Sandwich Plates Research Articles

Analysis of Stability and Oscillations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Function Method

In this paper, the R-function method is used for the first time to study the stability and oscillations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the outer layers of the plate are made of functionally graded materials (FGM), and the filler is isotropic, namely ceramic. The differential equations of motion were obtained using the usual first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of FG materials with even and uneven porosity distribution were obtained. The proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method was used along with the R-function method. The developed algorithms and software are tested on test examples and compared with known results obtained using other methods. A number of problems of stability and oscillations of the FG of porous sandwich plates with a complex geometric shape for various layer stacking schemes, various boundary conditions and laws of porosity distribution have been solved.

The effect of the various porous layers on thermomechanical buckling of FGM sandwich plates

This study focuses on the thermal buckling behavior of sandwich porous plates made up of metal-ceramic functionally graded material (FGM) components using a new sinusoidal high order shear theory. The sandwich plate consists of a core plate made of either pure metal or pure ceramic, with face layers composed of a functional gradient of metal and ceramic constituents. This study examined the porosity and four porosity distribution functions in plates with FGM face layers and nonlinear temperature increase and material grading index of the face layers on the thermal buckling loads of sandwich plates.

Investigation of the vibration problem of sandwich heterogeneous orthotropic plates

In this study, the solution of the free vibration problem of sandwich plates consisting of heterogeneous orthotropic layers is presented. First, the Kirchhoff-Love theory (KLT) for homogeneous plates is extended to sandwich plates composed of heterogeneous orthotropic layers. Within the framework of Donnell theory, after establishing the basic relations of multilayer plates, governing equations are derived based on Airy stress and deflection functions. The solution of the governing equations is carried out by the Galerkin method and the analytical expression is found for the linear frequency of sandwich plates consisting of heterogeneous orthotropic layers. Finally, the effects of various factors such as heterogeneity, number of layers and their arrangement on the free vibration frequency of sandwich plates are examined.

Buckling and Post-buckling of Sandwich Plate with Functionally Graded Graphene Origami Reinforced Core Layer in Hygrothermal Environment

The buckling and post-buckling of magneto-electric-elastic (MEE) sandwich plate are presented. The core layer consists of epoxy matrix reinforced with graphene origami auxetic metal-material in which the volume fraction of graphene origami is assumed to vary the thickness direction in three different distributions. For MEE face sheets, the proportions of ferroelectric and ferromagnetic components are chosen equally. The Reddy's higher order shear deformation plate theory forms the basis for establishing the governing equations. The axial compressive loading- deflection amplitude relation and the expression of critical buckling loading are obtained through the application of Galerkin method. The method's accuracy is validated by comparing its results with those published by other authors. The influences of various parameters on the buckling and post-buckling of the sandwich plate are investigated in details. 

Vibration analysis of magneto-electro-elastic sandwich plate with auxetic graphene reinforced metal matrix composite core

This research addresses analytical solutions for vibration performance of simply supported sandwich plate subjected to coupled mechanical-electric-magnetic-thermal loads. The plate is made of graphene reinforced metal matrix composite (GRMMC) core and magneto-electro-elastic (MEE) face sheets. Three graphene distribution patterns, FG-X, FG-O, and UD are considered for evaluating the reinforcement efficiency of graphene. The Reddy’s higher order shear deformation plate theory and Hamilton’s principle are employed to formulate the equations of motion of the sandwich plate. Then, using double trigonometric functions for variables and applying Bubnov–Galerkin procedure, the system of nonlinear second-order differential equations is constructed to reveal the natural frequency, frequency ratio, and dynamic response of the sandwich plate. The influences of graphene distribution patterns and volume fraction, magnetic and electric potentials, temperature change, and volume fraction of piezoelectric phase are discussed in details. This research provides basis for the design of sandwich composite structures, especially smart structures and devices.

Couple-stress thermoelasticity of three-dimensional multilayered composites

This work presents a comprehensive analysis of field solutions for three-dimensional multilayered composites within the framework of the couple-stress thermoelasticity. Using double Fourier series expansion solutions, the powerful and elegant mathematical Stroh formalism is extended to include the thermal coupling with the couple-stress elasticity theory to capture small-scale microstructural effects. The size-dependent layered approach leads to concise and general eigenrelations for each homogeneous orthotropic plate, while the unconditionally stable dual-variable technique is used to propagate the extended displacement/temperature fields and force-/tangential couple-tractions through the internal interfaces of the multilayered structures. Closed-form expressions are derived for the recursive layer-to-layer relations, as well as for the temperature, heat flux, displacement, stress and couple-stress field components, with respect to simply-supported structures subjected to combined thermal and mechanical loading. Application examples, including highly anisotropic fiber-reinforced composites, show significant deviations from the classical thermoelasticity, demonstrating the critical importance of considering the microstructural characteristics of interface-dominated materials. The results result come from a series of scenarios, covering mechanical and thermomechanical loading conditions, changes in aspect ratios and stacking sequences within multilayered systems, and the consequences of varying the number of sandwich plates.

