Analysis Of Composite Sandwich Plates Research Articles

Nonlinear 2D-DQ volume-preservative global–local dynamic analysis of composite sandwich plates with soft hyperelastic cores and viscoelastic Winkler-Pasternak foundations

Nonlinear large amplitude vibration and dynamic deformations of sandwich plates with composite face sheets and hyperelastic cores that encounter large thickness changes during the vibration are investigated here for the first time. Moreover, a new global–local zigzag hyperelastic plate theory that considers the incompressibility and large transverse deformability of the core, and employs transverse normal strains whose order is higher than that of the in-plane strains is proposed. The plate is resting on a viscoelastic Winkler-Pasternak substrate, exposed to various spatial and time distributions of loads, and experiencing a diversity of edge conditions. The governing equations of motion are obtained by using Hamilton’s principle, von Kármán’s assumptions, and the series expansion of the volume-preserving strain energy density function. A 2D differential quadrature (2D-DQ) technique is employed for the spatial discretization of a structure with both constitutive and kinematic nonlinearities, for the first time. The time-dependent combination of the nonlinear coupled motion equations and boundary conditions is treated by an iterative/updating Runge-Kutta time-marching technique and the effects of the thickness and aspect ratio of the plate, viscoelastic and shear parameters of the foundation, types of the edge conditions, constitutive parameters of the composite materials, fiber orientation angle, and magnitude and distribution pattern of the loads on the resulting dynamic lateral deflections are studied. Results reveal that while the vibration frequencies and amplitudes of the face sheets are quite different, the damping is more remarkable when stiffer cores are utilized. Moreover, the effects of the higher vibration modes are more apparent in looser edge conditions, smaller fiber angles, and special excitation frequencies.

An improved asymptotic homogenization method for vibration analysis of composite sandwich plates with lattice grids

An improved asymptotic homogenization method for vibration analysis of composite sandwich plates with lattice grids

A refined first-order piecewise shear deformation model for vibration analysis of composite sandwich plates

In this paper, for reducing the number of independent generalized displacements of the traditional piecewise model to decrease the number of vibration equations, a refined piecewise shear deformation model considering the effect of rotary inertias and shear deformation for vibration analysis of laminated composite and sandwich plates is presented. Unlike the conventional piecewise model, the significant novelty of the proposed theory is that the new proposed piecewise theory reduces the number of independent generalized displacements from 9 to 8. Some relevant assumptions, dividing the transverse displacement into bending and shear parts, are introduced into the traditional piecewise model, and the displacement fields of the refined piecewise shear deformation theory are obtained. Next, the governing equations are derived by employing Hamilton’s principle and solved by the closed-form Navier method. Then, the present solutions are compared with those available in the previous literature for confirming their validity. Finally, the variations of frequencies and loss factors with system parameters are evaluated and presented graphically.

Structural analysis of composite sandwich plates with enhanced pyramid lattice core using VAM-based reduced-order equivalent model

To overcome the issues of low face sheet–core interface strength and out-of-plane bearing capacity in the traditional pyramid lattice sandwich structure, a composite sandwich plate with enhanced pyramid lattice core (CSP-EPL) is investigated. A two-dimensional reduced-order equivalent model (2D-REM) based on the variational asymptotic approach is developed to study its static and dynamic responses. The accuracy and efficiency of the proposed model are verified by comparison with three-dimensional finite element (3D-FEM) results under different boundary conditions, including global static displacement, global buckling, local field recovery, and free and forced vibration. The predicted results of 2D-REM are in good agreement with those of 3D-FEM, and the computational efficiency is improved. Finally, the influence of geometric parameters of type III reinforcements on the equivalent stiffness is thoroughly examined, which helps to further reduce the weight and improve the bearing capacity of CSP-EPL.

