Rectangular Sandwich Plates Research Articles

Dynamic response of double-layer rectangular sandwich plates with graded foam cores under blast loading

In this paper, dynamic response of a fully clamped double-layer (DL) rectangular sandwich plate with graded foam cores (GFC) under blast loading is studied theoretically and numerically. Based on the yield criterion, an analytical model for dynamic response of a DL rectangular sandwich plate with GFC is established under blast loading. With the use of the inscribing and circumscribing squares of the exact yield locus, the bound of the analytical solution of the dynamic response of a double-layer rectangular sandwich plate with GFC is obtained. By neglecting the effect of bending moments, the membrane mode solution of a DL rectangular sandwich plate with GFC in large deflection is obtained. Finite element analysis (FEA) is performed using ABAQUS/Explicit software. The effects of interlayer factor, average yield strength of graded foams, and gradient properties of graded foams on the dynamic response of DL rectangular sandwich plate with GFC are considered. The analytical predictions are in excellent accord with the numerical ones. It is demonstrated that the proposed analytical model is effective to predict the blast response of a DL rectangular sandwich plate with GFC.

Influence of Transverse Normal Strain on Buckling and Vibration of Sandwich Plates

This study presents the buckling and free vibration behavior of simply supported square and rectangular sandwich plates. A third-order shear deformation theory considering both the transverse shear and normal deformations is used. The condition of zero transverse shear stresses on the top and bottom surfaces of the plate is satisfied. Hence, the present theory does not require the shear correction factor generally associated with the first-order shear deformation theory. Governing equations and boundary conditions are obtained using the principle of minimum potential energy. The closed-form solutions of simply supported sandwich plates are obtained. The effect of the side-to-thickness ratio and plate aspect ratio on buckling and free vibration responses of simply supported square and rectangular sandwich plates is examined. Parametric effects of face sheet thickness ratios and load factor upon the critical buckling load for uniaxial and biaxial buckling analysis of square and rectangular sandwich plates for different staking sequences are studied. All numerical solutions are obtained using MATLAB® programs. The results obtained from the present theory are compared with those from classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, and the exact three-dimensional elasticity solutions as applicable.

Global buckling response of sandwich panels with additively manufactured lattice cores

This paper deals with the analytical and numerical global buckling analysis of rectangular sandwich plates utilized AlSi10 Mg in both facesheets and lattice cores. In this study, six different strut-based lattice core models are designed. Additionally, the buckling resistance of lattice panels is compared with a typical honeycomb panel. Analytical studies were carried out using Kirchoff plate theory (CLPT), first-order shear deformation theory (FSDT) coded on MATLAB and finite element (FE) analyses in Abaqus. In the theoretical approaches, the Navier solution is derived for sandwich plates with simply supported boundary conditions at all edges. In the FE analyses, validated homogenized lattice structures models were used to avoid excessive numbers of elements and to save computational time. The parametric effects of side-to-thickness ratio, and different designed core cells on global buckling responses are investigated. As a result of comparing the analytical results with the FE model, a good agreement is obtained, and it is found that analytical buckling analyses FSDT can be used within certain size limits for the global buckling analysis of lattice core sandwich structures.

Frequency Assessment of Sandwich Rectangular Plates with an Anisogrid Core and GPLRC Face Sheets

Frequency Assessment of Sandwich Rectangular Plates with an Anisogrid Core and GPLRC Face Sheets

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation.

Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh-Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed.

Symmetrical wrinkling of compressed composite SSCF facings of a rectangular sandwich plate

Results of the study of symmetrical facing wrinkling of compressed rectangular composite sandwich plates with orthotropic faces and core are presented in the paper. Two parallel edges of the plate facings are simply supported, one edge is clamped, and another edge is free (SSCF). The wrinkling problem is solved using the Ritz method in which the total energy functional of plate faces and core is obtained based on the original model, considering nonlinear variation of the transverse displacement of the core material from the value of facing’s deflection to zero. Application of the Ritz method yields formulas for the calculation of critical compressive load. The critical load is found using a minimization with respect to the parameter of the wrinkling waves evolution and the parameter characterizing the rate of fading of the transverse displacement. Based on the derived formulas, the effects of facing and core thicknesses, and modulus elasticity of core material on the critical wrinkling load are studied. The results of calculations are verified using a finite element analysis. It is shown that the value of critical load calculated based on the proposed model is more accurate compared to that calculated using the Winkler-Pasternak model, particularly for the sandwich plates with thin faces and thick core.