Dynamic analysis of functional gradient porous sigmoidal sandwich plates

Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core is isotropic. For different models of porosity distribution (sigmoid uniform and nonuniform), analytical expressions were obtained to calculate the effective properties of FGM. For rectangular plates, a comparison of the obtained results with known results obtained using other approaches is shown. Calculations for plates with a complex shape are presented in the form of tables and graphs. The influence of the volume fraction of ceramics, the different types Of FGM and the coefficient of porosity on the natural frequencies of the plate is analyzed.

Nonlinear geometric fluid-structure interaction model of multilayered sandwich plates in contact with unbounded or bounded fluid flow

Based on the Kirchhoff-Love theory and von Kármán's geometric nonlinearity, the nonlinear vibration analysis of multilayered sandwich plates under ideal flow is presented. Rectangular plates are considered to be laminated of orthotropic composite layers as upper and lower face sheets as well as a central lightweight core made of functionally graded (FG), anisogrid lattice or metal foam materials. Three coupled equations of motion are reformulated into one decoupled governing equation in terms of transverse deflection (w) using the method of inverse differential operator. For the first time, an impermeability condition is developed that considers the moderately large deflection of the contact surface in order to correct the pressure distribution of fluid flow. Based on the potential flow theory, closed-form expressions of hydrodynamic pressure are obtained for different fluid boundary conditions including infinite depth of fluid, flow bounded by a rigid wall and flow between two identical elastic plates. Then, the Galerkin and multiple-scale perturbation methods are used to obtain closed-form solution of nonlinear natural frequency in terms of maximum vibration amplitude. Finally, case studies are presented to investigate the effects of geometric ratios, boundary condition, material distribution, layup, characteristics of flow and geometric nonlinearity on the response quantities. Findings indicate that the large deformation term in the developed impermeability condition has significant effect on the pressure distribution and its effect is more pronounced for thicker plates with larger mode number in the flow direction. Therefore, the novel nonlinear fluid-structure interaction model should be considered to study flow-induced dynamic behavior of sandwich plates with different boundary conditions. In addition, the snap-through behavior is seen in the nonlinear frequency-upstream speed curves and the incipient points of dynamic instability can vary remarkably with the fluid boundary conditions.

FINITE ELEMENT ANALYSIS FOR DYNAMIC RESPONSE OF VISCOELASTIC SANDWICHED STRUCTURES INTEGRATED WITH ALUMINUM SHEETS

Passive vibration attenuation of modern mechanical structures is one of the most essential technologies applied to the arsenal of modern mechanical structures. In this work, dynamics analysis is performed on viscoelastic (VE) sandwich beam and plate by using finite element method. The proposed structure is composed of a VE core and aluminum face sheets as substrate layers on both sides of the structure. Small-strain VE material is modeled based on complex constant moduli model and numerical method is used to develop the finite element (FE) shear model based on first-order shear deformation theory (FSDT) and Hamilton principle. In modal analysis, model-effective mass analysis is performed to investigate its dominant mode shape and sweet spot at resonance using C3D20 and CPS8 elements. The former is indicated as a 3-D element with 20 nodes while the latter is indicated as a 2-D plane strain element with eight nodes. In harmonic analysis, resonance frequency is obtained based on mode superposition method to evaluate the steady-state response of VE sandwich beam via maximum deformation. Thereafter, the results are compared against analytical solutions from the literature. Moreover, a parametric study shows that the natural frequency of the beam did not change with the increase in core thickness. However, normalized loss factor of VE sandwich beam is directly proportional to VE damping factor and the thickness of VE core layer. Based on frequency response function, the results of resonance frequencies for VE beam are in the range of modal natural frequency.

