Rectangular Sandwich Plates Research Articles

New HSDT for free vibration analysis of elastically supported porous bidirectional functionally graded sandwich plate using collocation method

The present paper deals with the free vibration response of elastically supported porous bidirectional functionally graded soft-core sandwich rectangular plate with proposed new tangent shape function-based higher-order transverse shear deformation theory. The theory is accomplished to uphold the continuity of transverse shear stresses and zero shear stress conditions on both the extreme surfaces of a plate. The bidirectional gradation varies through the thickness ( z-axis) and length ( x-axis) directions. The effective material properties are calculated via the modified power-law. The governing differential equations (GDEs) of motion are acquired via the Hamilton principle. The inverse multi-quadric radial basis function-based Collocation method is implemented to discretize the GDEs obtained by strong form formulation. The current theory and method’s accuracy and efficacy are validated by comparing the present results with existing results in the literature. Studies show that the results of the proposed theory are in close agreement with 3D approach. Numerical results are obtained with a different scheme of sandwich layers for free vibration analysis. Effects of grading index, porosity fraction, two parameters foundation, different scheme, and the span to thickness ratio on free vibration response have been discussed. New results for free vibration response in porous media are presented with different skin materials.

Influence of aperture shape on dynamic behaviors of sandwich plates by means of improved isogeometric analysis and experimental tests

Due to assembly and lightweight design, various apertures are involved in composite and sandwich plates, which will influence the natural frequencies and vibration modes of these structures. If the influence mechanism of aperture shapes on dynamic characteristics of composite and sandwich plates is not clarified, structural safety will be significantly impacted as external loads are close to the natural frequencies of composite plates with apertures. Nevertheless, experimental tests in conjunction with accurate analysis on the dynamic response of composite and sandwich plates with different aperture shapes are less reported in published literature, so the influence mechanism of aperture shapes on dynamic characteristics of composite and sandwich plates is required to be clarified precisely. Thus, a novel refined sinusoidal higher-order theory (RSHT) combined with isogeometric analysis (IGA) is proposed, where the improved bending strip method (IBSM) has been reconstructed to satisfy approximately the C1-continuity in multi-patch IGA. Four sets of tests on free vibration of rectangular sandwich plates with different sizes of circular cutouts are carried out to verify the reliability of the proposed method. Numerical results and experimental tests show that the proposed RSHT can predict more accurately the influence of aperture shapes on dynamic behaviors of sandwich plates, and the influence mechanism of aperture shapes on dynamic characteristics of sandwich plates has been illustrated, which can provide a reference for other investigators.

Hygro-thermal-dynamic problem of asphalt pavement system subjected to a moving harmonic load

This article considers the multi-layer asphalt pavement system as a rectangular sandwich plate and utilizes the first-order shear deformation theory (FSTD) of plates to analyze the hygro-thermo-dynamic response of a porous viscoelastic asphalt system subjected to a mobile harmonic load. The porosity of asphalt layer is assumed to be distributed along the thickness and in-plane directions in some common traits: uniform, varying symmetric and varying asymmetric. A combination of Hamilton’s principle and Fourier series analysis allows one to derive and solve the motion equations. This step is followed by a comparison with available data in the literature and using finite element tools to verify the accuracy of the developed formulation. In addition, the effects of the excitation frequency, load velocity, viscoelastic medium, distribution of porosity in different directions, and variations of temperature and moisture on the response of described system are carefully investigated, indicating the necessity of taking all these parameters into account when designing such systems. Interestingly, the varying symmetric distribution offers certain advantages that makes it a better choice for porosity dispersal.

