Dynamic Response Of Sandwich Plates Research Articles

Static and dynamic response of pyramidal lattice sandwich plate with composite face sheets reinforced by graphene platelets

For the pursuit of lightweight structures with excellent mechanical performance, sandwich structures with lightweight cores and strengthened face sheets have become popular in the advanced engineering fields in recent years. In this paper, the nonlinear static and dynamic responses of the sandwich plate constructed with the aluminum pyramidal lattice core and functionally graded graphene platelets reinforced composite (FG-GPLRC) face layers are analyzed. The partial differential equations of the pyramidal lattice sandwich plate considering the geometric nonlinearity are achieved based on the Reddy’s third order shear deformation theory (TSDT), which are solved by the combination of finite element model, Raphson’s method and Newmark numerical integration method. Four different types of the impact loads including the step loading, triangular loading, half-sine loading and exponential loading with the same peak value and duration time are investigated. The influences of the thickness-to-truss radium ratio and the angle of the truss core, as well as the weight fraction and distribution patterns of graphene platelets (GPLs) over the face sheets under different impact loads and different boundary conditions are analyzed. According to the numerical results, it is concluded that the sandwich plate with higher weight fraction of GPLs, lower thickness-to-truss radium ratio, and higher angle of the truss core can exhibit better performance in both static and dynamic loading conditions. The FG-X distribution of GPLs presents the best dynamic performance as compared to the other GPL distributions. The combination of lightweight truss core with the advanced GPLRC face sheets is instructive for potential applications and further research.

Nonlinear low-velocity impact analysis of sandwich plates with titanium face sheets and porous aluminum core reinforced by GPLs

This study examines the nonlinear dynamic response of sandwich plates under low-velocity impacts (LVIs), which consist of a porous aluminum foam core with functionally graded (FG) graphene platelets (GPLs) reinforcement and two titanium alloy face sheets. The finite element method is employed to perform the numerical simulations and the Hertz contact theory is used to model the impact behavior. The generic Halpin-Tsai model, which incorporates the porosity effect, is adopted to estimate the mechanical properties of core made of the FG-GPLRC, based on the experimental data of the closed-cell aluminum alloy foam. The simulation results reveal that the FG-X configuration has the highest impact resistance, and that the addition of GPLs improves the impact performance. Moreover, a thicker core can reduce both the first contact time and the vibration period of plates, while a looser boundary condition can prolong the vibration time after the first impact. Additionally, a higher impactor velocity, mass and radius lead to a higher deflection and contact force. The oblique impact decreases the impact energy. This work provides a lighter and stiffer design for structure engineers when components suffer low-velocity impact.

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

This study examines the nonlinear dynamic response of sandwich plates placed on the Kerr elastic substrate under blast loading. The plate is composed of an auxetic honeycomb core and functionally graded material (FGM) coating layers. The volume fraction of FGM is determined following the power-law model (P-FGM). The equations of motion of the plate are formulated by using the first-order shear deformation theory (FSDT) in conjunction with the use of the Airy stress function. The Runge-Kutta scheme, with the assistance of the Galerkin technique, is utilized in the present study to obtain numerical results for the nonlinear dynamic response of the plate. After verifying the proposed solution, the influences of material characteristics, blast loading, elastic substrate, and geometry parameters on the free vibration and nonlinear dynamic behavior of the plate are investigated comprehensively. The results show that negative Poisson’s ratio has a significant effect on the linear and nonlinear vibration characteristics of the auxetic-FGM sandwich plate.

Free vibration and nonlinear dynamic response of sandwich plates with auxetic honeycomb core and piezoelectric face sheets

This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation.

