Sandwich Microplates Research Articles

Computer Simulation for Determination of Critical Buckling Temperatures of Sandwich Microplates with Cellular Core and CNT-RC Piezoelectric Patches via MSGT

This study introduces a computational simulation which leads to obtaining the critical buckling temperatures of a sandwich microplate which is modeled based on the modified strain gradient theory. This theory includes three material length scale parameters. The core of the microstructure is made from cellular materials which is treated with piezoelectric carbon nanotubes-reinforced composite patches. An advanced trigonometric hyperbolic shear deformation theory, eliminating the need for shear correction factors, is employed to analyze the microstructure. Thickness-dependent variations in structural characteristics are observed based on predefined functions. The equilibrium equations are derived using the virtual displacement principle. Fourier series functions provide an analytical way of solving these equations. The findings are verified by comparison with earlier research that was published and used fewer complex combinations. The study looks at how several important factors affect the structure’s reaction to thermal buckling.

Analysis of vibro-acoustic characteristics of functionally graded sandwich microplates under thermal-electric effects

Based on the hyperbolic tangent parabola mixed shear deformation theory, the paper studied the sound radiation and the sound insulation of the functionally graded (FG) sandwich microplates under thermal-electric effects. The sandwich plate is composed of piezoelectric skin layers and FGM core layer. By using Hamilton’s principle, a size-dependent model considering the thermal-piezoelectric effects are established. The acoustic response and sound insulation are calculated with Rayleigh integral and solid-fluid coupling conditions. The accuracy of the presented method is verified by the numerical simulations. Then the effects of various parameters on the vibro-acoustic characteristics are analyzed and discussed. Numerical results show that the temperature variations, the length scale parameter to thickness ratio and the gradient index have great impacts on the FG sandwich microplates.

Formulation of non-local space-fractional plate model and validation for composite micro-plates

It is challenging to design nano/micro-devices because of their small size and tight engineering tolerances. Computer-aided design uses mathematical models of device parts, but contemporary models are not precise enough to capture all characteristics of the materials at the nano/micro-scale. In this work, we propose a novel mathematical model for composite nano/micro-plates in bending in the framework of a space-fractional continuum mechanics approach. This model yields closer mapping of experimental results compared to existing formulations. The developed theory is named the space-Fractional Kirchhoff–Love Plate (s-FKLP). We investigate how the parameters of the s-FKLP model, responsible for the scale effect description, affect the bending behavior of the micro-plates, considering different support conditions. In addition, we compare the results predicted by s-FKLP with the previously developed simpler (one-dimensional) space-Fractional Euler–Bernoulli Beam (s-FEBB) model to show that the choice of structural analysis strategy can influence design decisions. Despite its greater complexity, the s-FKLP is a more versatile approach to modeling micro-sized structures than the s-FEBB. The proposed s-FKLP model is empirically validated using real sandwich micro-plates. We conclude model alignment with the experimental data indicating that the model is suitable for representing sandwich micro-plates. We also find that the model’s length scale parameter corresponds to the microstructure’s grain size. The findings of this research may have implications for future work in the design and optimization of micro-sized devices.

Stochastic collocation method for thermal buckling and vibration analysis of functionally graded sandwich microplates

Thermal buckling and vibration behaviors of functionally graded (FG) sandwich microplates are investigated by using a unified higher-order shear deformation theory and stochastic collocation (SC) method. Uniform and linear distributions are considered for thermal effect and lognormal distributions are used to characterize the variability of the materials properties. The governing equations are derived by using Hamilton’s principle and solved by Ritz’s approach. To demonstrate the effectiveness and accuracy of the current model, the results from SC are compared with those from Monte Carlo Simulation. The effects of boundary conditions, temperature distribution, thickness-to-length ratio, material scale characteristics and power-law index on the fundamental frequencies and critical buckling temperature of the FG sandwich microplates are investigated. The FG sandwich microplates’ stochastic analysis provides some new findings that may be utilized as references in the future.

