This paper develops the Refined Zigzag Theory (RZT) for nonlinear dynamic response of an axially moving functionally graded (FG) nanobeam integrated with two magnetostrictive face layers based on the modified couple stress theory (MCST). The sandwich nanobeam (SNB) subjected to a temperature difference and both axial and transverse mechanical loads. The material properties of FG core layer depend on the environment temperature and are assumed to vary in thickness direction. The SNB is surrounded by elastic medium which is simulated by visco-Pasternak model. The von-Karman nonlinear strain-displacement relationships are employed to consider the effect of geometric nonlinearities. In order to obtain governing motion equations and boundary conditions the energy method as well as Hamilton’s principle is applied. The differential quadrature method (DQM) is used for space domain and the Newmark-β method is taken into account for time domain response of the axially moving SNB. The detailed parametric study is conducted to investigate the effects of surrounding elastic medium, material length scale parameter, magnetostrictive layers, temperature difference, environment temperature, velocity of the SNB, axial and transverse mechanical loads and volume fraction exponent on the dynamic response of the SNB. Results indicate that the maximum deflection of the system can be controlled by employing negative values of velocity feedback gain values. Also, the system loses its stability when the velocity of SNB is increased. تفاصيل المقالة

The current article investigates the free vibrations of a three-layer beam. The middle layer of this structure is selected from porous material. For modeling the porous layer, linear pro-elasticity relationships are applied, while Young's modulus and its density vary along the thickness. The upper and lower layers of the structure are reinforced with graphene nanoplates and can take different configurations as Parabolic, linear, and uniform. In this study, with the help of Halpin-Tsai modified theory, equivalent composite coefficients will be extracted. The equations of motion in three layers are derived with the help of third order shear theory, energy method and Hamilton's Principle. Among the significant results of this article, we can mention the effect of amplifiers in improving the vibration behavior of the beam, the effect of pore pressure and volume fraction of reinforcement on the frequency of vibrations. The results of this research can be applied in marine, aerospace, and civil industries. تفاصيل المقالة

This paper investigates the frequency response of a smart sandwich plate made of magnetic face sheets and reinforced core with nano-fibers. The effective elastic properties of composite core reinforced with carbon nanotube are estimated by the extended rule of Mixture. The orthotropic visco-Pasternak foundation is examined to study orthotropic angle, damping coefficient, normal, and shear modulus. The top and bottom face sheets of the sandwich are magnetic and their vibrations are controlled by a feedback control system and magneto-mechanical couplings. Also, the sandwich plate is subjected to the compression and extension in-plane forces in both x and y directions. Five coupled equations of motion are derived using Hamilton’s principle. These equations are solved by the differential quadrature method. The analysis performed by the third-order shear deformation theory (Reddy’s theory) shows useful details of the effective parameters such in-plane forces, modulus of elastic foundation, core-to-face sheet thickness ratio and controller effect of velocity feedback gain on the dimensionless frequency of the sandwich plate. The analysis of such structures can be discussed in the military, aerospace and civil industries. تفاصيل المقالة

This study deals with the free vibration of the sandwich plate made of two smart magnetostrictive face sheets and an electro-rheological fluid core. Electro-rheological fluids are polymer-based material that changes its viscosity under the applied electric field. A feedback control system follows the magnetization effect on the vibration characteristics of the sandwich plate when subjected to the magnetic field. It is assumed that there is no slip between layers, so the stress-strain relations of each layer are separately considered. Energy method is utilized in order to derive the five coupled equations of motion. These equations are solved by differential quadrature method (DQM). Results of this study show the rheology response of fluid in presence of electric field where the core gets hard and the dimensionless frequency increases. Also, the significant effect of thickness and aspect ratios and velocity feedback gain are discussed in detail. Such intelligent structures can replace in many of the systems used in automotive, aerospace and building industries as the detector, warning, and vibration absorber etc. تفاصيل المقالة

In this paper, a numerical solution is presented for static and dynamic stability analysis of carbon nanotube (CNT) reinforced beams resting on Pasternak foundation. The beam is considered to be exposed to compressive axial and follower forces at its free end. The beam is modeled based on the Reddy’s third order shear deformation theory and governing equations and external boundary conditions are derived using Hamilton’s principle. The set of governing equations and boundary conditions are solved numerically using differential quadrature method. Convergence and accuracy of results are confirmed and effect of various parameters on the stability region of the beam is investigated including volume fraction and distribution of CNTs, width and thickness of the beam and elastic and shear coefficients of the foundation. تفاصيل المقالة

In this article, dynamic stability analysis of bi-directional functionally graded materials (BDFGMs) beam rested on visco-Pasternak foundation under harmonic excitation is studied. Also, BDFGMs beam is subjected to a transversely uniformly distributed temperature rising and it is assumed that the material properties to be temperature-dependent. According to the exponential and power law distributions, thermo-mechanical properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions. Based on various shear deformation theories (e.g. Euler-Bernoulli, Timoshenko, third order shear deformation and sinusoidal shear deformation theories), the stability equations of BDFGMs beam is derived by applying the Hamilton's principle. The generalized differential quadrature method (GDQM) in conjunction with the Bolotin method is utilized to solve the differential stability equations under SS, SC and CC boundary conditions. To validate the present analysis, a comparison study is carried out with the results found in the literature and a good agreement is observed compared to the reported results. Finally, numerical results are presented to study the influences of the gradient index, length-to-thickness ratio, temperature rise and foundation parameters on the dynamic stability region of BDFGMs beam. The results of presented paper can be used to the optimal design and assessment of the structural failure. تفاصيل المقالة

