrated that by taking the effects of surface free energy into account, a very good agreement is achieved between the results of the developed size-dependent continuum shell model and those of MD simulation.

Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells

Abstract In this paper, the electro-elastic surface/interface model is introduced to investigate the surface energy effect on the nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. On the basis of classical shell theory and von-Karman-Donnell-type geometric nonlinearity, the fundamental equations for vibration are given. By considering the constitute relations for surfaces, the total energy of the orthotropic piezoelectric cylindrical nano-shell is obtained. The governing equations of motion are derived from Hamilton's principle and solved by using the homotopy perturbation method (HPM). Afterwards, the results without surface effect are compared and validated with the datum available in the literature, and the influences of surface parameters and geometric characteristics on the nonlinear free vibration of the orthotropic piezoelectric cylindrical nano-shell are examined.

Design and simulation of high sensitive cylindrical nanogear shell sensors according to localized surface plasmon resonance

Localized surface plasmon resonance wavelength depends on intrinsic and environmental factors of nanoparticles. One of the most important factors is the shape of nanoparticles. The effects of nanoparticles shape on the surface plasmon resonance wavelength shift are simulated and investigated. We have observed that the sensitivity of single cylindrical nanoshell with inner and outer radiuses of 20 and 25nm and length of 70nm is 509nm/RIU while the sensitive nature of nanogear with the same size is 603nm/RIU. It is nearly four times the sensitivity of solid spherical nanoparticles and two times the sensitivity of solid nanorods.

Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory

In this article, a cylindrical functionally graded shell model is developed in the framework of nonlocal strain gradient theory for the first time. For this purpose, the modeled cylindrical FG nanoshell, its equations of motion and corresponding boundary conditions are derived by Hamilton’s principle and the first-order shear deformation theory. Generalized differential quadrature method is applied to discretize the equations of motion. The results of the proposed model are compared with those of the Eringen’s nonlocal, strain gradient, modified couple stress and classical theories. The conclusion of this comparison is that the nonlocal strain gradient theory combines advantages of nonlocal and strain gradient theories by applying both material length scale parameter and a nonlocal parameter in the model to consider the significance of strain gradient stress field and nonlocal elastic stress field, respectively. Furthermore, the effects of the material length scale, nonlocal parameter, FG power index, circumferential wave numbers and length of shell on vibrational behavior of the nonlocal strain gradient FG nanoshell for simply supported and clamped–clamped boundary conditions are investigated.

Boundary Layer Modeling of Nonlinear Axial Buckling Behavior of Functionally Graded Cylindrical Nanoshells Based on the Surface Elasticity Theory

The main purpose of the present study is to examine the axial buckling and postbuckling response of cylindrical nanoshells made of functionally graded (FG) materials in the presence of surface free energy effects. To accomplish this purpose, an efficient size-dependent shell model is introduced through combination of the classical shell theory with the well-known Gurtin–Murdoch surface elasticity theory. The volume fraction of FG nanoshells made of the mixture of aluminum and silicon is defined using a power law function. Also, in order to eliminate the stretching–bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the principle of virtual work, the non-classical governing differential equations and boundary conditions are derived. Subsequently, the governing equations are deduced to the boundary layer-type equations incorporating simultaneously the nonlinear large deflections and size effect. Finally, a perturbation-based solving process is put to use to predict the size-dependent critical buckling loads and related postbuckling equilibrium curves for FG nanoshells with various values of material property gradient index and shell thickness. It is found that the surface free energy effect is more prominent for FG nanoshell with lower shell thickness and higher material property gradient index.

Thermo-electro-mechanical buckling analysis of cylindrical nanoshell on the basis of modified couple stress theory

In the present study, the buckling of piezoelectric cylindrical nanoshell subjected to an axial compression, an applied voltage and uniform temperature change resting on Winkler-Pasternak foundation is studied analytically. The modified couple stress theory combined with the geometrical nonlinear shell model is employed to derive the equilibrium equations and boundary conditions. The numerical results are proposed for the buckling of simply supported cylindrical nanoshell using the Navier-type solution. Thus, the effects of different parameters such as dimensionless length scale parameter, length and thickness to radius ratio, temperature change, external electric voltage and Winkler and Pasternak foundation stiffness on critical buckling load are illustrated. It is shown that increase in dimensionless length scale parameter results in increasing critical buckling load and even intensifying the influence of other parameters, such as length and thickness, on critical buckling load.

Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory

Vibration of functionally graded sandwich (FGS) cylindrical nanoshell is investigated. For this purpose, the first shear deformable shell theory as well as material length scale parameter as considered by the couple stress theory is used, and Hamilton’s principle is employed to derive the equations of motion of the FGS cylindrical nanoshell and the boundary conditions. In the end, using Navier solution, the natural frequency is determined for three types of FGS cylindrical nanoshells. Results of the new model are compared with the classical theory. According to the results, the rigidity of the FGS cylindrical nanoshell in the couple stress theory is higher than that in the classical theory, which leads to increased natural frequency. Besides, the effect of the material length scale parameter on natural frequency of the FGS cylindrical nanoshell in different wavenumbers and lengths is considerable.

Imperfection sensitivity of the nonlinear axial buckling behavior of FGM nanoshells in thermal environments based on surface elasticity theory

A size-dependent shell model which accounts for geometrical imperfection sensitivity of the axial postbuckling characteristics of a cylindrical nanoshell made of functionally graded material (FGM) is proposed within the framework of the surface elasticity theory. In accordance with a power law, the material properties of the FGM nanoshell are supposed to vary through the shell thickness. In order to eliminate the stretching-bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the virtual work’s principle, the non-classical governing differential equations are derived and then deduced to boundary layer-type ones. After that, a perturbation-based solution methodology is employed to predict the size dependency in the nonlinear instability of perfect and imperfect axially loaded FGM nanoshells with various values of shell thickness, material property gradient index and different uniform temperature changes. It was seen that for thicker FGM nanoshells in which the surface free energy effects diminish, the influence of the initial geometric imperfection on the critical buckling load is higher than its influence on the minimum load of the postbuckling domain. It is also found that through reduction of the surface free energy effects, the influence of material property gradient index on the critical end-shortening of FGM nanoshell decreases.