Free vibration and buckling analysis of composite sandwich plates in thermal environment

In this work, a first-order discrete layer model is performed to deal with the free vibration and buckling analysis of composite sandwich plates in thermal environment. Owing to considering the effect of rotary inertias and shear deformation, thin-to-moderately thick shells can be analyzed. The differential equations of motion are derived from Hamilton’s principle, and account for the nonlinear variation of the in-plane and transverse displacements through the thickness due to temperature variation. These equations are solved by means of the closed-form Navier method, and validated by comparing the numerical results obtained by the present method with the findings published in literatures. Finally, the variation tendency of critical buckling temperature with material parameters is evaluated and shown graphically.

An Investigation into the Application of Generalized Differential Quadrature Method to Bending Analysis of Composite Sandwich Plates

In this work, based on the First Order Shear Deformation Theory (FSDT), an attempt is made to explore the applicability and accuracy of the Generalized Differential Quadrature Method (GDQM) for bending analysis of composite sandwich plates under static loading. Comparative studies of the bending behavior of composite sandwich plates are made between two types of boundary conditions for different cases. The effects of fiber orientation, ratio of thickness to length of the plate, the ratio of thickness of core to thickness of the face sheet are studied on the transverse displacement and moment resultants. As shown in this study, the role of the core thickness in deformation of these plates can be reversed by the stiffness of the core in comparison with sheets. The obtained graphs give very good results due to optimum design of sandwich plates. In Comparison with existing solutions, fast convergent rates and high accuracy results can be achieved by the GDQ method.

Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response

This paper presents the free vibration analysis of composite sandwich plates and doubly curved shells with variable stiffness. The reinforcing fibers are located in the external skins of the sandwich structures according to curved paths. These curvilinear paths are described by a general expression that combines power-law, sinusoidal, exponential, Gaussian and ellipse-shaped functions. As a consequence, the reinforcing fibers are placed in these orthotropic layers in an arbitrary manner, in order to achieve the desired mechanical properties. The effect of this variable fiber orientation on the natural frequencies is investigated by means of several parametric studies. As far as the structural theory is concerned, an equivalent single layer approach based on the well-known Carrera Unified Formulation is employed. The Murakami’s function is added to the kinematic model to capture the zig-zag effect, when the soft-core effect is significant. Thus, several higher order shear deformation theories are taken into account in a unified manner. The differential geometry is employed to describe the reference surface of doubly curved shells and panels, which are characterized by variable radii of curvature. The numerical solution is obtained using the generalized differential quadrature method, due to its accuracy and stability features. The present solution is compared with the results available in the literature or obtained by finite element commercial codes.

Free vibration analysis of composite sandwich plates with different truss cores

ABSTRACTThe free vibration of composite truss core sandwich plates is investigated. The natural frequencies of the sandwich plate are calculated by using the classic laminated plate theory, the first-order shear deformation theory, Reddy's third-order shear deformation theory, and a Zig-Zag theory. The differences between the natural frequencies, obtained from the four theories, are compared. The influences of structural parameters on the natural frequencies and the ratios of natural frequency to equivalent density of the sandwich plates with pyramidal core, tetrahedral core, and 3D-Kagome core are studied with the aid of the Zig-Zag theory.

Nonlinear Vibro-Acoustic Analysis of Composite Sandwich Plates with Skin–Core Debondings

A numerical model was developed for nonlinear vibro-acoustic analysis of a skin–core debonded sandwich plate immersed in an infinite fluid and subjected to time-varying loads. The structural model of the plate was formulated using a modified variational principle in conjunction with a multilevel partitioning procedure. The nonlinear contact constraints on the detached interfaces of the plate were imposed by using the Nitsche’s method. This led to a stable contact solution that does not depend on the penalty parameter as strongly as in the traditional penalty approach. A time-domain Burton–Miller boundary integral formulation was employed to couple with the structural model of the plate to determine the acoustic field, which avoids spurious instabilities in long-time simulations. Comparisons of the present results were made with solutions obtained from finite element analyses. The results show that both the structural and acoustic responses of a sandwich plate can be significantly affected by the presence of a debonding. For a debonded sandwich plate under harmonic excitation forces, the vibration and acoustic responses of the plate consist of not only the fundamental excitation frequencies, but also subharmonic and superharmonic components and combination harmonics of the excitation frequencies. The effect of the debonding size on the nonlinear vibration and acoustic-radiation responses of sandwich plates was investigated.