Nonlinear thermoelastic wave propagation in general FGM sandwich rectangular plates

The present work is dedicated to investigating the thermoelastic wave propagation behavior of sandwich rectangular plates (SRP) made of functionally graded material (FGM). The main contribution lies in the partial modification of basic theoretical expressions and solution methods to improve the accuracy of practical system models. An analytical model with three types of general configurations is established. The porosity distribution in FGM layers depends on the degree of mixture of the constituent materials, with the FGM layers without porosity taken as a reference model. The effect of porosity within FGMs is addressed through a refined analytical formulation of material properties, and the temperature-dependent material properties of FGM sandwich structures (FGMSS) maintain continuity through the thickness. This improved framework introduces a porosity function encompassing three distinct structural and geometrical functions: the core-to-thickness ratio (CTR), porosity volume fraction (PVF), and porosity distribution function (PDF). It is worth mentioning that the theoretical expressions maintain good continuity and reliability under the influence of thermal conditions and system parameters of the proposed structures. Furthermore, considering the generation of thermal strain energy (TSE) caused by thermal expansion of the structure in the normal direction, an improved analytical approach for determining TSE in rectangular plate structures is then investigated by introducing the Green's nonlinear strain (GNS). Hamilton's principle is applied to derive the wave motion equations and analytical solutions for the wave dispersion relations are derived. Furthermore, accurate numerical simulation is performed and the solution is verified with data available in published resources. In addition, we present a systematic parametric analysis to examine the effects of porosity, configuration, power-law exponent (PLE), PVF, CTR, temperature, and wave number on the thermoelastic wave propagation behavior of FGMSRP.

Flutter analysis of laminated fiber-reinforced magnetorheological elastomer sandwich plate resting on an elastic foundation using an improved first-order shear deformation theory

Magnetorheological elastomers (MREs) are polymers with viscoelastic properties that can be adjusted by manipulating the magnetic field. When MREs are combined with reinforcing fabrics, a new category of materials known as MRE composites (MRECs) can be created, which not only possess the characteristics of MREs but also enhance their rigidity. This study focuses on investigating the supersonic aeroelastic instability of a rectangular sandwich plate with a laminated MREC core layer and functionally graded materials with porosities as face layers. Additionally, the sandwich plate is supported by an elastic foundation and subjected to supersonic airflow. This investigation presents an improved first-order shear deformation theory, postulating a parabolic distribution of shear stresses. Consequently, the transverse shear stresses are rendered as zero at the surface of every individual layer; thus, the requirement for shear correction in this theory is eliminated. In addition, 8-node elements are implemented to circumvent the necessity for distinct handling of shear-locking. The aeroelastic pressure acting on the structure is considered using first-order piston theory. Micromechanical approaches, such as Halpin‐Tsai and rule of mixture approaches, are employed to determine the effective mechanical properties of the core and face layers. The dynamic equations of the structure are derived using Hamilton’s principle and the finite element method. The study also examines the impact of different magnetic fields, fiber volume fraction, elastic foundation factors, layering angles, geometry, and boundary conditions on flutter frequency.

The nonlinear instability of transverse vibration behavior of functionally graded materials sandwich rectangular plates of under a harmonic loading and subsonic flow

This work is devoted to studying the combined action of periodic in-plane load and tangential subsonic flow on the nonlinear mechanism of the out-plane deformation of the functionally graded composite plate. Three distribution functions are proposed to investigate the distribution of the transverse shear strains and stresses across the thickness of the plates. By using Hamilton’s variational principle, the equations governing the plate instability boundaries are formulated. A nonlinear differential equation describing the first mode of the plate dynamic instability behavior by employing Galerkin’s method. The method of multiple time scales is used to obtain a periodic one-mode solution, which directly leads to the solvability condition. The different resonance cases for the interaction between the frequency of out- plane deformation and the external forces are discussed to discover the extent of the sandwich functionally graded material (FGM) rectangular plate resistance in the presence of external influences. Various bifurcation diagrams for different cases of resonance are obtained versus the basic parameters. In view of this study, we could get a deeper look at the complexity of frequency components in resonance responses of the sandwich FGM rectangular plate. The results could provide some suggestions for the sandwich plate’s vibration reduction design or fault diagnosis field or design fault diagnosis.

