Sandwich Nanobeam Research Articles

Stability analysis of sandwich double nanobeam-system with varying cross-section interconnected by Kerr-type three-parameter elastic layer

In this study, the endurable buckling load of the elastically connected parallel sandwich nano-beams with varying cross-sections is assessed. In this regard, a layered beam system consisting of two parallel axially loaded tapered sandwich nanobeams that are interconnected via a Kerr-type three-parameter elastic foundation is considered. The geometric properties are assumed to be changed exponentially along the length of the beam element. The governing equilibrium equations of the system are described by a set of three coupled homogeneous differential equations, which originates in the context of Eringen's non-local elasticity theory and Euler beam model. Then, the numerical differential quadrature technique is used to estimate the endurable axial critical loads. Eventually, a comprehensive parameterization research is performed to investigate the sensitivity of linear buckling resistance to tapering ratio, nonlocal parameter, stiffness of elastic connections, volume fraction exponent, and thickness ratio. The research work of the present study is novel, and the attained numerical outcomes can be used as benchmarks for future researches in this field.

Modeling of size dependent buckling behavior of piezoelectric sandwich perforated nanobeams rested on elastic foundation with flexoelectricity

This article presents a size dependent mathematical model and an analytical solution methodology to accurately simulate and analyze the size dependent buckling behavior of piezoelectrically layered sandwich nanobeams with perforated core embedded in an elastic medium with flexoelectricity. The electric enthalpy energy function is expressed in terms of the electric and the flexoelectric effects. Regular squared cutouts perforation pattern is adopted for the perforated core. Closed forms for the equivalent geometrical parameters of perforated core are developed. The shear deformation effect is incroporated using the Timoshenko beam theory (TBT). To capture the nonlocality and the microstructure length scale effects, the nonlocal strain gradient elasticity theory is modified and adopted to include the electromechanical nonclassical effects. The Hamiltonian principle is utilized to derive the equilibrium equations. An analytical solution methodology is developed to derive closed forms for critical buckling loads. The developed solution procedure is implemented into a MATLAB software code. The accuracy of the developed procedure is verified by comparing obtained results with corresponding cases reported in the literature. Influences of different design variables on the electromechanical buckling behavior are explored through intensive parametric studies. Results obtained showed the significant effects of the flexoelectricity and the piezoelectric parameters on the size dependent buckling behavior of piezoelectric sandwich nanobeams with perforated core. Size dependent electromechanical as well as mechanical buckling behaviors could be controlled by adjusting these parameters. The developed procedure and the obtained numerical results are helpful in many technological and industrial applications as MEMS and NEMS.

Magnetic field effects on the thermomechanical vibration behavior of functionally graded biocompatible material sandwich nanobeams

This study focuses on modeling and analyzing the thermomechanical vibration behavior of sandwich nanobeams made from biocompatible zirconia and Ti-6Al-4V materials. The sandwich nanobeam is composed of the materials mentioned earlier, featuring a porous structure in the core layer. The sandwich nanobeam experiences significant thermal load and is subjected to a horizontal external electromagnetic field. The equations of motion for the sandwich nanobeam were derived through the application of the sinusoidal high-order shear stress theorem and the constitutive equation based on nonlocal strain gradient elasticity. The equations were converted into equations of motion using Hamilton’s principle, incorporating the thermal load and the Lorentz force generated in the electromagnetic field, and solved using the Navier method. Analyses were conducted on the thermomechanical vibration behavior of the sandwich nanoplate, taking into consideration the properties of the sandwich layers, the impact of temperature, and the intensity of the applied horizontal magnetic field. The impact of the porous core layer in the sandwich nanoplate on the porosity volume ratio and porosity distribution function in thermomechanical behavior has been established. Research has demonstrated that the application of an external magnetic field can effectively mitigate the adverse impacts of thermal loads caused by high temperatures.

Size-dependent nonlinear vibration analysis of nonlocal magneto-electro-elastic sandwich nanobeam based on Reddy’s third-order shear deformation theory

Size-dependent nonlinear vibration analysis of nonlocal magneto-electro-elastic sandwich nanobeam based on Reddy’s third-order shear deformation theory

Effect of the magnetic field on the thermomechanical flexural wave propagation of embedded sandwich nanobeams