Analytical study on the dynamic mechanical behaviours of foam-core sandwich plate under repeated impacts

The foam-core sandwich structures are probably subjected to repeated impact loadings in engineering applications, resulting in structural plastic deformation and accumulative damage. A valuable analytical approach is needed to predict the accumulative plastic deformation of foam-core sandwich structures under repeated impacts. In this paper, an analytical model of the dynamic responses of foam-core sandwich plates under repeated impacts is proposed using the circumscribing yield locus and the inscribing yield locus based on the rigid-perfectly plastic theory. By employing the principle of energy dissipation rate balance, the analytical expressions of structure permanent deformation and peak force are obtained from the iteration of initial conditions. In addition, polyvinyl chloride (PVC) foam has steady chemical properties and corrosion resistance, which can better adapt to the practical environment and meet the needs of structural protection. To validate the proposed analytical model, the repeated impact dynamic mechanical behaviours of PVC foam-core sandwich plates were experimentally and numerically studied. Results show that theoretical results such as the permanent deformation, peak force, and deformation modes of foam-core sandwich plates under repeated impacts are in good agreement with experimental and numerical results. With the increase in impact numbers, the global bending deformation and local indentation deformation of facesheets increase, the PVC foam core layer is constantly being compressed, and the bottom facesheet plays an increasingly important part in the repeated impact energy absorption with a maximum value of 29.20 %.

Buckling Stability and Vibration Characteristics of Functionally Graded Graphene Platelet-Reinforced Composites Multi-Arc Concave Honeycomb Sandwich Panels Under Thermal Loading

The utilization of functionally graded graphene platelet-reinforced composites (FG-GPLRC) and honeycomb sandwich constructions is prevalent in the field of engineering. Therefore, it is crucial to investigate the buckling and vibration properties of these materials under heat circumstances. This paper specifically focuses on the vibration and thermal buckling characteristics of a novel multi-arc concave honeycomb sandwich plate (MACHSP) equipped with an adjustable positive-negative Poisson’s ratio. The governing equations of motion for the system are derived based on the first-order shear deformation theory in conjunction with Hamilton’s principle. The formulation of the system’s characteristic equation involves the establishment of displacement functions that satisfy distinct boundary conditions. Using computational programming, natural frequencies, mode shapes, and critical buckling temperatures of MACHSP with three different FG-GPLRC distributions under thermal influences are determined. Subsequently, these results are compared with outcomes from finite element simulations and findings from previously published literature. Additionally, the amplitude-frequency response characteristics of the structure under harmonic excitation are analyzed, followed by a discussion of the impact of structural parameters on its buckling and vibration characteristics. The results indicate that the established theoretical model for predicting the buckling and vibration characteristics of MACHSP with FG-GPLRC distribution aligns well with simulation models and prior research. In contrast to solid plates, MACHSP not only achieves a substantial reduction in weight but also demonstrates a significant increase in natural frequency. Furthermore, graphene platelets have the potential to enhance the structure’s natural frequency values and critical buckling temperatures. Lastly, various structural parameters exert a notable influence on the structure’s performance.

Hybrid Fuzzy PID Sound Radiation Control of a Functionally Graded Porous GPL-Reinforced Plate with Piezoelectric Sensor and Actuator Layers

This paper is the first attempt to investigate the sound radiation control of a functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) plate integrated with piezoelectric face sheets. A spatial state-space formulation based on the linear 3D piezoelasticity theory is utilized to derive a semi-analytic solution for the coupled vibroacoustic response of the simply-supported arbitrarily thick composite plate. A comprehensive parametric study examines the effect of GPLs’ distribution, weight fraction, and porosity parameters of the core layer on the radiated sound power. Then, the best material configuration is selected to be actively controlled. A hybrid Fuzzy Proportional-Integral-Derivative (FPID) controller, which utilizes an FPID controller integrated with a classical PID controller, is employed to mitigate sound radiation from the smart sandwich plate via the volume velocity approach. The gain parameters of the proposed controller are tuned using the Bat optimization algorithm. Finally, the performance of the active control strategy in attenuating radiated sound power is investigated through several numerical simulations. Results show the proposed control scheme's robustness and rapid disturbance rejection performance.

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

The effects of the foam and FGM distributions on thermomechanical buckling response of sandwich plates

Natural frequency analysis of sandwich plate with auxetic honeycomb core and CNTRC face sheets using analytical approach and artificial neural network

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details.

Free vibration and sound radiation of ABH-type functionally graded sandwich plates under elastic boundary restraints

Based on the first-order shear deformation theory, the free vibration and sound radiation of ABH-type functionally graded sandwich plates (ABH-type FG sandwich plate) under elastic boundary restraints are studied. The displacement field of the plate is described as an improved form of double Fourier cosine series and several closed-form auxiliary polynomial functions. The dynamic equation is solved by using the Rayleigh-Ritz method. The accuracy of the present method is validated and the effects of thickness variation coefficients and elastic boundary restraints on the vibr-acoustic characteristics are discussed. The research can provide an idea for the design of sandwich structures.