Optimization of damping characteristics of tapered MWCNT/glass fiber reinforced composite rectangular sandwich plates: A higher-order finite element formulation

The research work presented in this paper is focused on the investigation of damping characteristics and structural optimization of the tapered composite hybrid smart rectangular sandwich plates. The composite rectangular hybrid sandwich plate contains the constraining and base layers made of multi-walled carbon nanotubes reinforced composite (CNTRC) face sheets and the core layer made of multi-walled carbon nanotubes reinforced magnetorheological elastomer. Higher-order shear deformation theory (HSDT) and finite element (FE) formulations are employed to derive the governing equations of the CNTRC rectangular hybrid smart sandwich plate. The performance of the derived HSDT model is validated by comparing the results in terms of natural frequencies evaluated using experimental tests on the composite hybrid smart sandwich structures under different support conditions. The influence of CNT reinforcement on the damping performance of the tapered rectangular hybrid smart sandwich plates are explored. Also, the optimal ply orientations of the tapered CNTRC rectangular sandwich plates with hybrid core is identified using the developed HSDT model coupled with Genetic Algorithm (GA) to enhance the natural frequencies and loss factors. Further, it can be observed that the reinforcement of CNTs in composites significantly influences the stiffness and damping characteristics of the tapered composite rectangular smart sandwich plates.

Three-Dimensional Transient Analysis of FGM Rectangular Sandwich Plate Subjected to Thermal Loading Using State Space Differential Quadrature Method

In this paper, transient response of functionally graded materials (FGM) rectangular sandwich plates subjected to thermal loading based on three-dimensional theory of elasticity is carried out. The facing layers are made of metal and ceramics whereas core layer is FGM with exponential function distribution. For the case of simply supported boundary conditions, obtained state space differential equations are solved analytically by using Fourier series expansions along the in-plane coordinates and Laplace transformation. For other edges, boundary condition semi-analytical method is used by applying differential quadrature method (DQM) along the in-plane direction and state space technique across the transverse coordinate. After carrying out the convergence of the present method, accuracy of this study is validated by comparing the numerical results with those reported in the literature. Finally, influences of the boundary conditions, length-to-thickness ratios, length-to-width ratios, time constant and the FGM graded index on elastic behavior of sandwich plate are examined.

Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

Effect of extreme in-plane and transverse stiffness ratios on frequencies and load transfer between face sheets and core of rectangular sandwich plates

Challenging issues for sandwich structures include accurately finding their frequencies and how the load transfers from face sheets to the core when their material stiffness ratio (FCSR) in either the axial or the transverse directions varies from 1 to 107. Here we use both the equivalent single layer and the layer wise shear and normal deformable plate theories to analyze problems for rectangular plates of different thickness/length ratios. The Ritz method with Jacobi polynomials as basis functions is employed to numerically solve three-dimensional linear elasticity theory equations. Transverse stresses are calculated using a one-step stress recovery scheme. It is found that the FCSR in the transverse direction determines the minimum degree of complete polynomials in the thickness coordinate needed to accurately compute the lowest six frequencies and the transverse stresses. New results include the following: (i) the FCSR in the transverse direction has a greater influence than that in the axial direction on the computed frequencies and transverse stresses, and (ii) whereas both transverse normal and shear stresses in the core contribute to transmitting loads between the two face sheets for FCSR < 103, however, only the former is effective for FCSR ≥ 105.

WITHDRAWN: Analytical and numerical investigation of buckling load of functionally graded materials with porous metal of sandwich plate

In this study, a new mathematical model is presented for a simply supported rectangular sandwich plate made of functionally graded materials (FGMs) with porosities to evaluate the buckling stresses with different design parameters. The rectangular imperfect FGM plate is assumed to have various porosity distributions through the plate thickness, while the upper and lower skins are made of homogenous materials. Mathematical models were derived based on the classical plate theory (CPT) principles, and the effect of changing porous index, elastic parameters, porosity ratio, and length to thickness ratios on the buckling stresses of the functionally graded sandwich plate was investigated. A numerical investigation with the assist of finite element analysis (FEA) was conducted using commercial software ANSYS 2020 R2. Eight-node SOLID186 elements are modeled and analyzed to validate the obtained results of the analytical solution. Also, systematic numerical analyses for the selected models to evaluate the buckling stresses in a sandwich structure with different boundary conditions and frequent FG plate layers are carried out. The results show that the critical buckling load of the FG sandwich plate is decreasing when the power-law index (k) and porosity percentage increase and increasing with higher aspect and slenderness ratios, and the increasing the number of layers leads to an increase in the accuracy of the results for the same FGM sandwich beam thickness. There is an acceptable convergence between analytical and numerical techniques with a percentage discrepancy no exceed 6%.