This work examines thermo-mechanical bending wave propagation in a sandwich nanobeam using advanced sandwich nanobeam and nanolocal strain gradient elasticity theories. The sandwich nanobeam is a unique structure with biocompatible ceramic ZrO2 and metal Ti6Al4V on the top and bottom sides. Sandwich nanobeam cores have functionally graded materials. This combination gives the nanobeam distinctive qualities and opens up many uses in diverse industries. The wave propagation equation is computed by applying the Navier method to the medium’s thermal, Lorentz, and viscoelastic equations of motion. The sandwich nanobeam is analyzed using four distinct models, taking into account its composition of ceramic and metal materials. The various factors that affect sandwich nanobeam bending wave propagation have been extensively studied. In the scenario where the magnetic field intensity is Hm = 0, an increase in temperature difference causes the wave frequency of all models (except Model 2) to decrease to zero, resulting in buckling. In Model 2, the sandwich nanobeam exhibits a phase velocity of 0.43 Km/s at ΔT = 0, which subsequently decreases by ∼9% to 0.39 km/s at ΔT = 500. These factors include the strength of the magnetic field, the impact of thermal loads, the nonlocal effect, the dimensions of the sandwich nanobeam, and the foundation’s influence. The findings of this research will help build nanosensor systems that can work in aerospace applications under extreme temperatures. These findings will contribute to the optimization of the design process, ensuring the reliability and functionality of the nanosensors under severe thermal conditions.

High frequency analysis of the functionally graded sandwich nanobeams embedded in elastic foundations using nonlocal quasi-3D theory

This study focuses on the high frequency analysis of the functionally graded sandwich nanobeams resting on elastic foundations for the first time. In the current work, two types of sandwich structures, namely hard-core and soft-core sandwich beams, are considered. The elastic foundations are modeled using a two-parameter foundation model with a spring layer and a shear layer. For the size-dependent effects, the nonlocal elasticity theory is employed in conjunction with a quasi-3D theory. Hamilton's principle is applied to establish the governing equations of the motion of the nanobeams. A comprehensive parametric study is provided to demonstrate the free vibration behaviors of the sandwich nanobeams in both low and high frequency modes, with more focus on the high frequency analysis. Therefore, the present results contribute to a deeper understanding of the dynamic response of the functionally graded sandwich nanobeams in the high frequency range.

Tailoring vibrational behavior in hybrid cellular sandwich nanobeams: a multiscale computational study

Tailoring vibrational behavior in hybrid cellular sandwich nanobeams: a multiscale computational study

Static bending and buckling of FG sandwich nanobeams with auxetic honeycomb core

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E, vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam.

Dynamic instability analysis of timoshenko FG sandwich nanobeams subjected to parametric excitation

According to the nonlocal theory, the dynamic instability and vibration of functionally graded (FG) porous sandwich nanobeams resting on a visco-elastic foundation under axial harmonic load are studied. In this paper the Timoshenko and nonlocal continuum theory are employed to take shear deformation, rotational bending and small-scale effects into account. The governing equations of motion are extracted using the nonlinear Von-Karman, and Hamilton approaches. Then, to turn the partial differential equations (PDEs) into ordinary differential equations (ODEs) in the case of equations of motion, the method of Galerkin is employed, followed by the use of the multiple time scale method to solve the resulting equations. According to the results of this study, it can be claimed that the porosity ratio is more effective than porosity distribution and nonlocal parameters on the amplitude response and dynamic instability regions. Moreover, to examine thermal increments, foundation characteristics, slenderness, and thickness ratios, the bifurcation diagrams are drawn and discussed. It is found that foundation and geometric characteristics are of the highest significance in the nonlinear response of the Timoshenko nanobeams. The main intention of this study is to present a holistic idea about the porous materials used in sandwich structures which can be used in many composite structures in aircraft and automobiles.

Static Buckling Analysis of FG Sandwich Nanobeams

Static Buckling Analysis of FG Sandwich Nanobeams

Coupled Newmark beta technique and GDQ method for energy harvesting and vibration control of the piezoelectric MEMS/NEMS subjected to a blast load

The controlled vibration and energy harvesting from a sandwich nanobeam, including two piezoelectric layers and a nanocomposite core, is investigated with the aid of nonlocal strain gradient theory. The nanobeam system is placed on an elastic substrate and under shockwave. The core layer is made of a reinforced composite made of a matrix polymer and carbon nanotubes (CNTs) along with carbon fibers (CF). The formulations along with end conditions are attained via Hamilton's principle and solved by the generalized differential quadrature method (GDQM) coupled with the Newmark beta method. Additionally, the vibration is controlled with two differential and integral gains. The impact of parameters such as elastic foundation, control gains, nonlocal factors, and parameters affecting the core material on forced vibration as well as energy harvesting is explored in detail. The current results are validated utilizing other publications. This work can be a basis for future studies on energy harvesting and controlled vibration on small scales.