A metamaterial sandwich plate with spring-lever-mass resonators

Sandwich plates are widely used in practical engineering, including civil engineering, transportation, aerospace, and other industrial fields. However, characteristics of high specific stiffness and strength cause poor performance in the vibro-acoustic fields. Therefore, resonators are introduced into the core of sandwich plates to improve their performance on vibration isolation. This paper proposes a new metamaterial sandwich plate, multiple spring-lever-mass resonators are introduced into the sandwich plate to obtain the low-frequency band gaps. The band structure of the metamaterial sandwich plate with spring-lever-mass resonators is calculated by the finite element method with the Bloch-Floquet theorem, and the band gap of the unit cell is obtained. The transmission spectra of the proposed structure are investigated to verify the accuracy of prediction results. The results show that effective performance on low-frequency vibration isolation via the metamaterial sandwich plate with spring-lever-mass resonators can be achieved, and this study can provide valuable references for related research and potential applications on the manipulation of wave propagation.

Failure mechanism and impact resistance of a novel all-composite double-corrugated sandwich plate under low-velocity impact

A novel composite double trapezoidal corrugated sandwich plate (CDTCSP) was prepared by mold hot pressing and secondary bonding of carbon fiber reinforced polymer (CFRP) prepregs. The DIT302E drop hammer testing machine with a hammerhead of 5.5 kg was selected to realize the impact test of the new corrugated sandwich structure and the all-composite trapezoidal corrugated sandwich plate (CTCSP) with three different energies of 10 J,30 J, and 50 J by changing the height. The failure modes of the two samples were further studied by experimental investigation along with the finite element model established in Abaqus/Explicit. Based on the verified numerical model, the failure process of CDTCSP under 30 J and 50 J impact energy is analyzed. At the same time, the effects of different impact positions and layup angles on the impact resistance of CDTCSP at 10 J energy were evaluated. It can be observed that as the impact energy increases, the peak load of the composite corrugated sandwich plate decreases. Compared with the traditional ones, the impact position has no noticeable effect on the overall impact resistance of CDTCSP. Based on the analysis of CDTCSP with five different layup parameters, it is found that the matrix compression failure extends along the fiber direction, and the peak load of the sample with all the surfacing layup of ± 45° is 17% larger than that of the sample with 0°.

Vibration characteristics of h-FGS plates resting on an elastic foundation under double blast loading

The main goal of this paper is to use the higher-order isogeometric analysis (IGA) to study the vibration behaviour of sandwich plates with an auxetic honeycomb core and two different functionally graded materials (FGM) skin layers (namely h-FGS plates) resting on an elastic foundation (EF) under double blast loading. Reddy's HSDT is used due to its simplicity and efficiency. The foundation model incorporates two parameters as springer stiffness (k1) and the shear layer stiffness (k2). The governing equation is derived from Hamilton's principle. After verifying the present approach, the effect of input parameters on the vibration characteristics of h-FGS plates is carried out in detail. The obtained results are expected to be useful for calculating and designing h-FGS plates in practice.

The effect of the foam structure on the thermomechanical vibration response of smart sandwich nanoplates

This study aimed to model the thermomechanical vibration behavior of sandwich nanoplates consisting of a foam or solid core layer and smart surface layers. The sandwich plate’s mechanical behavior is analyzed using the nano-size effect, nonlocal strain gradient theory, and sinusoidal higher-order plate theory. Hamilton’s principle is employed to derive the equations of motion, which are subsequently solved using the Navier method. The impacts of temperature, foam structure, foam void ratio, smart materials, and the external electric and magnetic potentials applied to the surface layers on the thermomechanical behavior of a sandwich plate have been analyzed.

Boundary Discontinuous Fourier analysis of clamped isotropic and cross-ply laminated plates via Unified Formulation

This paper presents an analytical solution for the static analysis of plates with clamped boundary conditions prescribed at the edges. The displacement field is expressed via the Carrera Unified Formulation (CUF) where an Equivalent-Single-Layer (ESL) approach is adopted. The governing equations are obtained by employing the principle of virtual displacements (PVD) statement. The main novelty is the use of the boundary-discontinuous Fourier-based approach to provide accurate numerical solutions. From thick to thin isotropic, cross-ply laminated and sandwich plates with different side-to-thickness ratios and stacking sequences are studied. Furthermore, the out-of-plane stresses are calculated via both the constitutive relation and the stress recovery technique. The accuracy of the proposed solution is verified by comparing the numerical results obtained with those from the literature and 3D FEM solutions. The present approach seems capable of handling not just fully clamped conditions but also mixed external conditions, which may include clamped and simply-supported edges. The solution approach provided in this article is unique, hence the proposed results might be useful as a benchmark for validating new plate theories and finite elements.