Nonlinear bending of FG metal/graphene sandwich microplates with metal foam core resting on nonlinear elastic foundations via a new plate theory

Nonlinear bending of functionally graded metal/graphene (FGMG) sandwich rectangular plate with metal foam core resting on nonlinear elastic foundations is elucidated in this article. A new shear deformation plate theory is presented to formulate the displacement field. The nonlinear partial differential equations considering the small size effect are established via the principle of virtual work. The nonlinearity is considered by using Von Karman’s strain-displacement relations. While, the size effect is captured by employing the modified couple stress theory. The upper and lower layers are made of aluminum as a matrix that reinforced with graphene platelets (GPLs). The GPLs are functionally graded through the thickness of the face layers according to a new cosine rule. Moreover, the metal foam core is also made of aluminum containing porosities that uniformly distributed or functionally graded through the core thickness. The governing equations are solved based on the Galerkin and Newton’s methods. The obtained results are examined by introducing some comparison examples. In addition, several parametric examples are discussed including the effects of the porosity type, GPLs distribution type, core-to-face thickness, elastic foundation stiffness, side-to-thickness ratio, plate aspect ratio and material length scale parameter on the nonlinear deflection and stresses of FGMG sandwich plate with metal foam core.

Size-dependent free vibration analysis of honeycomb sandwich microplates integrated with piezoelectric actuators based on the modified strain gradient theory

Size-dependent free vibration analysis of honeycomb sandwich microplates integrated with piezoelectric actuators based on the modified strain gradient theory

Dynamic Behaviors of Thermal–Electric Imperfect Functionally Graded Piezoelectric Sandwich Microplates Based on Modified Couple Stress Theory

Dynamic Behaviors of Thermal–Electric Imperfect Functionally Graded Piezoelectric Sandwich Microplates Based on Modified Couple Stress Theory

Modified couple stress theory for wave propagation in viscoelastic sandwich microplates with FG-GPLRC core and piezoelectric face sheets as sensor and actuator

In the present investigation, wave propagation of the viscoelastic sandwich microplates with functionally graded graphene nanoplatelets’ reinforced composite (FG-GPLRC) core and piezoelectric face sheets as sensor and actuator has been analyzed by the refined zigzag theory (RZT). Electromagnetic field is exposed to core and piezoelectric layers. Young's modulus, mass density, and Poisson's ratio are calculated based on the modified Halpin–Tsai model and rule of mixtures because FG-GPLs are arranged as uniform, parabolic, and linear patterns along the thickness of core. In addition, viscoelastic properties of the structure are simulated by the Kelvin–Voigt model. The system is located on an orthotropic visco Pasternak medium. The modified couple stress theory (MCST) is applied to simulate the microscale effects of the structure. Hamilton's principle is utilized for deriving the motion equations. Phase velocity, cut-off, and escape frequencies are computed with an analytical solution. The influence of valuable parameters, such as geometrical dimensions of the system, magnetic field, external voltage, small scale parameter, viscoelastic structural damping coefficient, various foundation types, weight fraction, and different distributions of GPLs on phase velocity, will be studied. The results of this study have a significant effect on the design and fabrication of sandwich micro-structures used in various industrial equipment.

Size effects on the vibro-acoustic characteristics of different types of functionally graded sandwich microplates

Due to the dynamic and acoustic characteristics of functionally graded microplates in micro- and nano-electro-mechanical systems, this paper established the vibro-acoustic governing equation of functionally graded (FG) sandwich microplates, which contains one material length scale parameter. Two types of FG sandwich microplates are studied, and the effects of different parameters on the vibro-acoustic characteristics are discussed. The results show that the size effect is significant when the thickness of microplate is close to the material length scale, especially at the higher order mode and for the thicker plate. Moreover, the sound insulation performance with the size effect increasing becomes better.

Fluid-structure interaction analysis of vibrating microplates in interaction with sloshing fluids with free surface

This study is concerned with the hydroelastic vibrations of sandwich micro-plates with functionally graded (FG) face sheets and metal core, interacting with sloshing liquid. For the purpose of the study, modified couple stress theory with variable length-scale parameter is applied to catch the small-scale effects of the structure. The mechanical properties of FG sandwich micro-plate and length scale parameter are supposed to be variable through the thickness of the structure. The displacement field is formulated based on fifth-order shear deformation theory which considers transverse shear stresses and rotary inertias. The liquid is assumed to be ideal, and the continuity equation is utilized to obtain liquid velocity potential associated with bulging and sloshing modes. After deriving kinetic and potential energies related to the micro-plate and liquid, Rayleigh-Ritz approach is applied to obtain vibrational characteristics of the system. Some comparison studies are made to confirm the reliability and efficacy of the present work. Finally, in the discussion section, wet frequencies of the sandwich micro-plate are analyzed in graphs and tables for various parameters.