Nonlinear buckling and postbuckling behavior of cylindrical shear deformable nanoshells subjected to radial compression including surface free energy effects

The objective of the present investigation is to predict the nonlinear buckling and postbuckling characteristics of cylindrical shear deformable nanoshells with and without initial imperfection under hydrostatic pressure load in the presence of surface free energy effects. To this end, Gurtin-Murdoch elasticity theory is implemented into the first-order shear deformation shell theory to develop a size-dependent shell model which has an excellent capability to take surface free energy effects into account. A linear variation through the shell thickness is assumed for the normal stress component of the bulk to satisfy the equilibrium conditions on the surfaces of nanoshell. On the basis of variational approach and using von Karman-Donnell-type of kinematic nonlinearity, the non-classical governing differential equations are derived. Then a boundary layer theory of shell buckling is employed incorporating the effects of surface free energy in conjunction with nonlinear prebuckling deformations, large deflections in the postbuckling domain and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is put into use in order to obtain the critical buckling loads and postbuckling equilibrium paths corresponding to various geometric parameters. It is demonstrated that the surface free energy effects cause increases in both the critical buckling pressure and critical end-shortening of a nanoshell made of silicon.

Influence of Anisotropy on Optical Bistability in Plasmonic Nanoparticles with Cylindrical Symmetry

In this paper, the effect of radial anisotropy on optical bistability in the cylindrical nanoshells is theoretically investigated within the quasi-static approximation. We consider two cases: when the shell is anisotropic and the core is nonlinear metal and when the core is anisotropic and the shell is a nonlinear metal. The dependence of optical bistability on the size of the nonlinear/anisotropic shell or core, the embedding medium, the anisotropy parameter, and the type of noble metals as candidates for plasmonics is studied and demonstrated. We show that by changing the type of the plasmonic metal, the switching threshold field changes can be used to design nanoparticle-based all-optical sensors. It is also shown that significant optical bistability and all-optical switching behavior can be obtained in the cylindrical nanoshells due to nonlinearity enhancement via the plasmonic structure.

Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory

In this paper, the free vibrations of a short cylindrical nanotube made of piezoelectric material are studied based on the consistent couple stress theory and using the shear deformable cylindrical theory. This new model has only one length scale parameter and can consider the size effects of nanostructures in nanoscale. To model size effects in nanoscale, and considering the nanotube material which is piezoelectric, the consistent couple stress theory is used. First, using Hamilton\'s principle, the equations of motion and boundary condition of the piezoelectric cylindrical nanoshell are developed. Afterwards, using Navier approach and extended Kantorovich method (EKM), the governing equations of the system with simple-simple (S-S) and clamped-clamped (C-C) supports are solved. Afterwards, the effects of size parameter, geometric parameters (nanoshell length and thickness), and mechanical and electric properties (piezoelectric effect) on nanoshell vibrations are investigated. Results demonstrate that the natural frequency on nanoshell in nanoscale is extremely dependent on nanoshell size. Increase in size parameter, thickness and flexoelectric effect of the material leads to increase in frequency of vibrations. Moreover, increased nanoshell length and diameter leads to decreased vibration frequency.

Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory

In this study, the governing equations of electromechanical vibration of cylindrical nanoshell made of functionally graded piezoelectric material (FGPM) are developed using the consistent couple stress theory and the cylindrical shell model. The new consistent couple stress has only one material length scale parameter and is able to consider size effects relating to the nanoshell structure in the nanoscale. The governing equations and boundary conditions are determined using the energy method and Hamilton’s principle. Afterwards, using Navier and Galerkin methods, the free vibration of a special model of FGPM nanoshell under different boundary conditions are investigated. Finally, the effect of different parameters such as dimensionless length scale parameter, variation of index, length-to-radius ratio, and radius-to-thickness ratio are investigated. It is demonstrated that the length-to-radius ratio, radius-to-thickness ratio, and dimensionless length scale parameter play a significant role in the vibration behavior of the FGPM cylindrical nanoshell based on the size-dependent piezoelectric theory.

Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory

In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.

Photonic states mixing beyond the plasmon hybridization model

A study is performed on a photonic-state mixing-pattern in an insulator-metal-insulator cylindrical silver nanoshell and its rich variations induced by changes in the geometry and dielectric media of the system, representing the combined influences of plasmon coupling strength and cavity effects. This study is performed in terms of the photonic local density of states (LDOS) calculated using the Green tensor method, in order to elucidate those combined effects. The energy profiles of LDOS inside the dielectric core are shown to exhibit consistently growing number of redshifted photonic states due to an enhanced plasmon coupling induced state mixing arising from decreased shell thickness, increased cavity size effect, and larger symmetry breaking effect induced by increased permittivity difference between the core and the background media. Further, an increase in cavity size leads to increased additional peaks that spread out toward the lower energy regime. A systematic analysis of those variations for a silver nanoshell with a fixed inner radius in vacuum background reveals a certain pattern of those growing number of redshifted states with an analytic expression for the corresponding energy downshifts, signifying a photonic state mixing scheme beyond the commonly adopted plasmon hybridization scheme. Finally, a remarkable correlation is demonstrated between the LDOS energy profiles outside the shell and the corresponding scattering efficiencies.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman’s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuckling characteristics of nanoshells with small sizes.