Stochastic Damped Free Vibration Analysis of Composite Sandwich Plates

In this paper, stochastic damped free vibration analysis of composite sandwich plates has been carried out using a nine node Heterosis plate bending element based on a first order shear deformation theory with a-priori shear correction factors. The plate bending element contains one transverse displacement and two rotations of the normals about the plate's mid-plane. Selective reduced integration scheme is adopted to integrate terms associated with the stiffness matrix formulations. Both lumped and consistent mass matrices are considered in the analysis. The accuracy and reliability of the present finite element formulation is verified with previously published results in the literature. New results are presented which are beneficial for designers of composite structures.

Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory

We present in this paper a simple and effective formulation based on a fifth-order shear deformation theory (FiSDT) in combination with isogeometric finite element analysis (IGA) for composite sandwich plates. The FiSDT yields non-linear distribution of the transverse shear stresses through the plate thickness and ensures a prior tangential stress-free boundary condition. The IGA uses same basis functions, namely B-splines or non-uniform rational B-splines (NURBS), for preserving the precisely geometric representation and providing the numerical solution. It enables to achieve easily the smoothness with arbitrary continuity order and in the present method the C1-continuity requirement of higher order shear deformation models is fulfilled. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical examples are given to show high accuracy of the proposed method.

Vibration Analysis of Composite Sandwich Plates by the Generalized Differential Quadrature Method

a viscoelastic core is considered. The governing equations and related boundary conditions are derived in terms of sectional force and moment resultants by using the principle of virtual work for free vibrations of the plate. The eigenvalue problem defined by these equations is solved by using the generalized differential quadrature method to obtain the frequencies and loss factors. Results are compared with the ones that exist in the literature for three plate problems. Lastly, a parametric analysis is carried out for sandwich plates with carbon fiber reinforced plastic face layers and a frequency-dependent viscoelastic core. Viscoelastic behavior is modeled based on the five-parameter fractional Zener model. The master curves and material properties of four different viscoelastic polymers are obtained from the experimental data thatexist in the literature. The effects of these polymericdamping materials on the vibration and damping characteristics of the sandwich plate are thoroughly studied. The eigenproblem is also solved by using the finite element method to verify the results of the generalized differential quadrature method.

Free Vibration Analysis of Composite Sandwich Plate with Viscoelastic Core

New Reddy-type elements based on Reddy’s higher-order theory are used in the analysis of composite sandwich plates with viscoelastic core, which is achieved by considering independent transverse displacements on two faces and linear variations through depth of plate core. In addition, Young modulus, rotational inertia, and kinetic energy of core are considered and core is assumed as 3D elastic structure with the properties of an orthotropic viscoelastic material. To improve the Reddy’s higher-order theory, a rectangular element with four nodes, which each node has seven degrees of freedom, is proposed. Hamilton’s principle has been used to obtain the equations of motion. A finite element code for structural response analysis of the free vibration is developed. The obtained results are compared with existence researches. The influence of material properties, lamination schemes, and fiber angle on natural frequencies of composite plates are investigated.

Consistent higher-order free vibration analysis of composite sandwich plates

Abstract The consistent higher-order dynamic formulation for foam-type (soft) core sandwich beams was extended to the case of composite sandwich plates. Eight dynamic governing equations and the corresponding boundary conditions were derived through the application of Hamilton’s principle. The extended formulation was applied to the free vibration analysis of soft-core and honeycomb-core sandwich plates with anti-symmetric and symmetric lay-ups. The vibration results for the thin and thick composite sandwich plates obtained using the extended formulation were consistent with the predictions of the higher order mixed layerwise theory for laminated and sandwich plates. To simplify the formulation for the case of symmetric sandwich plates, the general dynamic formulation was decoupled into two systems of equations representing symmetric and anti-symmetric vibrations. The numerical study demonstrates the importance of the present formulation for the prediction of higher mode vibration response of composite sandwich plates.