Analytical investigation of the refined zigzag theory for electro-magneto vibration response of the viscoelastic FG-GPLRC sandwich microplates

Vibration behaviors of the viscoelastic sandwich microplates with graphene nanoplatelets (GPLs)-reinforced/Epoxy layer as core and sensor/actuator layers as piezoelectric face sheets are checked in this study. Small scale effects on the structure are computed by nonlocal elasticity modified couple stress theory (MCST). The piezoelectric layers and the core are exposed to the electromagnetic field. Modified Halpin-Tsai model and rule of mixtures (ROM) are assumed to obtain mechanical properties due to functionally graded graphene nanoplatelets (FG-GPLs)’s distributions as uniform, parabolic and linear. The viscoelastic sandwich piezoelectric microplates are embedded in orthotropic Visco Pasternak medium. In addition, the Kelvin-Voigt model is employed to calculate the viscoelastic properties of the structure. The equations of motion are derived using Hamilton’s principle based on refined zigzag theory (RZT). The effects of some remarkable parameters such as geometrical dimensions of the system, magnetic field, external voltage, small scale parameter and etc. are used to investigate frequency and damping of the system. Furthermore, decrement in system frequency is indicated when external voltages grow from to It is expected that this research will be able to address the challenges ahead in smart equipment and devices, and with control capability, it also can be used in the high-tech parts.

Modified couple stress-based nonlinear static bending and transient responses of size-dependent sandwich microplates with graphene nanocomposite and porous layers

This paper investigates the nonlinear static bending and dynamic transient responses of the rectangular and circular sandwich microplates composed of functionally graded graphene nanocomposite (GNC) face sheets and a porous polymeric core layer based on the modified couple stress theory (MCST) within the isogeometric analysis (IGA) framework. The four-variable higher-order shear deformation refined plate theory (RPT) and the von Kármán large deflection assumption are synthetically employed to describe the kinematics of the microplate. The nonlinear governing equations of motion are derived from the Hamilton’s principle. The nonlinear bending problem is solved by the Newton–Raphson technique under a displacement criterion strategy, while the dynamic responses under transient loads are obtained by the Newmark integration scheme in conjunction with Newton–Raphson iterative procedure. Comparisons are carried out to test the accuracy of iteration procedure in present formulation and the reliability in capturing small scale effect of present model. Obtained outcomes reveal that raising the material length scale (MLS) parameter and volume fraction index of graphene nanofillers both leads to reductions in nonlinear static deflections, dynamic amplitudes of deflection and periods of motion. The examples for porosity coefficient show that embedding pores in core layer leads to slight changes in terms of static and dynamic responses and an improvement in weight reduction of the sandwich microplate.

Thermo-mechanical buckling analysis of FG-GNPs reinforced composites sandwich microplates using a trigonometric four-variable shear deformation theory

The current study is aimed to investigate the thermo-mechanical buckling responses of the sandwich microplate with Graphene nanoplatelets (GNPs)-reinforced Epoxy core fully bonded to single-walled carbon nanotubes (SWCNTs)-reinforced piezoelectric patches. The face sheets were exposed to the electric field and the microplate was assumed to locate on the Pasternak elastic substrate. The GNPs and SWCNTs were dispersed throughout the core and face thickness according to some specific functions. To consider the shear deformation effect, tangential shear deformation theory (TSDT), as a trigonometric higher-order theory, was used. The size effects were also included through applying and the modified strain gradient theory (MSGT). The virtual displacement principle was utilized to derive the governing equations and then by employing an analytical method, they were solved. The validity of the results was confirmed by comparing the results for simpler state with previously published ones. A parametric study is provided to observe behavior of the microstructure in different conditions. It was observed that GNPs and CNTs dispersion patterns play an important role in the microplate buckling behavior, as well as temperature variations. The outcomes of this work may help to manufacture more efficient engineering smart structures, such as micro/nanoelectromechanical systems.