In this article, curvature effects on elastic thermal buckling of double-walled carbon nanotubes under axially compressed force are investigated using cylindrical shell model. Also, the small scale effect is taken into account in the formulation. The dependence of the interlayer van der Waals (vdW) pressure on the change of the curvatures of the inner and outer tubes at that point is considered. The effects of the surrounding elastic medium, curvature and the vdW forces between the inner and outer tubes increase the critical buckling load under thermal and axial compression loads, while small scale effect decreases it. تفاصيل المقالة

In this study, electro-thermo-mechanical nonlinear vibration and instability of embedded piezoelectric micro-tube is carried out based on nonlocal theory and nonlinear Donnell's shell model. The smart micro-tube made of Poly-vinylidene fluoride (PVDF) is conveying an isentropic, incompressible fluid. The detailed parametric study is conducted, focusing on the remarkable effects of mean flow velocity, fluid viscosity, elastic medium modulus, temperature change, imposed electric potential, small scale and aspect ratio on the vibration behavior of the micro-tube. It has been found that stability of the system is strongly dependent on the imposed electric potential. Results of this investigation could be applied for optimum design of sensors and actuators in the sensitive applications. تفاصيل المقالة

In this article, magneto-thermo-elastic stresses and perturbation of magnetic field vector are analyzed for a thick-walled cylinder made from polystyrene, reinforced with functionally graded (FG) single-walled carbon nanotubes (SWCNTs) in radial direction, while subjected to an axial and uniform magnetic field as well as a transient thermal field. Generalized plane strain state is considered in this study. The SWCNTs are assumed aligned, straight with infinite length. Two types of variations in the volume fraction of SWCNTs were considered in the structure of the FG cylinder along the radius from inner to outer surface, namely: functionally graded increasing (FG Inc) and functionally graded decreasing (FG Dec) which are then compared with uniformly distributed (UD) layouts. The constitutive equations of this type of reinforced polymeric cylinder are derived by Mori-Tanaka method. Following the introduction of a second order partial differential equation derived from the equations of motion and stress-strain relationships and solving by a semi-analytical method, distribution of stresses and perturbation of magnetic field vector are obtained. Results indicate that maximum radial and circumferential stresses occur in FG Inc and FG Dec layouts, respectively. Maximum perturbation of magnetic field vector is not affected by UD layout. تفاصيل المقالة

In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) conveying viscous fluid is investigated based on Eringen's theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on fluid-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW) interaction between the inner and outer nanotubes is taken into account and the surrounding elastic medium is simulated as Winkler and Pasternak foundation. Considering the charge equation for coupling of mechanical and electrical fields, Hamilton's principle is utilized to derive the motion equations based on the von Kármán theory. Dynamic buckling load is evaluated using differential quadrature method (DQM). Results show that dynamic buckling load depends on small scale factor, viscosity, elastic medium parameters and temperature changes. Also, dynamic instability region is discussed for various conditions. تفاصيل المقالة

Flow induced vibration and smart control of elastically coupled double-nanotube-systems (CDNTSs) are investigated based on Eringen’s nonlocal elasticity theory and Euler-Bernoulli beam model. The CDNTS is considered to be composed of Carbon Nanotube (CNT) and Boron-Nitride Nanotube (BNNT) which are attached by Pasternak media. The BNNT is subjected to an applied voltage in the axial direction which actuates on instability control of CNT conveying nano-fluid. Polynomial modal expansions are employed for displacement components and electric potential and discretized governing equations of motion are derived by minimizing total energies of the CDNTS with respect to time-dependent variables of the modal expansions. The state-space matrix is implemented to solve the eigen-value problem of motion equations and examine frequencies of the CDNTS. It is found that Pasternak media and applied voltage have considerable effects on the vibration behavior and stability of the system. Also, it is found that trend of figures have good agreement with the other studies. The results of this study can be used for design of CDNTS in nano / Micro -electro-mechanical systems. تفاصيل المقالة

The buckling and postbuckling behaviors of a composite beam with single delamination are investigated. A three-dimensional finite element model using the commercial code ANSYS is employed for this purpose. The finite elements analyses have been performed using a linear buckling model based on the solution of the eigenvalues problem, and a non-linear one based on an incremental-iterative method. The large displacements have been taken into account in the nonlinear analysis. Instead of contact elements a new delamination closure device using rigid compression-only beam elements is developed. Effect of delamination length, position through thickness and stacking sequence of the plies on the buckling and postbuckling of laminates is investigated. It has been found that significant decreases occur in the critical buckling loads after a certain value of the delamination length. The position of delamination and the fiber orientation also affect these loads. تفاصيل المقالة