Static and dynamic instability analysis of tapered CNTRC sandwich plates under uniform and non-uniform in-plane loadings using spline finite strip method

This paper presents the buckling analysis of rectangular sandwich plates with pure polymeric tapered cores and functionally graded carbon nanotube (FG-CNT) reinforced composite face sheets under static and harmonic dynamic loads. One uniform and four linearly-varying patterns are considered for the applied in-plane loads. The effective material properties of face sheets, in which the polymeric matrix is reinforced with aligned single-walled carbon nanotubes (SWCNT), are estimated using the extended rule of mixture. A higher-order zigzag shear deformation theory, which has the same number of dependent unknowns as the first-order theory, is employed to express the plate's displacement field. The governing equations are derived using Hamilton's principle and discretized by the spline finite strip method. The dynamic instability regions of plates with uniform and variable thickness are obtained by employing Bolotin's method. The accuracy of the present method is demonstrated by considering the problems for which solutions are available. A detailed numerical study is conducted to examine and compare the effects of different parameters, including the taper angle, type of the applied in-plane load, static and dynamic load factors, length-to-width ratios, the volume fraction of CNT, distribution pattern of CNTs along the thickness direction, temperature, and boundary conditions on the behavior of sandwich plate.

Analytical and Numerical Investigation of Buckling Behavior of Functionally Graded Sandwich Plate with Porous Core

ABSTRACT This research presents a new analytical model for the buckling analysis of a functionally graded rectangular sandwich plate with all edges simply supported and subjected to in-plane loading conditions. The sandwich plate comprises a porous metal core with an isotropic metal that serves as a skin. The functionally graded core metal has a varied distribution of porosities in accordance with the plate thickness, which may lead to variation in material properties. By considering classical plate theory principles, the kinematic relations are used to obtain the analytical solution. The effects of changing gradient index, elastic parameters, porosity distribution, slenderness ratio, boundary conditions, and core materials on buckling stresses and dynamic response of functionally graded sandwich plates are presented. A numerical study on elastic buckling using finite element analysis (FEA) was employed to examine the accuracy of the proposed analytical solution. From the obtained results, it is found that the porosity coefficients play significant influences on the buckling behavior and reliability of the FG sandwich structures.

Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions

Extended higher-order sandwich plate theory is used to analyze the free vibrations of rectangular sandwich plates with compressible core. Accordingly, first-order shear deformation theory is used to model the laminated face sheets. Besides, the in-plane and transverse displacements of the core are assumed to be cubic and quadratic functions of the thickness coordinate, respectively. To deduce the governing equations, Hamilton’s principle is used. Then, based on the Rayleigh-Ritz method, single series expansions with two-variable orthogonal polynomials – namely, the orthogonal plate functions – are considered to approximate the displacement components. Lastly, a generalized eigenvalue problem is solved to obtain the free vibrational characteristics of sandwich plates with both symmetric and anti-symmetric lay-ups subjected to various boundary conditions. The method is validated against the results obtained by different methods in the literature. Finally, the effects of the plate side-to-thickness ratio, in-plane aspect ratio, and core-to-face sheets thickness ratio on the natural frequencies are discussed.

