Rectangular Sandwich Plates Research Articles

Cylindrical bending of an elastic rectangular sandwich plate on a deformable foundation

Cylindrical bending of an elastic rectangular sandwich plate having a rigid filler and resting on an elastic foundation is considered. To describe the kinematics of the plate, asymmetric across its thickness, the hypotheses of broken normal are assumed. The reaction of the foundation is described by the Winkler model. A system of equilibrium equations is derived, and its exact solution is obtained in terms of displacements. A numerical analysis of the solution is presented.

THE EFFECT OF TRANSVERSE SHEAR AND NORMAL DEFORMATIONS ON THE THERMOMECHANICAL BENDING OF FUNCTIONALLY GRADED SANDWICH PLATES

A thermomechanical bending analysis for a simply supported, rectangular, functionally graded material sandwich plate subjected to a transverse mechanical load and a through-the-thickness thermal load is presented using the refined sinusoidal shear deformation plate theory. The present shear deformation theory includes the effect of both shear and normal deformations and it is simplified by enforcing traction-free boundary conditions at the plate faces. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The equilibrium equations of different sandwich plates are given based on various plate theories. A number of examples are solved to illustrate the numerical results concern thermo-mechanical bending response of functionally graded rectangular sandwich plates. The influences played by transversal shear and normal deformations, plate aspect ratio, side-to-thickness ratio, volume fraction distributions, and thermal and mechanical loads are investigated.

Free Vibration Analysis of Sandwich Plates with a Uniformly Distributed Attached Mass, Flexible Core, and Different Boundary Conditions

The free vibration analysis of rectangular sandwich plates with a flexible core both with and without a uniformly distributed attached mass on the top facesheet is carried out using the finite element method (FEM) through ANSYS parametric design language, which is validated by several literatures through some numerical examples. The model uses the 8-node shell 99 element to model the composite laminates of the top and bottom facesheets of the sandwich plate and 20-node high-order solid 95 element in order to model the flexible PVC core. The validated finite element model is then used to study the parametric effects of geometry such as aspect ratio, length-to-thickness ratio, core thickness-to-plate thickness ratio, the size and the stiffness of the attached mass on the natural frequencies of the sandwich plate as well as the normal and shear stresses. The use of FEM also allows studying the effect of different boundary conditions for both the top and the bottom facesheets of sandwich plates with or without distributed attached mass. Numerical results that hitherto not reported in the literature have been presented in this article. The results presented in this investigation could be useful to acquire a better insight into the behavior of sandwich laminates carrying attached mass for engineering designers of sandwich structures. The results are presented and compared with the latest Numerical results found in literature.

스펙트럴유한요소법을 적용한 점탄성층 샌드위치평판의 진동해석

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

Free vibration and forced harmonic response of an electrorheological fluid-filled sandwichplate

A dynamic model for the electric field-dependent steady-state vibrational responseof a rectangular sandwich plate with a tunable electrorheological fluid (ERF)interlayer, subjected to a general harmonic transverse excitation, is developed.Hamilton’s principle and the classical thin plate theory are applied to derivea set of fully coupled dynamic equations of motion along with the associatedgeneral boundary conditions. Assuming simply-supported edge conditions, thedisplacement components of the ERF-based sandwich plate are postulated by meansof generalized double Fourier series with frequency-dependent coefficients. Thenatural frequencies and modal loss factors are subsequently determined by solving acomplex eigenvalue problem. Analytical solutions are also obtained for the forcedvibration characteristics of the adaptive structure under different external transverseexcitations of varying frequency (0–300 Hz) and applied electric field strength (0–3.5 kV mm−1). Primary attention is focused on the effects of electric field magnitude, geometric aspectratio, loading type, and ER core layer thickness on the dynamic characteristics of thesandwich plate. In addition, an effort is made to find the optimal electric field which yieldsminimized vibration amplitude for each excitation frequency. Limiting cases are consideredand good agreements with the numerical solutions available in the literature areobtained.

Three-Dimensional Elasticity Solution for Sandwich Plates With Orthotropic Phases: The Positive Discriminant Case

A three-dimensional elasticity solution for rectangular sandwich plates exists only under restrictive assumptions on the orthotropic material constants of the constitutive phases (i.e., face sheets and core). In particular, only for negative or zero discriminant of the cubic characteristic equation, which is formed from these constants (case of three real roots). The purpose of the present paper is to present the corresponding solution for the more challenging case of positive discriminant, in which two of the roots are complex conjugates.

Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

This work presents a multiscale model of viscoelastic constrained layer damping treatments for vibrating plates/beams. The approach integrates a finite element (FE) model of macroscale vibrations and a micromechanical model to include effects of microscale structure and properties. The FE model captures the shear deformation of the viscoelastic core, rotary inertial effects of all layers, and viscoelastic boundaries of the plate. Comparison with analytical and FE results validates the proposed FE model. A self-consistent (SC) model makes the micro to macro scale transition to approximate the effective behavior a heterogeneous core. Modal damping resulting from the presence of voids and negative stiffness regions in the core material is modeled. Results show that negative stiffness regions in the viscoelastic core material, even at low volume fractions, yield superior macroscopic damping behavior. The coupled SC and FE models provide a powerful multiscale predictive design tool for sandwich beams and plates.

Three-dimensional vibration analysis of functionally graded material sandwich plates

Free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three-dimensional linear theory of elasticity. Two common types of FGM sandwich plates, namely, the sandwich with FGM facesheet and homogeneous core and the sandwich with homogeneous facesheet and FGM core, are considered. The three displacements of the plates are expanded by a series of Chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions. The natural frequencies are obtained by Ritz method. Rapid convergence is observed in this study. The natural frequencies of simply supported power-law FGM sandwich plates are compared with results from different two-dimensional plate theories. Parametric study is performed for varying volume fraction, layer thickness ratios, thickness–length ratios and aspect ratios of the sandwich plates.