This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the coupled system. The three vibrational states including out-of-phase vibration, in-phase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient theory is higher than the Eringen's and modified couple stress theories. Moreover, the small scale effect in the case of in-phase vibration is higher than that in the other cases. This study might be useful for the design of nano-devices in which GNRs act as basic elements. تفاصيل المقالة

In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are derived. The differential quadrature (DQ) method is applied to obtain the nonlocal frequency of coupled visco-CNTs system. The effects of various parameters such as the longitudinal magnetic field, visco-Pasternak foundation, Knudsen number, surface effect, aspect ratio and velocity of conveying viscous are specified. It is shown that the longitudinal magnetic field is responsible for an up shift in the frequency and an improvement of the instability of coupled system. Results also reveal that the surface effect and internal conveying fluid plays an important role in the instability of nano coupled system. Also, it is found that trend of figures have good agreement with previous researches. It is hoped that the nonlinear results of this work could be used in design and manufacturing of nano/micro mechanical system in advanced nanomechanics applications where in this study the magnetic field is a controller parameter. تفاصيل المقالة

Nonlocal vibration of double-smart nanobeam-systems (DSNBSs) under a moving nanoparticle is investigated in the present study based on Timoshenko beam model. The two smart nanobeams (SNB) are coupled by an enclosing elastic medium which is simulated by Pasternak foundation. The energy method and Hamilton’s principle are used to establish the equations of motion. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, elastic medium coefficients, external voltage, length of SNB and the mass of attached nanoparticle on the frequency of piezoelectric nanobeam. The results depict that the imposed external voltage is an effective controlling parameter for vibration of the piezoelectric nanobeam. Also increase in the mass of attached nanoparticle gives rise to a decrease in the natural frequency. This study might be useful for the design and smart control of nano-devices. تفاصيل المقالة

Thermal stress analysis of a thick-walled cylinder reinforced with functionally graded (FG) single-walled carbon nanotubes (SWCNTs) is considered in radial direction. Thick-walled cylinder is subjected to a thermal field. Two layouts of variations in the volume fraction of SWCNTs were considered in the composite cylinder along the radius from inner to outer surface, where their names are incrementally decreasing (Inc Dec) and incrementally increasing (Inc Inc). Micromechanical models based on the Mori-Tanaka is used to define effective macroscopic properties of the nano composite shell. Using equations of motion, stress-strain and their corresponding constitutive correlations of a polystyrene vessel, a second order ordinary differential equation was proposed based on the radial displacement. The higher order governing equation was solved in order to obtain the distribution of displacement and thermal stresses in radial, circumferential and axial directions. The results indicate that FG distributions of SWCNTs have significant effect on thermal stresses and displacements in axial, radial and circumferential directions, so that in Inc Inc layout, the radial and circumferential stresses are lower than of other FG structures. تفاصيل المقالة

Time-dependent creep analysis is crucial for the performance and reliability of piezoactuators used for high-precision positioning and load-bearing applications. In this study history of stresses, deformations and electric potential of hollow rotating cylinders made of functionally graded piezoelectric material (FGPM), e.g., PZT_7A have been investigated using Mendelson’s method of successive elastic solution. Loading is composed of an internal pressure, a distributed temperature field, an inertia body force and a constant electric potential difference between the inner and outer surfaces of the FGPM cylinder. All the mechanical, thermal and piezoelectric properties are assumed to be the same power functions of the radial graded direction. Using equations of equilibrium, strain displacement, stress-strain relation and the electric potential equation a differential equation containing creep strains for displacement is derived. A semi-analytical method in conjunction with the method of successive approximation has therefore been proposed for this analysis. It has been found that a major redistribution for electric potential take place throughout the thickness. Electric potentials are increasing with time in the same direction as the compressive radial stress histories. That is the electric potential histories are induced by the compressive radial stress histories during creep deformation of the FGPM cylinder. تفاصيل المقالة

In this paper, a radially piezoelectric functionally graded rotating disk is investigated by the analytical solution. The variation of material properties is assumed to follow a power law along the radial direction of the disk. Two resulting fully coupled differential equations in terms of the displacement and electric potential are solved directly. Numerical results for different profiles of inhomogeneity are also graphically displayed. تفاصيل المقالة

In this study, free vibration of a foam-core orthotropic smart composite cylindrical shell (SCCS) filled with a non-viscous compressible fluid, subjected to combined electro-thermo-mechanical loads is investigated. Piezoelectric polymeric cylindrical shell, is made from polyvinylidene fluoride (PVDF) and reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). Characteristics of the equivalent composite are determined using micro-electro-mechanical models. The poly ethylene (PE) foam-core is modeled based on Winkler and Pasternak foundations. Employing the charge equation for coupling electrical and mechanical fields, the problem is turned into an eigenvalue one, for which analytical frequency equations are derived considering free electrical and simply supported mechanical boundary conditions at circular surfaces at either ends of the cylindrical shell. The influence of electric potential generated, filled-fluid, orientation angle of DWBNNTs, foam-core and a few other parameters on the resonance frequency of SCCS are investigated. Results show that SCCS and consequently the generated Φ improve sensor and actuator applications in several process industries, because it not only increases the vibration frequency, but also extends economic viability of the smart structure. تفاصيل المقالة