A novel Gaussian higher-order plate theory for dynamic response of porous sandwich plates with different geometries

With the wide application of lightweight structures, it is necessary to precisely and efficiently predict dynamic response of sandwich plates for the dynamic safety of sandwich structures in service life. Due to the weak normal stiffness of the core, the used higher-order shear deformation theories (HSDTs) are required to consider the transverse normal strain. To the best knowledge of authors, the most efficient and accurate higher-order theory including transverse normal strain merely contains six independent unknowns. However, the existing six-unknown higher-order theories may be incapable of accurately forecasting the dynamic response of the soft-core sandwich plates attributing to the huge mismatches of mechanical properties. Therefore, a novel Gaussian higher-order plate theory (NGHPT) with six independent variables has been developed for the free and forced vibration of sandwich plates, where the transverse shear function is defined by Gaussian function and Fourier transformation to approximately fulfill the continuity requirement of transverse shear stresses at the interfaces. Meanwhile, the isogeometric analysis (IGA) is utilized to handle complex geometries. Compared to the existing HSDTs with six unknowns, the NGHPT can more accurately predict the dynamic behaviors of sandwich plates, which is verified by several experimental tests. Furthermore, a comprehensive parametric study on various sandwich plates including square, circular, elliptical and annular shapes, has been carried out to evaluate the influence of fiber orientation, distribution of internal pores and porosity coefficient on the dynamic response, which can provide suggestions for the future designs of porous sandwich plates to meet specific dynamic requirements.

Analytical study on the dynamic response of foam-core sandwich plate under wedge impact

In this paper, the dynamic responses of sandwich plate with foam core subjected to wedge impact are theoretically investigated. An analytical model of fully clamped foam-core sandwich plate under low-velocity wedge impact is developed based on the approximate yield criteria and rigid-perfectly plastic theory. Besides, the horizontal impact experiments and numerical simulations of polyvinyl chloride (PVC) foam-core sandwich plates were conducted to verify the accuracy of analytical prediction model. Results show that the analytical prediction results of foam-core sandwich plate under wedge impact such as the permanent deformations and impact force as well as deformation distribution are consistent with the experimental and numerical results. Furthermore, the geometrical parameters such as wedge width and aspect ratio of sandwich plate as well as foam core thickness on the dynamic responses are theoretically performed. Results showed that the deformation reaches to maximum with aspect ratio of 1and the permanent deformation declines with the increase of wedge width and foam core thickness.

Transient Responses of Sandwich Plates with a Functionally Graded Porous Core: Jacobi–Ritz Method

This study examined the transient or dynamic response of sandwich plates with a functionally graded porous core under the action of time-dependent loads. The plates had two isotropic faces at the top and bottom layers, and the middle layer was made of an open-cell material with functionally graded internal pores. By using the first-order shear deformation theory, the equations of motion used to describe the dynamic behavior of the plates were applied to generate accurate results with less computational effort. To solve the equations of motion, the Ritz method based on the Jacobi polynomials for the admissible displacements, cooperating with the time integration of Newmark, was used to find out the dynamic response of the plates. The results of the numerical experiments revealed that the plates carrying a larger number of internal pores at the middle zone of the core had a great improvement in flexural stiffness, providing less deflection under dynamic loads. The observed results of the plates’ dynamic behavior related to the effects of the porosity coefficient, plate’s geometrical ratio, dynamic loading types, porous distributions of the core, etc. are shown in the form of graphs and tables, which can be used as a benchmark for future research.

Dynamic Response of Sandwich Thick Plates with FG Face Sheets and Porous Core in Thermal Environments using Nonlocal Strain Gradient Theory Approach

Based on nonlocal strain gradient theory approach, we have analyzed the nonlinear dynamic response and vibration of sandwich thick plates with functionally graded (FG) face sheets and FG porous core subjected to mechanical, thermal and blast loads on elastic foundations. Three types of porosity, including symmetric porosity distribution, non-symmetric porosity distribution, uniform porosity distribution have been considered of sandwich plate. The system of dynamic governing equations of motion is obtained by utilizing Hamilton’s principle and solved by Bubnov-Galerkin method for a case of simply supported sandwich plate. Numerical results are presented and verified with other studies. The influence of nonlocal and strain gradient parameters, materials and porosity volume fraction, geometrical characteristics and parameters of elastic foundations on fundamental frequencies and dynamic response of the sandwich plates are elucidated.