On uncertainty modeling of thermoelastic vibration for porous nanosandwich beams with gradient core based on nonlocal higher order beam model

In the present paper, the size-dependent random thermoelastic vibration analysis of porous nanosandwich beams with gradient core are demonstrated based on the nonlocal higher order beam model. The nonlocal elasticity theory incorporation with the higher order shear deformation theory is used to describe the kinematic and constitutive relations. The governing equations are obtained from minimum potential energy principle. The finite element method is used to solve the governing equations. Three types of the FG sandwich nanobeams with three types of porous cores are taken into account, and the influences of these structures and porosity types on the deterministic and stochastic behavior of sandwich beams are thoroughly discussed. Initially convergence and validation study is preformed to validate the present theoretical model by comparing the present results with the several previous works and Monte Carlo Simulation (MCS). Further, a comprehensive parametric study is performed to demonstrate the influence of the length to thickness ratio, degree of uncertainty in the material properties, nonlocal parameter, porosity distribution type, porosity volume fraction, temperature change, and gradation of material on the deterministic and stochastic behaviors of the FG nanosandwich beams. The developed model and computed results may be useful in the precise and reliable design of the components of nanodevices and systems.

Dynamic Analysis of a Piezoelectrically Layered Perforated Nonlocal Strain Gradient Nanobeam with Flexoelectricity

This study presents a mathematical size-dependent model capable of investigating the dynamic behavior of a sandwich perforated nanobeam incorporating the flexoelectricity effect. The nonlocal strain gradient elasticity theory is developed for both continuum mechanics and flexoelectricity. Closed forms of the equivalent perforated geometrical variables are developed. The Hamiltonian principle is exploited to derive the governing equation of motion of the sandwich beam including the flexoelectric effect. Closed forms for the eigen values are derived for different boundary conditions. The accuracy of the developed model is verified by comparing the obtained results with the available published results. Parametric studies are conducted to explore the effects of the perforation parameters, geometric dimensions, nonclassical parameters, flexoelectric parameters, as well as the piezoelectric parameters on the vibration behavior of a piezoelectric perforated sandwich nanobeam. The obtained results demonstrate that both the flexoelectric and piezoelectric parameters increased the vibration frequency of the nanobeam. The nonlocal parameter reduced the natural vibration frequency due to a decrease in the stiffness of the structures. However, the strain gradient parameter increased the stiffness of the structures and hence increased the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the ration of the value of the nonlocal parameter to the strain gradient parameter. This model can be employed in the analysis and design of NEMS, nanosensors, and nanoactuators.

Mechanical analysis of bi-functionally graded sandwich nanobeams

In this study, the bending, free vibration and buckling analysis of a novel bi-functionally graded sandwich nanobeam are investigated for the first time via a nonlocal refined simple shear deformation theory. The novel sandwich beam consists of one ceramic core and two different functionally graded face sheets, which has a significant potential application in various fields of practical engineering and industry. The Eringen's nonlocal elastic theory has been used in cooperation with a refined simple shear deformation theory as well as Hamilton's principle to derive the equations of motion. Closed-form solution based on Navier's technique is used to solve the equations of motion of simply supported nanobeams. The present numerical results are compared with the available solutions to demonstrate the accuracy of the present theory. The influence of some parameters such as the slender ratio, the power-law index, the skin-core-skin thicknesses and the small-scale parameter on the bending, free vibration and buckling behavior of bi-functionally graded sandwich nanobeams are carried out carefully.

Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment

This paper presents a mathematical continuum model to investigate the static stability buckling of cross-ply single-walled (SW) carbon nanotube reinforced composite (CNTRC) curved sandwich nanobeams in thermal environment, based on a novel quasi-3D higher-order shear deformation theory. The study considers possible nano-scale size effects in agreement with a nonlocal strain gradient theory, including a higher-order nonlocal parameter (material scale) and gradient length scale (size scale), to account for size-dependent properties. Several types of reinforcement material distributions are assumed, namely a uniform distribution (UD) as well as X- and O- functionally graded (FG) distributions. The material properties are also assumed to be temperature-dependent in agreement with the Touloukian principle. The problem is solved in closed form by applying the Galerkin method, where a numerical study is performed systematically to validate the proposed model, and check for the effects of several factors on the buckling response of CNTRC curved sandwich nanobeams, including the reinforcement material distributions, boundary conditions, length scale and nonlocal parameters, together with some geometry properties, such as the opening angle and slenderness ratio. The proposed model is verified to be an effective theoretical tool to treat the thermal buckling response of curved CNTRC sandwich nanobeams, ranging from macroscale to nanoscale, whose examples could be of great interest for the design of many nanostructural components in different engineering applications.