This paper reports an analytical method to show the effect of electrostatic and Casimir forces on the pull-in instability and vibration of single nano-plate (SNP) carrying a moving nanoparticle. Governing equations for nonlocal forced vibration of the SNP under a moving nanoparticle considering electrostatic and Casimir forces are derived by using Hamilton’s principle for the case when two ends are simply supported. The problem is solved by using the analytically and the time integration methods. The detailed parametric study is considered, focusing on the remarkable effects of the nanoparticle position, nonlocal parameters, nano-plate length, mode number, electric voltage of the Casimir parameter, and dielectric spacer with an initial gap on vibration of SNP. تفاصيل المقالة

In this article, the magneto-thermo-elastic problem of exponentially graded material (EGM) hollow rotating disk placed in uniform magnetic and temperature fields is considered. Exact solutions for stresses and perturbations of the magnetic field vector in EGM hollow rotating disk are determined using the infinitesimal theory of magneto-thermo-elasticity under plane stress. The material properties, except Poisson’s ratio, are assumed to depend on variable of the radius and they are expressed as exponential functions of radius. The direct method is used to solve the heat conduction and Hyper-geometric functions are employed to solve Navier equation. The temperature, displacement, and stress fields and the perturbation of the magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effect of in-homogeneity on the stresses and the perturbation of magnetic field vector distribution are demonstrated. The results of this study are applicable for designing optimum EGM hollow rotating disk. تفاصيل المقالة

In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed to obtain the critical buckling load of polymeric piezoelectric nanoplate for classical plate theory (CPT) and first order shear deformation theory (FSDT). The influences of various parameters on the biaxial nonlocal critical buckling load with respect to the local critical buckling load ratio () of nanoplate are examined. Surface stress effects on the surface biaxial critical buckling load to the non-surface biaxial critical buckling load ratio () can not be neglected. Moreover, the effect of residual surface stress constant on is higher than the other surface stress parameters on it. increases by applying the external voltage and magnetic fields. The nonlocal deflection to local deflection of piezoelectric nanocomposite plate ratio () decreases with an increase in the nonlocal parameter for both theories. And for FSDT, decreases with an increase in residual stress constant and vice versa for CPT. تفاصيل المقالة

In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects, nonlocal elasticity theory is applied due to its simplicity and accuracy. The small-size effects and slip boundary conditions of nano-flow are taken into account through Knudsen number (Kn). The Y-SWCNT is surrounded by elastic medium which is simulated as nonlinear Visco-Pasternak foundation. Using energy method and Hamilton’s principle, the nonlinear governing motion equation is obtained. The governing motion equation is solved using both Galerkin procedure and Homotopy analysis method (HAM). Numerical results indicate the significant effects of the mass and velocity of the fluid flow, strength of longitudinally magnetic field, (Kn), angle between the centerline of carbon nanotube and the downstream elbows, nonlocal parameter and nonlinear Visco-Pasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nano-devices in which Y-shaped nanotubes act as basic elements. تفاصيل المقالة

In this study, thermo-nonlocal vibration of double bonded graphene sheet (DBGS) subjected to 2D-magnetic field under biaxial in-plane pre-load are presented. The elastic forces between layers of graphene sheet (GS) are taken into account by Pasternak foundation and the classical plate theory (CLPT) and continuum orthotropic elastic plate are used. The nonlocal theory of Eringen and Maxwell’s relations are employed to incorporate the small-scale effect and magnetic field effects, respectively, into the governing equations of the GSs. The differential quadrature method (DQM) is used to solve the governing differential equations for simply supported edges. The detailed parametric study is conducted, focusing on the remarkable effects of the angle and magnitude of magnetic field, different type of loading condition for couple system, tensile and compressive in-plane pre-load, aspect ratio and nonlocal parameter on the vibration behavior of the GSs. The result of this study can be useful to design of micro electro mechanical systems and nano electro mechanical systems. تفاصيل المقالة

In this work, nonlocal vibration of double of carbon nanotubes (CNTs) system conveying fluid coupled by visco-Pasternak medium is carried out based on nonlocal elasticity theory where CNTs are placed in uniform temperature change and magnetic field. Considering Euler-Bernoulli beam (EBB) model and Knudsen number, the governing equations of motion are discretized and Ritz method is applied to obtain the frequency of coupled CNTs system. The detailed parametric study is conducted, focusing on the remarkable effects of the Knudsen number, aspect ratio, small scale, thermo-magnetic fields, velocity of conveying fluid and visco-Pasternak medium on the stability of coupled system. The results indicate that magnetic field has significant effect on stability of coupled system. Also, it is found that trend of figures have good agreement with the previous researches. Results of this investigation could be applied for optimum design of nano/micro mechanical devices for controlling stability of coupled systems conveying fluid under thermo-magnetic fields. تفاصيل المقالة

In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip boundary condition and small size effect of nano flow are considered using Knudsen number. The Gurtin–Murdoch elasticity theory is applied for incorporation the surface stress effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The motion equations are derived based on the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is used in order to calculate the dynamic instability region (DIR) of visco-SWCNTs induced by pulsating fluid. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of SWCNTs. The results depict that increasing magnetic field and considering surface effect shift DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems. تفاصيل المقالة