Dynamic response of sandwich plates with GLARE face-sheets and honeycomb core under metal foam projectile impact: Experimental and numerical investigations

Aluminum honeycomb sandwich plate with fiber metal laminate (FML) as panel can combine the advantages of FML face-sheet and honeycomb core, and has advantages of high specific strength / specific stiffness, lightweight and good energy absorption performance. In this paper, the dynamic response of aluminum honeycomb sandwich plates with Glass Laminate Aluminum Reinforced Epoxy (GLARE) face-sheets under metal foam projectile impact is studied. The single foam projectile impact test is conducted to study the dynamic response of honeycomb sandwich plates with GLARE face-sheets. The debonding between metal and composite layers of the front face-sheet, the fiber fracture, buckling, shear and fracture of core are observed. Also, the multiple foam projectile impact test is carried out to study the impact resistance of the sandwich plate. The numerical calculation is conducted, numerical results are compared with experimental ones. Influences of the impulse, face-sheet thickness, fiber laying angle, honeycomb height, wall thickness of core and cell length of honeycomb on impact resistance and energy absorption of sandwich plates are discussed. It is found that the improvement range of the maximum deflection of back face-sheet gradually decreases with the increase of face-sheet thickness. In addition, by increasing the impulse, decreasing the face-sheet thickness and decreasing the core stiffness, the energy absorption of sandwich plates under metal foam projectile impact can be enhanced. These findings can be used to guide the optimal design of FML sandwich structures under metal foam projectile impact.

Dynamic response of gradient double-corrugated sandwich plate subjected to underwater blast loads

A multilayer gradient double-corrugated sandwich plate was designed, and the finite element method was employed to investigate numerically the dynamic responses of the sandwich plate subjected to underwater blast loads. ALE modeling method was adopted to simulate the fluid-structure interaction between the water and sandwich plate. TNT explosive was modeled by the JWL model, and the 304 stainless steel used for the double-corrugated sandwich plate was modeled by Johnson-Cook constitutive model. The peak deflection of the back face sheet, the support reaction at the edge of the sandwich plate, and the energy absorption of the structure were discussed to assess the underwater blast resistance of the double-corrugated sandwich structure. The results show that the configuration P2 with the increasing core relative density has a better blast resistance ability and the weakest upper core layer of the configuration P2 has the greater contribution to reducing the impulse transmission to the sandwich structure.

Impact of aperture on dynamic response of sandwich plates with aluminium face-sheets and PMI core based on an alternative finite element formulation and experiments

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear modulus at the adjacent layers. Thereby, such issue is less studied by using the efficient models and experimental testing, so an alternative sinusoidal-type finite element formulation is to be proposed to precisely predict dynamic response of the form-core sandwich structures with apertures. The proposed finite element formulation can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates. In order to appraise strictly capability of the proposed model, experimental tests on natural frequencies of three groups of specimens with different apertures have been carried out. Moreover, four specimens in each group are tested to reduce the testing errors, which is less reported in the published literature. In addition, three-dimensional Finite Element Method (3-D FEM) is also selected to account for the good performance of the present model. Finally, the impact of aperture diameter on the natural frequencies of the sandwich structures is both experimentally and numerically investigated, which can serve as a reference for other researchers.

A numerical evaluation on nonlinear dynamic response of sandwich plates with partially rectangular skin/core debonding

Abstract As one of the most dangerous defects in the sandwich panel, debonding could significantly degrade load carrying capacity and affect dynamic behaviour. The present work dealt with debonding detection of the rectangular clamped hybrid sandwich plate by using ABAQUS software. The influence of various damage ratios on the linear and nonlinear dynamic responses has been studied. The finite element model was initially validated by comparing the modal response with the experimental test. Rectangular debonding was detected by comparing dynamic responses of free and forced vibrations between intact and debonded models. A wide range of driving frequency excitation corresponding to transient and harmonic concentrated loads was implemented to highlight nonlinear behaviour in the intermittent contact in the debonded models. The results showed that debonding existence contributed to the natural frequency reduction and modes shape change. The numerical results revealed that debonding affected both the steady-state and impulse responses of the debonded models. Using the obtained responses, it was detected that the contact in the debonded region altered the dynamic global response of the debonded models. The finding provided the potential debonding diagnostic in ship structure using vibration-based structural health monitoring.