Thermo-elastic buckling of honeycomb micro plates integrated with FG-GNPs reinforced Epoxy skins with stretching effect

Halpin-Tsai and extended rule of mixture (ERM) schemes are used to evaluate the effective material properties of composite face sheets of a micro-scaled sandwich rectangular plate, to assess its thermo-elastic buckling behavior, in the current paper. For more details, it should be added that under evaluation model, which is resting on a Pasternak elastic foundation, is a honeycomb micro structure which is made of Nomex or Glass Phenolic and, to integrity, is patched with two same composite layers including graphene nanoplatelets (GNPs) dispersed through Epoxy resin. Great novelty of quasi-3D hyperbolic shear deformation theory (QHSDT) which accounts for stretching effect, virtual displacement principle, and modified couple stress theory (MCST) produced a good motivation to hire it to extract equations related to the current sandwich micro plate. Finally, variations of critical loads of thermal and mechanical buckling considered in figures and tables to examine the effect of different parameters’ changes on them. As an example, based on acquired results, the sensitivity of thermo-mechanical critical buckling loads to the internal aspect ratio of honeycomb core ϕ0 and force intensity distributions is proved where force intensity enhancement is caused critical buckling load reduction.

Fundamental frequency of a corner-supported rectangular sandwich plate with the central lumped mass

An efficient method of calculation of the fundamental frequency of a corner-supported composite sandwich plate having a lumped mass at its centre is proposed in this work. The corresponding dynamic problem is solved using the Hamilton principle and the Rayleigh-Ritz method. The panel is modelled using the first order shear deformation theory. The panel deflection and angles of rotation are approximated based on certain combinations of trigonometry functions. Application of the Rayleigh-Ritz method allowed the original system of equations to be reduced to a homogeneous system of linear algebraic equations of the seventh order with respect to unknown coefficients of approximating functions. The fundamental frequency is found as a minimum eigenvalue of this system. Using this solution, the effects of the geometric parameters of the panel and the value of lumped mass were investigated. The results of the calculations were successfully verified by comparisons with the outcomes of the finite-element computations. The efficiency of the proposed methodology was demonstrated in the design analysis of the corner-supported composite sandwich panel with the central lumped mass subject to a constraint imposed on the value of fundamental frequency.

Buckling analysis of rectangular sandwich plates with functionally graded graphene-reinforced face layers

The buckling analysis of a rectangular sandwich plate smoothly reinforced with multilayered graphene nanoplatelet is presented. The equations of equilibrium are extracted using the principle of minimum total potential energy and the first-order shear deformation theory for the thick sandwich plate. Different graphene distributions are considered through the thickness of the plate, and the rule of mixture is used to obtain the effective properties of the reinforced nanocomposite. To solve the equations, the Fourier series is employed to describe the displacement components and the boundary conditions are considered to be simply supported for all edges. The results are verified with available research, and the effects of some important parameters on the buckling load of the sandwich plate are studied.

On the buckling of advanced composite sandwich rectangular plates

In this paper, higher order closed-formed analytical solutions for the buckling analysis of functionally graded sandwich rectangular plates are obtained using a unified shear deformation theory. Three-layered sandwich plates with functionally graded skins on top and bottom; and isotropic core in the middle are considered for the study. The material properties of skins are varied through the thickness according to the power-law distribution. Two types of sandwich plates (hardcore and softcore) are considered for the detail numerical study. A unified shear deformation theory developed in the present study uses polynomial and non-polynomial-type shape functions in terms of thickness coordinate to account for the effect of shear deformation. In the present theory, the in-plane displacements consider the combined effect of bending rotation and shear rotation. The parabolic shear deformation theory of Reddy and the first-order shear deformation theory of Mindlin are the particular cases of the present unified formulation. The governing differential equations are evaluated from the principle of virtual work. Closed-formed analytical solutions are obtained by using the Navier’s technique. The non-dimensional critical buckling load factors are obtained for various power-law coefficients, aspect ratios and skin-core-skin thickness ratios.