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal forces from adjacent and non-adjacent elements on deflection are considered. The Eringen’s theory is utilized due to its capability to consider the size effect. Based on Hamilton’s principle, motion equations as well as boundary conditions are derived and solved by means of hybrid analytical-numerical method. It is believed that the presented general foundation model offers an exact and effective new approach to investigate vibration characteristics of this kind of structures embedded in an elastic medium. The results of this investigation may provide a useful reference in controlling systems in nano-scale. تفاصيل المقالة

This paper discusses static and dynamic response of nanoplate resting on an orthotropic visco-Pasternak foundation based on Eringen’s nonlocal theory. Graphene sheet modeled as nanoplate which is assumed to be orthotropic and viscoelastic. By considering the Mindlin plate theory and viscoelastic Kelvin-Voigt model, equations of motion are derived using Hamilton’s principle which are then solved analytically by means of Fourier series -Laplace transform method. The parametric study is thoroughly accomplished, concentrating on the influences of size effect, elastic foundation type, structural damping, orthotropy directions and damping coefficient of the foundation, modulus ratio, length to thickness ratio and aspect ratio. Results depict that the structural and foundation damping coefficients are effective parameters on the dynamic response, particularly for large damping coefficients, where response of nanoplate is damped rapidly. تفاصيل المقالة

In this study, a semi analytical method for transverse and axial vibration of single-walled boron nitride nanotube (SWBNNT) under moving a nanoparticle is presented. The surrounding elastic medium as Pasternak foundation and surface stress effect are included in the formulations of the proposed model. Using Timoshenko beam theory (TBT), Hamilton’s principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. The influences of surface stress effects, spring and shear parameters of Pasternak foundation and aspect ratio are also investigated on the free and forced vibration behavior of SWBNNT under moving a nanoparticle. Through an inclusive parametric study, the importance of using surrounding elastic medium in decrease of normalized dynamic deflection is proposed. It is demonstrated that the values of shear modulus have significant role on the vibration behavior of SWBNNT. The influences of surface stresses on the amplitude of normalized dynamic deflection are also discussed. The output result's of this study has significant influences in design and production of micro electro mechanical system (MEMS) and nano electro mechanical system (NEMS) for advanced applications. تفاصيل المقالة

This article presents an exact solution for an axisymmetric functionally graded piezoelectric (FGP) rotating disk with constant thickness subjected to an electric field and thermal gradient. All mechanical, thermal and piezoelectric properties except for Poisson’s ratio are taken in the form of power functions in radial direction. After solving the heat transfer equation, first a symmetric distribution of temperature is produced. The gradient of displacement in axial direction is then obtained by assuming stress equation in axial direction to be zero. The electric potential gradient is attained by charge and electric displacement equations. Substituting these terms in the equations for the dimensionless stresses in the radial and circumferential directions yield these stresses and using them in the mechanical equilibrium equation a nonhomogeneous second order differential equation is produced that by solving it, the dimensionless displacement in radial direction can be achieved. The study results for a FGP rotating hollow disk are presented graphically in the form of distributions for displacement, stresses and electrical potential. تفاصيل المقالة

Nonlinear free vibration analysis of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium is studied in this paper based on classical (local) Euler-Bernoulli beam theory. Using the averaging method, the nonlinear free vibration responses of DWCNTs are obtained. The result is compared with the obtained results from the harmonic balance method for single-walled carbon nanotubes (SWCNTs) and DWCNTs. The effects of the surrounding elastic medium, van der waals (vdW) forces and aspect ratio of SWCNTs and DWCNTs on the vibration amplitude are discussed. The error percentage of the nonlinear free vibration frequencies between two theories decreases with increasing the spring constant of elastic medium. Results are also shown that if the value of the spring constant is lower than (), the nonlinear free vibration frequencies are increased. In this case, the effect of the spring constant on frequency responses is significant, while if the value of the spring constant is higher than (), the curve of frequency responses has a constant value near to 1 and therefore the effect of the spring constant on frequency responses is negligible. تفاصيل المقالة

The use of intelligent nanocomposites in sensing and actuation applications has become quite common over the past decade. In this article, electro-thermo-mechanical nonlinear dynamic buckling of an orthotropic piezoelectric nanocomposite (PNC) cylindrical shell conveying viscous fluid is investigated. The composite cylindrical shell is made from Polyvinylidene Fluoride (PVDF) and reinforced by zigzag boron nitride nanotubes (BNNTs) where characteristics of the equivalent PNC being determined using micro-mechanical model. The poly ethylene (PE) foam-core is modeled based on Pasternak foundation. Employing the charge equation, Donnell's theory and Hamilton's principle, the four coupled nonlinear differential equations containing displacement and electric potential terms are derived. Harmonic differential quadrature method (HDQM) is applied to obtain the critical dynamic buckling load. A detailed parametric study is conducted to elucidate the influences of the geometrical aspect ratio, in-fill ratio of core, viscoelastic medium coefficients, material types of the shell and temperature gradient on the dynamic buckling load of the PNC cylindrical shell. Results indicate that the dimensionless critical dynamic buckling load increases when piezoelectric effect is considered. تفاصيل المقالة