Structural impact damage of metal honeycomb sandwich plates

Dynamic response of sandwich plates with a metal honeycomb core under low-velocity impact has been investigated. Experiments of the fully clamped sandwich plates subjected to low-velocity impact of the drop-hammer with a hemispherical nose have been conducted and plastic failure modes have been measured. Structural damage mechanism of sandwich plates has been identified and explored. It is found that finite element simulations of these experiments are in good agreement with the experimental measurements. Analytical solutions for permanent deflections and peak impact forces are derived and capture the experimental results with reasonable accuracy. It is shown that the impact positions have important influence on the dynamic response of sandwich plates subjected to low-velocity impact. The impact resistance of sandwich plate decreases from the central position to the non-central positions.

Nonlinear dynamic response of sandwich plates with functionally graded auxetic 3D lattice core

This paper presents full-scale modeling and nonlinear dynamic analysis of sandwich plates with auxetic 3D lattice core, which is further designed to possess three functionally graded (FG) configurations through the plate thickness direction for the first time. The effective Poisson’s ratio (EPR) and fundamental frequencies of auxetic 3D lattice metamaterials are analyzed and verified by static and vibration tests using specimens fabricated by 3D printing. Considering the large deflection nonlinearity of sandwich plates and the accompanying changes in effective properties of lattice microstructures, full-scale FE modeling and nonlinear dynamic thermal–mechanical analysis are performed, with material properties assumed to be temperature dependent. Numerical results revealed that the auxetic core can significantly reduce the dynamic deflections, in comparison with its counterpart with positive EPR. Furthermore, FG configurations have distinct effects on the natural frequencies and dynamic deflection–time curves of sandwich plates, along with EPR–deflection curves in the large deflection region.

On dynamic response of rectangular sandwich plates with fibre-metal laminate face-sheets under blast loading

This paper focuses on the analytical and numerical analyses to predict the dynamic response of fully clamped rectangular sandwich plates with fibre-metal laminate face-sheets and metal foam cores under blast loading. Based on the rigid-plastic material approximation with modifications, simple models are developed for the dynamic response of sandwich plates with fibre-metal laminate face-sheets. The so-called ‘bounds’ and the membrane mode solution for dynamic response of rectangular sandwich plates are obtained. The effects of the composite volume fraction, the ratio of metal layer strength to composite layer strength, relative density and relative strength on the dynamic response are discussed. The finite element calculation is carried out to study the dynamic response of the sandwich plates under blast loading. Good agreement is achieved between the analytical solutions and numerical results. This work provides the efficient method that reasonably captures dynamic response of the rectangular sandwich plates subjected to the blast loading.

New Higher-Order Models for Sandwich Plates with a Flexible Core and their Accuracy Assessment

Two higher-order analytical models based on a new higher-order theory for sandwich plates with flexible cores are developed considering the effect of the core material density and skin-to-core-stiffness-ratio (SCSR). The main difference between the two models is the role of the flexible core in the dynamic response of sandwich plates with cores of different stiffnesses. Firstly, the governing equations of a simply supported sandwich plate with a flexible core are derived based on the two models, and the analytical solutions are determined by using Navier’s approach. Then, the free vibration, static, dynamic bending and stress field characteristics of the sandwich plates with different SCSRs are investigated. The results obtained by the proposed method are compared with other published results. In particular, an accuracy assessment of the present dynamic models is conducted for different SCSRs. Finally, conclusions on the applicability of the proposed method and other theories on sandwich plates with different SCSRs are drawn.

Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory

This paper deals with the dynamic response of sandwich plates subjected to blast load. The sandwich plate is composed of auxetic honeycombs core layer with negative Poisson's ratio integrated with nanocomposite at the top and bottom surfaces. The nanocomposite layers are reinforced by carbon nanotubes (CNTs) where the effective material properties are calculated by Mori-Tanaka approach considering agglomeration effects. Due to the existence of CNTs, the structure is subjected to magnetic field. Based on the Kelvin-Voigt theory, the viscoelastic properties of the structure are considered. The viscoelastic medium is simulated by orthotropic visco-Pasternak model. Utilizing sinusoidal shear deformation theory (SSDT), the motion equations are derived based on Hamilton's principle. Differential cubature method (DCM) in conjunction with Newmark method is used for obtaining the dynamic deflection of the sandwich structure for different boundary conditions. The effects of various parameters such as structural damping, viscoelastic medium constants, geometric parameters of plates, volume fraction and agglomeration of CNTs, duration of blast pulse, geometrical parameters of auxetic honeycombs core and magnetic field on the dynamic deflection of the sandwich structure are investigated. The results reveal that by reinforcing the structure with CNTs, the dynamic deflection induced by blast load decreases about 59%. In addition, with increasing the geometrical parameters of auxetic honeycombs core, the dynamic deflection will be enhanced.