Spectral collocation method for free vibration of sandwich plates containing a viscoelastic core

Viscoelastic constrained layer damping is a simple and efficient method for reducing noise, vibration, and fatigue in metal structures. In this work, a spectral collocation method utilizing a layer-wise plate theory was established to inspect the vibration characteristics of a sandwich plate with a viscoelastic core. The displacements of each layer satisfied the Mindlin plate theory. The core's transverse shear stress remained constant. The three layers’ transverse displacements were assumed to be identical. The displacement fields were reduced to nine variables by utilizing the interfaces’ continuity of the displacements. The equations of motion were obtained by utilizing Hamilton’s principle. The viscoelastic core’s material properties were considered as frequency-dependent. To address the complex eigenvalue problem, an iterative algorithm was used. The theoretical results were compared with published theoretical and experimental data for fully clamped rectangular sandwich plates to validate the proposed method. The modified Oberst beam method was applied by fitting the impulse response function to obtain the adhesive’s frequency-dependent storage modulus and loss factor. The natural frequencies and corresponding loss factors of three sandwich plates with different adhesives were measured by conducting impact tests. The numerical results from the present theoretical method agreed well with the measured results.

Elastic buckling of a rectangular sandwich plate with an individual functionally graded core

Elastic buckling of a rectangular sandwich plate with an individual functionally graded core

Experimental and numerical analysis of uni-axial buckling of single-phase functionally graded porous polymeric sandwich plates

The porosity gradient functionally graded material (PFGM) is one of the most popular types of FGM, in which the porosity in the material is made to change in the specified direction. This study looks into the buckling problems of rectangular sandwich plates made of single-phase porous functionally graded materials (PFGMs), commonly used in aircraft structures and biomedical applications. A compression test was performed on the 3D-printed polymeric FG specimens bonded with two thin solid face sheets on the upper and lower surfaces. The critical stress of well-designed and fabricated 3D printed FGM plate samples with various metal core types is determined using a PC installed on universal testing equipment (UTM). The effect of different essential parameters (such as porous ratio, gradient exponent, and aspect ratio) on buckling load and total deformation were explored.The finite element method (FEM) was used to run a numerical simulation on elastic buckling using ANSYS 2021 R1 software to validate the experimental results. The load-displacement relationships and deformed morphologies were investigated using experiments and numerical analysis. The topology arrangement and relative density of the polymer core were examined using the SEM micro-tomography test based on porosity distribution to check the resistance of the sandwich to buckling load. PETG/Al sandwich plates have been found to have critical buckling loads that are 2.52 % higher than PLA/Al sandwich plates, while TPU/Al sandwich plates show increased essential loads of buckling of 5.139 %. The FEM and experiment results show that the existence of porosity in the PLA core in the PFGM plate can reduce the buckling strength tremendously, about 10.52% and 6.8 %, respectively. It was evident that the numerical results show a good agreement with the experimental findings, with a maximum discrepancy of no more than 12 % occurring at the (TPU/Al) sandwich plate with a porosity of 30%.

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

Analytical solutions founded on three-dimensional theories play a crucial role in evaluating the credibility and precision of different plate theories and numerical methodologies. While Levy-type analytical solutions are widely recognized, they have been primarily confined to purely elastic plates. This study introduces a Levy-type analytical series solution for three-dimensional vibrations in a sandwich rectangular plate featuring a functionally graded material (FGM) core, along with piezoelectric material (PM) layers on the top and bottom surfaces. The behaviors of the FGM and PM layers were described using three-dimensional elasticity and piezoelasticity theories, respectively. In this study, the displacement functions and electric potential of each layer were expanded by Fourier series and polynomial auxiliary functions. An analytical series solution was then established by satisfying the governing equations of each layer, the mechanical and electric boundary conditions on the six faces of the plate, and the continuity conditions on the interfaces between the PM and FGM layers. To validate the proposed solutions, in-depth convergence studies were conducted for the vibration frequencies of the first six modes of sandwich square plates with various boundary conditions on the other pair of side faces. The well-converged results were then compared with published data based on various plate theories to verify the accuracy of these published data. Finally, accurate nondimensional frequencies were tabulated for the first six modes of sandwich rectangular plates with various aspect ratios, thickness-to-width ratios, PM-to-FGM layer thickness ratios, power law indices for the FGM layer, and six combinations of boundary conditions. These new numerical results when piezoelectric coupling is considered should be very useful to future analytical and numerical studies.