Using harmonic differential quadrature (HDQ) method, nonlinear vibrations and instability of a smart composite cylindrical shell made from piezoelectric polymer of polyvinylidene fluoride (PVDF) reinforced with boron nitride nanotubes (BNNTs) are investigated while clamped at both ends and subjected to combined electro-thermo-mechanical loads and conveying a viscous-fluid. The mathematical modeling of the cylindrical shell and the resulting nonlinear coupling governing equations between mechanical and electrical fields are derived using Hamilton’s principle based on the first-order shear deformation theory (FSDT) in conjunction with the Donnell's non-linear shallow shell theory. The governing equations are discretized via HDQ method, and solved to obtain the resonant frequencies and critical flow velocities associated with divergence and flutter instabilities as well as re-stabilization of the system. Results indicate that the internal moving fluid plays an important role in the instability of the cylindrical shell. Application of a smart material such as PVDF improves significantly the stability and vibration of the system. تفاصيل المقالة

The axially compressed buckling of a double-walled carbon nanotabe surrounded by an elastic medium using the energy and the Rayleigh-Ritz methods is investigated in this paper. In this research, based on the elastic shell models at nano scale, the effects of the van der Waals forces between the inner and the outer tubes, the small scale and the surrounding elastic medium on the critical buckling load are considered. Normal stresses at the outer tube medium interface are also included in the current analysis. An expression is derived relating the external pressure to the buckling mode number, from which the critical pressure can be obtained. It is seen from the results that the critical pressure is dependent on the outer radius to thickness ratio, the material parameters of the surrounding elastic medium such as Young’s modulus and Poisson’s ratio. Moreover, it is shown that the critical pressure descend very quickly with increasing the half axial wave numbers. تفاصيل المقالة

Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE)-based micromechanical model. This study indicates how buckling resistance of composite cylindrical shell may vary by applying thermal and electrical loads. Applying the reverse voltage or decreasing the temperature, also, increases the critical axial buckling load. This work showed that the piezoelectric BNNT generally enhances the buckling resistance of the composite cylindrical shell. تفاصيل المقالة

In this research, a control feedback system is used to study the free vibration response of rectangular plate made of magnetostrictive material (MsM) for the first time. A new trigonometric higher order shear deformation plate theory are utilized and the results of them are compared with two theories in order to clarify their accuracy and errors. Pasternak foundation is selected to modelling of elastic medium due to considering both normal and shears modulus. Also in-plane forces are uniformly applied on magnetostrictive nano-plate (MsNP) in x and y directions. Nonlocal motion equations are derived using Hamilton’s principle and solved by differential quadrature method (DQM) considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, elastic medium, compression and tension loads and small scale effect on vibration behaviour of MsNP especially the controller effect of velocity feedback gain to minimizing the frequency. These finding can be used to active noise and vibration cancellation systems in micro and nano smart structures. تفاصيل المقالة

In this study an analytical method is developed to obtain the response of electro-magneto-thermo-elastic stress and perturbation of a magnetic field vector for a thick-walled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potential difference between its inner and outer surfaces. The thermal, piezoelectric and mechanical properties except the Poisson’s ratio are assumed to vary with the power law functions through the thickness of the hollow sphere. By solving the heat transfer equation, in the first step, a symmetric distribution of temperature is obtained. Using the infinitesimal electro-magneto-thermo-elasticity theory, then, the Navier’s equation is solved and exact solutions for stresses, electric displacement, electric potential and perturbation of magnetic field vector in the FGPM hollow sphere are obtained. Moreover, the effects of magnetic field vector, electric potential and material in-homogeneity on the stresses and displacements distributions are investigated. The presented results indicate that the material in-homogeneity has a significant influence on the electro-magneto-thermo-mechanical behaviors of the FGPM hollow sphere and should therefore be considered in its optimum design. تفاصيل المقالة

Elastic stability of ring and stringer-stiffened cylindrical shells under axial, internal and external pressures is studied using Ritz method. The stiffeners are rings, stringers and their different arrangements at the inner and outer surfaces of the shell. Critical buckling loads are obtained using Ritz method. It has been found that the cylindrical shells with outside rings are more stable than those with inside rings under axial compressive loading. The critical buckling load for inside rings is reducing by increasing the eccentricity of the rings, while for outside ring stiffeners the magnitude of eccentricity does not affect the critical buckling load. It has also been found that the shells with inside stringers are more stable than those with outside one. Moreover, the stability of cylindrical shells under internal and external pressures is almost the same for inside and outside arrangements of stringers. The results are verified by comparing with the results of Singer at the same loading and boundary conditions. تفاصيل المقالة

One of the most promising materials in nanotechnology such as sensors, actuators and resonators is annular Boron Nitride sheets (ABNSs) due to excelled electro-thermo-mechanical properties. In this study, however, differential quadrature method (DQM) and nonlocal piezoelasticity theory are used to investigate the nonlinear vibration response of embedded single-layered annular Boron Nitride sheets (SLABNSs). The interactions between the SLABNSs and its surrounding elastic medium are simulated by nonlinear Pasternak foundation. A detailed parametric study is conducted to elucidate the influences of the nonlocal parameter, elastic medium, temperature change and maximum amplitude on the nonlinear frequency of the SLABNSs. Results indicate that with increasing nonlocal parameter, the frequency of the coupled system becomes lower. The results are in good agreement with the previous researches. تفاصيل المقالة