Efficient Energy Funnelling by Engineering the Bandgap of a Perovskite: Förster Resonance Energy Transfer or Charge Transfer?

Energy funnelling enables directional carrier transfer along cascaded energy levels, which can be employed to significantly improve energy transfer efficiency and photoelectronic performances. However, the exact mechanism is still under intensive debate on whether Förster resonance energy transfer (FRET) or charge transfer (CT) is playing the dominant role, hindering broad practical device design and applications. Herein, a spectroscopic method is developed to unveil the energy funnelling mechanism by comparing and modeling the photoluminescence (PL) spectra excited by pulsed and continuous-wave (CW) lasers. The applicability of this method is verified in a typical energy funnelling system constructed by engineering the bandgap of a perovskite. Composite hexagonal microplates (MPs) with FAPbBr3, FAPb(BrxI1-x)3, and FAPbI3 (formamidinium = FA) at the surface, middle mezzanine, and bottom layers are synthesized by a two-step chemical vapor deposition (CVD) method, which introduces a directional energy funnelling from wide-bandgap FAPbBr3 to narrow-bandgap FAPbI3. By using the spectroscopic method developed in this work, we reveal that charge transfer is the dominant mechanism for energy funnelling in the FAPbBr3/FAPb(BrxI1-x)3/FAPbI3 sandwich MP. This study not only provides novel insights into the energy funnelling in multiple-bandgap perovskite systems but also develops a widely applicable spectroscopic method to explore the energy funnelling mechanism in other graded bandgap systems.

Transient instability analysis of viscoelastic sandwich CNTs-reinforced microplates exposed to 2D magnetic field and hygrothermal conditions

Transient size-dependent mechanical and thermal buckling analyses of sandwich microplates with viscoelastic core and single-walled carbon nanotubes (CNTs)-reinforced face sheets are introduced in this paper. The CNTs are uniformly distributed or functionally graded (FG) through the thickness of the face layers. The viscoelastic sandwich microplate is resting on three-parameter viscoelastic foundations that modeled according to the viscoelastic Kelvin-Voigt model with a shear layer. Effects of a 2D magnetic field as well as hygrothermal conditions on the present analyses are studied. The modified couple stress model containing one material length scale parameter is employed to capture the small scale effect. A body force (Lorentz force) is deduced from Maxwell’s magnetic equations, that is applied to each particle of the structure. The higher-order shear deformation plate theory with four unknowns is utilized to describe the displacement field. The stability equations are obtained using the principle of virtual displacement. By applying Navier method, the stability equations are solved to obtain the mechanical and thermal buckling of viscoelastic sandwich microplates. Various numerical examples are presented including the effects of the length scale parameter, moisture concentration, magnetic field parameter and other parameters on the buckling of the viscoelastic FGCNTs-reinforced sandwich microplates.

Size-Dependent Hygro-Thermal Buckling of Porous FGM Sandwich Microplates and Microbeams Using a Novel Four-Variable Shear Deformation Theory

Based on a new shear deformation theory and the modified couple stress theory, in this paper, the hygro-thermal buckling of porous FGM sandwich microplates and microbeams is investigated. Unlike the classical elasticity theory, the present model involves a material length scale parameter, and, thereby, can capture the small size effect. The four-variable shear deformation theory with a new shape function is utilized to derive the governing stability equations for the microplates and microbeams from the principle of virtual work. The present microstructures are composed of three layers and subjected to hygro-thermal conditions. The core is assumed to be fully homogeneous and isotropic material. While, the face layers are made from porous functionally graded materials that vary only in the thickness direction. The governing equations are solved analytically to obtain the thermal buckling of FGM sandwich microplates and microbeams under humidity effects. The temperature rise and moisture concentration are graded uniformly, linearly or nonlinearly through the thickness. Comparison studies are made between the present results and those available in the literature to check the validity of the obtained formulations and results. Moreover, the effects played by the length scale parameter, power-law exponent, moisture concentration, core thickness and other parameters on the thermal buckling of microplates and microbeams are all investigated.