Numerical Investigations of Multilayered Sandwich Structures under Free Vibrations

Abstract: Important structural properties of composite materials, such as high strength-to-weight and high stiffness-to-weight ratios, have resulted in a great need for these materials in various engineering industries, such as Mechanical, Civil, Automobile and Aerospace Engineering. This paper presents results from numerical investigations using software based on Finite Element Method (FEM) and its comparison with other theories from the literature under free vibrations of 5 and 7 layered sandwich plates. This study utilizes the finite element method to perform modal analysis of a sandwich composite plate with a honeycomb core. In this paper, the modal responses of a flat rectangular sandwich plate with a honeycomb core using FEM software are presented. To confirm the accuracy and reliability of the current model, validation with present literature is studied. In this study, aluminum honeycomb is used as the core materials, while glass fiber reinforced composite is used for the top and bottom of the plate to examine modal responses. Free vibration responses are investigated for the various boundary situations. The modal analysis of composite sandwich constructions was investigated, and the results were verified using available literature. The sandwich structure was solved using a finite element approach, which was modeled in ABAQUS software. The results indicated that frequencies by FEM software are in good agreement with other literature results.

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.

Flutter characteristics of a rectangular sandwich plate with laminated three-phase polymer/GNP/fiber face sheets and an auxetic honeycomb core in yawed supersonic fluid flow

Flutter characteristics of a rectangular sandwich plate with laminated three-phase polymer/GNP/fiber face sheets and an auxetic honeycomb core in yawed supersonic fluid flow

Natural Frequencies of Soft-Core Composite Sandwich Plates Reinforced by FG Graphene Platelets

Superior mechanical properties such as ultrahigh stiffness and strength along with amazing physical properties have led to the use of nano graphene platelets (GPLs) as a reinforcement in polymer composite structures such as sandwich plates. In this research, free vibration analysis of rectangular sandwich plates with functionally graded (FG) GPL-reinforced face sheets and a soft core is investigated. A high-order three-layer accurate sandwich plate theory is employed to model the soft-core sandwich structure. Third order shear deformable plate theory is applied for functionally graded graphene nano-composite face sheets while second and third order polynomials are used for displacements of the soft core. In this theory, the transverse flexibility of the core as well as the continuity conditions of transverse shear stresses are assumed. Hamilton’s principle is applied to extract the motion equations and the corresponding analytical solutions are presented. The effects of materials properties and geometrical parameters on the natural frequencies of the sandwich plates are studied. A comparison of the present results in particular cases with those of published studies confirms the accuracy of the present analysis. Results show that the natural frequencies of the sandwich plates are enhanced by reinforcing the face sheets with GPLs.

On dynamic response of double-layer rectangular sandwich plates with FML face-sheets and metal foam cores under blast loading

On dynamic response of double-layer rectangular sandwich plates with FML face-sheets and metal foam cores under blast loading

Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets

In this paper, the free vibration and uniaxial, biaxial, and shear buckling analyses of a sandwich plate with an auxetic honeycomb core and two laminated three-phase polymer/GNP/fiber face sheets are investigated. The sinusoidal shear deformation theory (SSDT) is utilized to model the plate, Hamilton’s principle is hired to derive the governing equations and boundary conditions, and a numerical solution is performed via the differential quadrature method (DQM). The effects of various parameters on the critical buckling loads and the natural frequencies of such a plate are examined such as the geometrical parameters of the auxetic honeycomb core, mass fractions of the GNPs and the fibers, and total thickness of the plate. Numerical results reveal that by increasing the thickness of the auxetic honeycomb core the critical buckling loads decrease and the natural frequencies experience an initial growth followed by a small reduction. It is concluded that the inclined angle in the auxetic honeycomb core has no remarkable effect on the critical buckling load, but affects the natural frequencies in all vibrational modes.

Navier solution for static and free vibration analysis of sandwich plate with auxetic honeycomb core resting on pasternak elastic foundation

This study investigates the bending behaviour and free vibration response of a rectangular sandwich plate with auxetic honeycomb core and functionally graded material (FGM) face sheets. Governing equations are established from Hamilton’s principle in the framework of the first-order deformation theory (FSDT). The Navier solution has been utilized to determine the deflection and the natural frequency of the simply supported sandwich plate. The reliability and accuracy of the proposed model have been validated via verification studies. The numerical investigations are conducted to investigate the influence of geometric parameters of auxetic material, volume fraction index of FGM, the thickness ratio of layers, and elastic foundation stiffness on deflection and fundamental frequency of the FG-Auxetic sandwich plate.