In this study, two-dimensional electro-mechanical analysis of a composite rotating shaft subjected to non-axisymmetric internal pressure and applied voltage is investigated where hollow piezoelectric shaft reinforced by boron nitride nanotubes (BNNTs). Composite structure is modeled based on piezoelectric fiber reinforced composite (PFRC) theory and a representative volume element has been considered for predicting the elastic, piezoelectric and dielectric properties of the composite rotating shaft. Distribution of radial, circumferential, shear and effective stresses and electric displacement in composite rotating shaft are determined based on Fourier series. The detailed parametric study is conducted, focusing on the remarkable effects of angular velocity, electric potential, volume fraction and orientation angle of BNNTs on the distribution of stresses. The results show that properties of the piezoelectric shaft as matrix have significant influence on the electro-mechanical stresses where the PZT-4 has less effective stresses against PVDF. Therefore, PZT-4 could be considered for improving optimum design of rotating piezoelectric shaft under electric field and non-axisymmetric mechanical loadings. تفاصيل المقالة

In this paper, forced vibration analysis of a single-layered graphene sheet (SLGS) under moving a nanoparticle is carried out using the non-local elasticity theory of orthotropic plate. The SLGS under moving the nanoparticle is placed in the elastic and viscoelastic foundation which are simulated as a Pasternak and Visco-Pasternak medium, respectively. Movement of the nanoparticle is considered as a linear movement with constant velocity from an edge to another edge of graphene sheet. Using the non-linear Von Kármán strain-displacement relations and Hamilton’s principle, the governing differential equations of motion are derived. The differential equation of motion for all edges simply supported boundary condition is solved by an analytical method and therefore, the dynamic displacement of SLGS is presented as a closed-form solution of that. The influences of medium stiffness (Winkler, Pasternak and damper modulus parameter), nonlocal parameter, aspect ratio, mechanical properties of graphene sheet, time and velocity parameter on dimensionless displacement (dynamic displacement to static displacement of SLGS) are studied. The results indicate that, as the values of stiffness modulus parameter increase, the maximum dynamic displacement of SLGS decreases. Therefore, the results are in good agreement with the previous researches. تفاصيل المقالة

In this article, axisymmetric buckling behavior of piezoelectric fiber reinforced polymeric composite (PFRPC) annular plate subjected to electro-thermo-mechanical field is presented utilizing principle of minimum potential energy. Boron-nitride nanotubes (BNNTs) are used as fibers. Full coupling between electrical, mechanical and thermal fields are considered according to a representative volume element (RVE)-based XY piezoelectric fiber reinforce composite (PEFRC) model. Assuming PFRPC material and its composite constituents to be linear, homogenous, orthotropic, and perfectly bonded with uniform applied field, the basic relation for the axisymmetric buckling of a circular plate subjected to radial compression, radial electrical field, and uniform temperature change are derived. The presented results show that BNNTs can be used as an effective supplement to improve mechanical behavior of polyvinylidene fluoride (PVDF). Also, at normal working conditions, the influence of thermal and mechanical fields is much higher than the electric one on the critical load; hence, this smart structure is best suited for applications as sensors than actuators. تفاصيل المقالة

In this paper, a semi-analytical solution for magneto-thermo-elastic problem in an axisymmetric functionally graded (FG) hollow rotating disk with constant thickness placed in uniform magnetic and thermal fields with heat convection from disk’s surfaces is presented. Solution for stresses and perturbation of magnetic field vector in a thin FG rotating disk is determined using infinitesimal theory of magneto-thermo-elasticity under plane stress conditions. The material properties except Poisson’s ratio are modeled as power-law distribution of volume fraction. The non-dimensional distribution of temperature, displacement, stresses and perturbation of magnetic field vector throughout radius are determined. The effects of the material grading index and the magnetic field on the stress and displacement fields are investigated. The results of stresses and radial displacements for two different boundary conditions are compared with the case of a thin FG rotating disk with the same loading and boundary conditions but in the absence of magnetic field. It has been found that imposing a magnetic field significantly decreases tensile circumferential stresses. Therefore, the fatigue life of the disk will be significantly improved by applying the magnetic field. The results of this investigation can be used for optimum design of rotating disks. تفاصيل المقالة

Microtubules (MTs) are fibrous and tube-like cell substructures exist in cytoplasm of cells which play a vital role in many cellular processes. Surface effects on the vibration of bioliquid MTs surrounded by cytoplasm is investigated in this study. The emphasis is placed on the effect of the motor protein motion on the MTs. The MT is modeled as an orthotropic beam and the surrounded cytoplasm is assumed as an elastic media which is simulated by Pasternak foundation. In order to consider the small scale effects, the modified couple stress theory (MCST) is taken into account. An analytical method is employed to solve the motion equations obtained by energy method and Hamilton’s principle. The influence of surface layers, bioliquid, surrounding elastic medium, motor proteins motion, and small scale parameter are shown graphically. Results demonstrate that the speed of motor proteins is an effective parameter on the vibration characteristics of MTs. It is interesting that increasing the motor proteins speed does not change the maximum and minimum values of MTs dynamic deflection. The presented results might be useful in biomedical and biomechanical principles and applications. تفاصيل المقالة