Size-dependent free vibration analysis of functionally graded porous piezoelectric sandwich nanobeam reinforced with graphene platelets with consideration of flexoelectric effect

This paper investigates the effect of flexoelectricity on the vibration responses of functionally graded porous piezoelectric sandwich nanobeam reinforced by graphene platelets (GPLs). The Euler–Bernoulli beam theory and the general modified strain gradient theory are employed to formulate the constitutive equations. Different distributions of porosity and GPLs dispersion patterns are considered and the Halpin–Tsai model is used to predict Young’s modulus and density of the nanobeam. The governing equations and boundary conditions are derived based on the general strain gradient theory and solved by differential quadrature method. A parametric study is accomplished to investigate the effects of flexoelectricity, size-dependence, porosity coefficient, GPLs weight fraction, porosity distributions as well as GPLs dispersion patterns on the fundamental frequency of composite nanobeam. Numerical results indicate that the porosity, GPLs and flexoelectricity can effectively influence the vibration behavior of nanobeam.

Nonlocal layerwise formulation for bending of multilayered/functionally graded nanobeams featuring weak bonding

The size-dependent bending of perfectly/imperfectly bonded multilayered/stepwise functionally graded nanobeams, e.g. multiwalled carbon nanotubes with weak van der Waals forces, with any arbitrary numbers of layers, exhibiting different material, geometrical, and length-scale properties, is studied through a layerwise formulation of the stress-driven nonlocal theory of elasticity and the Bernoulli-Euler beam theory. The formulation is also valid for the continuously graded nanobeams, where the through-the-thickness material gradation with any arbitrary distribution is approximated in a stepwise manner through many layers. The size-dependency of each layer is accounted for through nonlocal constitutive relationships, which define the strains at each point as the output of integral convolutions in terms of the stresses in all the points of the layer and a kernel. Linear elastic uncoupled interfacial laws are implemented to model the mechanical response of the interfaces. The size-dependent system of equilibrium equations governing the deformations of the layers are derived and subjected to the variationally consistent edge boundary conditions and the constitutive boundary conditions associated with the stress-driven integral convolution. The formulation is applied to multilayered and sandwich nanobeams and the effects of the interfacial imperfections on the displacement fields and the interfacial displacement jumps are studied. It is found that the interfacial imperfections have greater impact on the field variables of multilayered nanobeams than that of the multilayered beams with the large-scale dimensions.

Buckling and free vibration analyses of a sandwich beam made of a soft core with FG-GNPs reinforced composite face-sheets using Ritz Method

The present paper studies buckling and free vibration analyses of sandwich beam. The sandwich beam is composed of a soft core integrated with functionally graded graphene nanoplatelets reinforced composite face sheets. Kinematic relations are developed based on Extended Higher-Order Sandwich Beam Theory (EHSPT). The governing equations are derived using Ritz-Lagrange formulation. The effective mechanical properties of epoxy/GPLs composites are obtained from the Halpin-Tsai micro-mechanical model and rule of mixture. The numerical results are obtained using the Ritz Method. The natural frequencies and buckling loads are obtained in terms of weight fraction and distribution of graphene nanoplatelets, length to thickness ratio, core to surface ratio, and different boundary conditions. Before presentation of complete numerical results, a comparative study is presented to check trueness and correctness of the results. It is concluded that maximum and minimum natural frequencies and critical buckling loads of sandwich nanobeam are obtained for FG-X and FG-O distributions, respectively.

Nonlinear dynamic analysis of temperature-dependent functionally graded magnetostrictive sandwich nanobeams using different beam theories

In the present study, nonlinear dynamic analysis of an embedded functionally graded sandwich nanobeam (FGSNB) integrated with magnetostrictive layers is investigated. The core layer of FGSNB, which is subjected to a time-dependent transverse load, is made of a two-constituent functionally graded material that the material properties of the functionally graded nanobeam are temperature dependent and assumed to vary in the thickness direction. The modified couple stress theory is taken into account so as to consider the small-scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of damping, shear and elastic effects of surrounded medium. Using energy method and Hamilton’s principle, the governing motion equations and related boundary conditions are obtained for different beam theories. Finally, the differential quadrature as well as Newmark-β methods are employed to obtain the nonlinear dynamic response of the functionally graded magnetostrictive sandwich nanobeam (FGMSNB), and therefore deflection-response curves are plotted to study the effects of small-scale parameter, surrounding elastic medium, magnetostrictive layers, geometrical parameters, material compositions of core layer, environment temperature and boundary conditions and nonlinear terms graphically. The results indicate that the magnetostrictive layers play a key role on the dynamic behavior of the FGMSNB. Moreover, comparing results with those obtained in Ghorbanpour Arani and Abdollahian (Mech Adv Mater Struct, 2017. https://doi.org/10.1080/15376494.2017.1387326 ) shows the importance of the nonlinear terms. The obtained results in this paper can be used as sensor and actuator in the sensitive applications.

Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory

A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.