An efficient four-variable I-L nonlocal static model of unsymmetrical sandwich rectangular plate with laminated facings

This paper presents a new, simple, containing only four unknown functions, individual-layer, static model for rectangular sandwich plate unsymmetrical with respect to its middle plane. The shear strains in the outer layers of the plate are neglected while the shear strains in the middle layer are variable and equivalent to zero on its outer surfaces. Local constitutive models of the layers consistent with the assumed kinematics are derived. A detailed analysis of all partial problems is presented. In order to determine the unknown functions, appearing in the kinematic model assumed, one needs to solve a set of three coupled partial differential equations and separately the fourth governing equation that contains only one unknown function. In the case of the plate symmetrical about its middle plane only two uncoupled partial differential equations for the bending problem must be solved. Deflections predicted by the present model for a symmetrical sandwich plate are compared with counterparts, existing in the literature, predicted by two theories that include flexibility of the middle layer of the plate. Good agreement of these results has been obtained.

Coexistence of bistable multi-pulse chaotic motions with large amplitude vibrations in buckled sandwich plate under transverse and in-plane excitations.

This paper researches the dynamic snap-through phenomena and the coexistence of the multi-pulse jumping chaotic dynamics in bistable equilibrium positions and the large amplitude nonlinear vibrations for a simply supported buckled 3D-kagome truss core sandwich rectangular plate under combined transverse and in-plane excitations based on the extended high-dimensional Melnikov method. According to the two-degree-of-freedom non-autonomous nonlinear dynamical system of the buckled truss core sandwich rectangular plate and the theory of normal form, it is found that some nonlinear terms have less effects on the nonlinear dynamic responses than other nonlinear terms. The extended high-dimensional Melnikov method is employed to investigate the dynamic snap-through phenomena and the bistable multi-pulse jumping chaotic vibrations around the upper-mode and the lower-mode for two different cases of buckling in the truss core sandwich rectangular plate. A numerical method is used to detect the bistable multi-pulse jumping chaotic vibrations around two stable equilibrium positions for the non-autonomous buckled truss core sandwich rectangular plate. The obtained theoretical and numerical results indicate that there exists the coexistence of the bistable multi-pulse jumping chaotic vibrations and the large amplitude nonlinear vibrations in the buckled truss core sandwich rectangular plate under combined transverse and in-plane excitations.

Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory

In this study, the free vibration and buckling responses of functionally graded nanoplates with magneto-electro-elastic coupling are studied for the first time using a nonlocal modified sinusoidal shear deformation plate theory including the thickness stretching effect. The constitutive relations for these kind of structures are defined. The equations of motion for rectangular sandwich plates in macro and nano scale are derived using a modified dynamic version of Hamilton's principle including a contribution of the electric and magnetic fields. The closed-form analytical solution to simply supported plates is obtained using Navier solution technique. A power-law distribution and a half cosine variation are used to model the variation of materials properties and electric/magnetic potentials, respectively. The analytical solutions are verified with well-known solutions in the literature. A parametric study was conducted to show the effect of nonlocal parameter, power-law index, predefined electric and magnetic fields, axial compressive and tensile forces, the aspect ratio of plates, and volume ratio of functionally graded and piezomagnetic layers on mechanical behaviors of nanoplates. Obtained numerical results can be used as benchmark values for validation of correctness of diverse analytical and numerical methods applied for design and analysis of composite nanoelectromechanical systems.

Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method.

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

Higher-Order Stability Analysis of Imperfect Laminated Piezo-Composite Plates on Elastic Foundations Under Electro-Thermo-Mechanical Loads

This article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner core. The structure is subjected to electro-thermo-mechanical loads simultaneously. One side of plate is rested on Pasternak type elastic foundation. The equilibrium equations of plate are derived based on the higher-order shear deformation theory of Reddy taking into account initial geometrical imperfection, nonlinear strain-displacement relations of von-Karman, temperature dependent properties, and different types of boundary conditions. Some numerical examples are presented to verify the accuracy of the proposed formulation. The effects of various parameters such as voltage on actuators, elastic foundation, imperfection, and pre-load condition on the buckling and postbuckling behaviors are studied. As an important finding of current research, there may be exists bifurcation point for imperfect plates by applying voltage on actuators.