In this article, electro-thermo nonlocal nonlinear vibration and instability of viscous-fluid-conveying double–walled boron nitride nanotubes (DWBNNTs) embedded on Pasternak foundation are investigated. The DWBNNT is simulated as a Timoshenko beam (TB) which includes rotary inertia and transverse shear deformation in the formulation. Considering electro-mechanical coupling, the nonlinear governing equations are derived using Hamilton’s principle and discretized based on the differential quadrature method (DQM). The lowest four frequencies are determined for clamped-clamped boundary condition. The effects of dimensionless small scale parameter, elastic medium coefficient, flow velocity, fluid viscosity and temperature change on the imaginary and real components of frequency are also taken into account. Results indicate that the electric potential increases with decreasing nonlocal parameter. It is also worth mentioning that decreasing nonlocal parameter and existence of Winkler and Pasternak foundation can enlarge the stability region of DWBNNT. تفاصيل المقالة

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation. تفاصيل المقالة

The high blood rate that often occurs in arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks and other diseases. However, vibration and instability analysis of carotid arteries are lacking. The objective of this study is to investigate the vibration and instability of the carotid arteries conveying blood under axial tension with surrounding tissue support. Arteries are modeled as elastic cylindrical vessels based on first order shear deformation theory (FSDT) within an elastic substrate. The elastic medium is simulated with visco-Pasternak foundation. The blood flow in carotid artery is modeled with non-Newtonian fluid based on Carreau, power law and Casson models. Applying energy method, Hamilton principle and differential quadrature method (DQM), the frequency, critical blood velocity and transverse displacement of the carotid arteries are obtained. It can be seen that increasing the tissue stiffness would delay critical blood velocity. The current model provides a powerful tool for further experimental investigation arteries tortuosity. In addition, the dimensionless transverse displacement predicted by Newtonian model is lower than that of non-Newtonian models. تفاصيل المقالة

This paper presents the surface piezomagnetoelasticity theory for size-dependent buckling analysis of an embedded piezoelectric/magnetostrictive nanobeam (PMNB). It is assumed that the subjected forces from the surrounding medium contain both normal and shear components. Therefore, the surrounded elastic foundation is modeled by Pasternak foundation. The nonlocal piezomagnetoelasticity theory is applied so as to consider the small scale effects. Based on Timoshenko beam (TB) theory and using energy method and Hamilton’s principle the motion equations are obtained. By employing an analytical method, the critical magnetic, electrical and mechanical buckling loads of the nanobeam are yielded. Results are presented graphically to show the influences of small scale parameter, surrounding elastic medium, surface layers, and external electric and magnetic potentials on the buckling behaviors of PMNBs. Results delineate the significance of surface layers and external electric and magnetic potentials on the critical buckling loads of PMNBs. It is revealed that the critical magnetic, electrical and mechanical buckling loads decrease with increasing the small scale parameter. The results of this work is hoped to be of use in micro/nano electro mechanical systems (MEMS/NEMS) especially in designing and manufacturing electromagnetoelastic sensors and actuators. تفاصيل المقالة

In this paper, the pull-in instability of piezoelectric polymeric nanocomposite plates reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) based on modified strain gradient theory (MSGT) is investigated. Various types of SWCNTs are distributed in piezoelectric polymeric plate and also surface stress effect is considered in this research. The piezoelectric polymeric nanocomposite plate is subjected to electro-magneto-mechanical loadings. The nonlinear governing equations are derived from Hamilton's principle. Then, pull-in voltage and natural frequency of the piezoelectric polymeric nanocomposite plates are calculated by Newton-Raphson method. There is a good agreement between the obtained and other researcher results. The results show that the pull-in voltage and natural frequency increase with increasing of applied voltage, magnetic field, FG-SWCNTs orientation angle and small scale parameters and decrease with increasing of van der Waals and Casimir forces, residual surface stress constant. Furthermore, highest and lowest pull-in voltages are belonging to FG-X and FG-O distribution types of SWCNTs. تفاصيل المقالة

In this study the effect of thermal stress on the torsional buckling of double walled carbon nanotubes is investigated. Moreover based on nonlocal continuum mechanic the buckling governing equations are obtained and equilibrium of Equations is generalized to double wall nanotubes. Also in this study the elastic medium, small scale effect and van der Walls force are considered. Also for simulation of the interaction between the polymer matrix and external tube Pasternak model is used. The numerical results indicate that critical buckling load occurs in the middle modes. Moreover for the Winkler related the Pasternak model the buckling occurs earlier. Results show that for rigid elastic medium in both case of Pasternak and Winkler models the buckling load is independent of their values Moreover from the result it can be seen that the buckling load has been increase as the thermal effect change. تفاصيل المقالة