A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal environment

The current work suggests a mathematical model for the dynamic response of sandwich plates subjected to a blast load using a numerical method. The sandwich structure is made from an auxetic honeycomb core layer integrated by multiphase nanocomposite facesheets. The facesheets are composed of polymer–carbon nanotube (CNT)–fiber where the equivalent material properties of the multiphase nanocomposite layers are obtained using fiber micromechanics and Halpin–Tsai equations in hierarchy. The top and bottom layers are subjected to magnetic field and the material properties of them are assumed temperature and moisture dependent. The Kelvin–Voigt model is employed to consider the viscoelastic properties of the structure. The sandwich structure is rested on a viscoelastic foundation which is modeled by orthotropic visco-Pasternak medium. Based on refined zigzag theory (RZT), energy method and Hamilton’s principle, the motion equations are derived. A new numerical method, namely differential cubature method (DCM) in conjunction with Newmark method is utilized for obtaining the dynamic deflection of the structure for different boundary conditions. The effects of various parameters such as blast load, viscoelastic foundation, structural damping, magnetic field, volume fraction of CNTs, temperature and moisture changes, geometrical parameters of honeycomb layer and sandwich plate are considered on the dynamic deflection of the structure. The results show that the magnetic field to the facesheets can be considered as effective parameters to control the dynamic deflection. In addition, hygrothermal condition leads to increase of 24% in the dynamic displacement of system.

Parametric study of dynamic response of sandwich plate under moving loads

Constrained layer damper is widely used in engineering applications to suppress the severe vibration of structural systems, especially for the cases with moving loads, such as sandwich beam or sandwich plate. The response analysis and parametric analysis of these sandwich structures under moving loads have not still understood comprehensively. To do this, a hybrid approach based on extended Rayleigh-Ritz solution together with penalty method and differential quadrature method is presented to predict the dynamic responses of sandwich plate with isotropic face plate and a viscoelastic core subjected to moving loads. Both the energy terms related to the sandwich plate and the energy terms introduced by boundary conditions are derived based on the first order shear deformation theory (FSDT) and expressed using the Rayleigh-Ritz solutions, and then the governing equation of motion of sandwich plate is obtained through Lagrange equation, which can model a sandwich plate with various boundary conditions. Different with classical Rayleigh-Ritz solutions, the admissible functions adopted here is a set of combination of simple polynomials and trigonometric functions, which just satisfy a totally unconstrained boundary condition, and penalty method is applied to handle constraints. Then the variations of the natural frequency, associated modal loss factor and vibration response with the parameters (such as thicknesses of constrained layer and damping layer, elastic modulus of constrained layer material, and shear modulus and loss factor of damping layer material) of sandwich plate are studied. Moreover, the variations of maximum dynamic deflections with different boundary conditions as well as moving speeds are investigated.

Damage behavior of honeycomb sandwich structure under low-energy impact

Honeycomb sandwich structure is widely used in aircrafts and ships to absorb impact energy. Damage caused by low-energy impact is difficult to investigate, but will significantly reduce the strength of the sandwich structure. This paper presented a systematical experimental study on the damage behavior of honeycomb sandwich structure under different configurations. Drop weight tests were carried out to investigate the effect of impact energy, core material and face plate structure on the dynamic response of sandwich plate. Delamination regions were obtained through ultrasonic scanning. Conclusions were made that the damage behavior of the face plate was similar with composite laminates while the energy absorption capacity was related to the parameters of the honeycomb core and the mismatch angle of the face plate.