Contact force history analysis of composite sandwich plates subjected to low-velocity impact

Usually the modified Hertzian contact law or experimental static indentation law has been used to analyze low-velocity impact response of composite laminates. In composite laminated plates subjected to low-velocity impact, usually indentation by impact is very small and also energy absorption by indentation is negligible, so ‘spring element method’, which proposed by author recently, can be well applied to investigate impact response. In the present study ‘lumped mass method’ also had been proposed by author to approximately calculate contact force history of composite laminates will be conceptually described as well as the spring element method. And it will be discussed that how the spring element method can be applied to composite sandwich plates. Finally numerical results easily obtained from finite element analysis based on the spring element method using general-purpose commercial FEM software is compared with experimental results. The comparison shows overall agreement.

Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory

Two new C0 assumed strain finite element formulations of Reddy's higher-order theory are used to determine the natural frequencies of isotropic, orthotropic, and layered anisotropic composite and sandwich plates. The material properties typical of glass fibre polyester resins for the skin and HEREX C70 PVC (polyvinyl chloride) foam materials for the core are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, degree of orthotropy, number of layers and lamination scheme on the natural frequencies. A consistent mass matrix is adopted in the present formulation. The results presented in this investigation could be useful for a better understanding of the behaviour of sandwich laminates under free vibration conditions and potentially beneficial for designers of sandwich structures.

Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theory

The dynamic behaviour of fibre reinforced plastic sandwich plates with PVC foam core is investigated in this paper. Recently, the authors have developed an analytical method based on Reddy's refined high-order shear deformation theory to study the dynamic behaviour of undamped fibre reinforced plastic (FRP) sandwich plates. The present paper explains how the dynamic constitutive material properties (obtained by carrying out DMTA tests) are introduced into the analytical model using the elastic–viscoelastic principle. The obtained equations of motion are used to carry out steady state analysis and to determine the natural frequencies and modal loss factors of specific composite sandwich plates.

Free vibration analysis of composite sandwich plates

AbstractThe fibre reinforced plastic (FRP) composite materials configured as sandwich panels are finding increased usage in a variety of structural applications. An important facet in correct usage is an understanding of the dynamic behaviour of such structural configurations. This paper addresses the issue of natural frequencies of sandwich plate panels. The closed-form solutions are obtained using Reddy's first- and higher-order shear deformation theories. The approaches are validated against results from a standard, commercially available finite element analysis package. The paper concludes with a detailed investigation of the influence of variation in material property parameters and plate geometry variables on the natural frequency.

Free vibration analysis of composite sandwich plates

The fibre reinforced plastic (FRP) composite materials configured as sandwich panels are finding increased usage in a variety of structural applications. An important facet in correct usage is an understanding of the dynamic behaviour of such structural configurations. This paper addresses the issue of natural frequencies of sandwich plate panels. The closed-form solutions are obtained using Reddy's first- and higher-order shear deformation theories. The approaches are validated against results from a standard, commercially available finite element analysis package. The paper concludes with a detailed investigation of the influence of variation in material property parameters and plate geometry variables on the natural frequency.

Buckling and Vibration Analysis of Composite Sandwich Plates with Elastic Rotational Edge Restraints

Thesmall-dee ectiontheorydevelopedforsimplysupportedorthotropicsandwichplatesisextendedfortheelastic buckling and free vibration analysis of anisotropic rectangular sandwich plates with edges elastically restrained againstrotation.Theplatedee ection andtransverseshearforcesarerepresentedby anindependentsetoffunctions that satisfy the essential boundary conditions for all and the natural boundary conditions for specie c cases. The Rayleigh‐Ritz method is used to solve for in-plane buckling loads and transverse natural frequencies through the solution ofaneigenvalueproblem. Thenumerical tablesincluded demonstratetheeffectsof elasticedgeconditions, aspectratio,andfacesheetplypatternonthebucklingloadsandnaturalfrequenciesofanisotropicsandwichplates.