Buckling of piezoelectric sandwich microplates with arbitrary in-plane BCs rested on foundation: effect of hygro-thermo-electro-elastic field

Buckling and post-buckling behaviors of simply supported microplates in complex environment are studied, where elastic foundation and hygro-thermal-electro-mechanical loads are considered. The first-order shear deformation theory is used to establish basic equations of the microplate considering the von Karman’s nonlinearity. The size-dependent effect is characterized by the modified couple stress theory. A unified boundary condition model is introduced to discuss various in-plane boundary conditions (BCs). Analytical solutions for critical mechanical/hygrothermal buckling loads and post-buckling paths of the microplate under different in-plane BCs are obtained by using the perturbation method and the Galerkin method, respectively. Results reveal that size-dependent effect and elastic foundation enhance the stiffness of the microplate. Transverse displacement of the microplate in the post-buckling stage increases with the external compressive load, temperature and moisture concentration, expressing a nonlinear curve. When the displacement constraint in the normal direction is applied on the microplate edge, the critical mechanical/hygrothermal buckling load decreases. These results can be utilized in the optimization design of the micro-electro-mechanical systems.

Influence of a 2D magnetic field on hygrothermal bending of sandwich CNTs-reinforced microplates with viscoelastic core embedded in a viscoelastic medium

The present work is concerned with the bending analysis of viscoelastic sandwich microplates with carbon nanotubes (CNTs)-reinforced face sheets under the effects of a 2D magnetic field as well as hygrothermal conditions. The core layer is assumed to be a fully homogeneous viscoelastic material, whereas the face sheets are made of a polymer matrix stiffened by uniformly distributed or functionally graded (FG) CNTs. The applied magnetic field results in a body force (Lorentz force) that is applied to each particle of the plate. In order to take into account the size effect, the modified couple stress theory is employed containing only one length scale parameter. The viscoelastic sandwich microplate is assumed to be resting on two layers of the foundations. The first is modeled as the viscoelastic Kelvin–Voigt model. However, the second represents the elastic Pasternak shear layer. Based on the sinusoidal four-variable plate theory, four governing equations are obtained involving Lorentz force and foundation interaction. An analytical solution for the obtained equations is presented to get the displacements and stresses of the reinforced sandwich plates. The present solution is examined by introducing comparison examples. Influences of the geometric parameters, material length scale parameter, magnetic field parameter, damping parameters, temperature rise, moisture concentration, and foundation coefficients on the bending of the FG-CNTs-reinforced viscoelastic sandwich microplates are discussed.

Piezoelectricity and length scale effect on the vibrational behaviors of circular sandwich micro-plates

In this paper, the vibrational behaviors of circular and annular sandwich micro-plates coupled with two piezoelectric layers are analytically studied. For defining the equations of motion, the Hamilton’s principle and the classical plate theory are used. In the micro-scale size, the properties of the material depend on dimensions, and therefore the modified couple stress theory is utilized to consider this effect. The electric potential of piezoelectric layers is obtained by satisfaction of the Maxwell equation. The natural frequencies for various boundary conditions in two kinds of open and close circuit electric conditions are calculated, and the effects of length scale and electrical field are studied. The results show that the natural frequencies for open piezoelectric micro-plates are larger than the closed ones.

Vibration and Buckling of Functionally Graded Sandwich Micro-Plates Based on a New Size-Dependent Model

Within the framework of re-modified couple stress theory, the Refined Zigzag Theory is added to the vibration and buckling analysis of sandwich micro-plates embedding functionally graded layers. The disparity between the scale effects along two orthogonal directions is considered through two orthogonal material length scale parameters (MLSPs). Meanwhile, the solutions of natural frequencies and buckling loads show an improved predictive capability through comparing the results with exact and quasi-3D solutions. Two types of functionally graded sandwich micro-plates with simply supported boundary conditions are taken as the illustrative examples, namely, an isotropic functionally grade sandwich micro-plate with a power law and an orthotropic one with an exponential law. The numerical results indicate that the present model can capture the varying scale effects along two orthogonal directions, particularly when the geometric size of the micro-plates is comparable to the MLSPs. When microscopic isotropy is observed, the present model can also make accurate predictions on those kinds of micro-structures by setting the two orthogonal MLSPs equal to each other. In addition, the scale effects are less obvious as the functionally graded sandwich micro-plate is getting thinner and harder; the grading index also has an influence on the scale effects, but this influence is simultaneously depending on the side-to-thickness ratio of the micro-plate.