Electro-elastic analysis of piezoelectric laminated plates

Based on the Kirchhoff hypothesis of normal-remain-normal, the present work analyses piezoelectric laminated plates, wherein poled piezoelectric laminae are transversely isotropic and function as actuators. A quadric electric field is induced inside a piezoelectric lamina under a given applied voltage and mechanical bending. The governing equations for the piezoelectric laminated plate derived from the principle of virtual work in terms of the electric enthalpy have the same forms as those for a conventional composite laminated plate. We use rectangular sandwich plates of Al/PZT/Al and PZT/Al/PZT with four simply supported edges to demonstrate the prediction of the maximum bending stress in the PZT layer. The analytic solutions are verified by three-dimensional finite element analysis.

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated

Finite element dynamic analysis of orthotropic sandwich plates with an electrorheological fluid core layer

The finite element dynamic analysis of an orthotropic rectangular sandwich plate with orthotropic base plate and constraining layer and an electrorheological (ER) fluid core is analyzed in the present paper. The orthotropic rectangular plate is covered an ER fluid core and a constraining layer to improve the vibrational behavior of the system. The finite element method and Hamilton’s principle are employed to derive the finite element equations of motion for the orthotropic sandwich plate. The effects of the natural frequencies and loss factors on the dynamic behavior of the orthotropic sandwich plate are studied. The rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. The ER fluid core is found to have a significant effect on the vibrational behaviors of the orthotropic sandwich plate. The modal dampings and the natural frequencies for the orthotropic sandwich plate are calculated for various electric fields. When an electric field is applied, the damping of the system is more effective. The effects of the thickness ratio of the base plate, ER fluid core, and the constraining layer on the natural frequencies and modal loss factors are also discussed.

Thermal Buckling of Composite Sandwich Plates

By considering that the total transverse displacement of a sandwich plate is the sum of the displacement due to bending of the plate and that due to shear deformation of the core, a 36-degree-of-freedom, high precision, higher-order triangular plate element was developed for the thermal buckling analysis of a rectangular composite sandwich plate. Numerical results show that the buckling mode that a sandwich plate will buckle into is dependent on the fiber orientation in the faces and the aspect ratio of the plate. For the square sandwich plate with angle-ply laminated faces, the highest critical buckling temperature is obtained with fibers orientated at 45°. For the rectangular [(±θ)2/core] s sandwich plate with an aspect ratio greater than 2, orientating the fibers in the faces to an angle around 63° will give the highest critical buckling temperature.

Edge effects in a sandwich plate: a plane problem

Edge effects in a rectangular sandwich plate with isotropic components are studied. The mathematical model is represented by the homogeneous equations of linear elasticity, which is indicative of an approximate approach in edge-effect theory. The initial equations are reduced to inhomogeneous ones and an exact problem is formulated. Approximate solutions are found by the mesh method. Discrete problems are based on the concept of base scheme. The mesh equations are written in an explicit form and then solved using a computation optimization procedure. As an example, edge-effect zones in a real composite are analyzed.

Thermal Postbuckling Behavior of Composite Sandwich Plates

By considering the total transverse displacement of a sandwich plate as the sum of the displacement due to bending of the plate and that due to shear deformation of the core, a 72 degrees of freedom high precision high order triangular-plate element is developed for the thermal postbuckling analysis of rectangular composite sandwich plates. Due to an uneven thermal expansion coefficient in the two local material directions, the buckling mode of the plate can be changed from one mode to another as the fiber orientation or aspect ratio of the plate is varied. By examining the local minimum of total potential energy of each mode, a clear picture of buckle pattern change is presented. Numerical results show that for a sandwich plate with cross-ply laminated faces, buckle pattern change may occur when the plate has a long narrow shape. However, for sandwich plates with angle-ply laminated faces, the buckling mode is dependent on the fiber orientation and aspect ratio of the plate. The effect of temperature gradient on the postbuckling behavior of the sandwich plate is limited except for angle-ply laminated sandwich plates with fiber angle greater than 70° or less than 20°.

Two Benchmarks to Assess Two-Dimensional Theories of Sandwich, Composite Plates

Two-dimensional theories and e nite elements are assessed to analyze displacement and stress e elds in sandwich, composites plates. Two benchmarks are used to conduct the assessment. The e rst benchmark is a sandwich plate loaded by harmonic distribution of transverse pressure for which a three-dimensional closed-form solution exists in the literature. The second benchmark is a rectangular sandwich plate loaded by a transverse pressure located at the center. More than 20 plate theories and e nite elements were implemented in a unie ed formulation recently proposed by the authors. Classical theories based on displacement assumptions are compared to advanced mixed modelsformulatedonthebasisofReissner’ smixedvariationaltheorem.Bothequivalentsingle-layermodelsaswell as layerwise models are considered. Analytical closed-form solutions and e nite elements are given. The considered benchmarks highlight both the performance and limitations of the considered two-dimensional theories. The convenience of layerwisedescription and advanced mixed theorieshas been demonstrated. Thesecond benchmark especially proved the need for layerwise models to capture the local effects.

FORCED AND FREE VIBRATIONS OF RECTANGULAR SANDWICH PLATES WITH PARAMETRIC STIFFNESS MODULATION

An active control of the resonant vibrations of a rectangular sandwich plate performed by the parametric stiffness modulation is analyzed. The controlled vibrations are those of the dominantly flexural type excited by the transverse force acting at the first resonant frequency of dominantly flexural vibrations. The stiffness modulation is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. The method of direct partition of motions is used that predicts an existence of the modal interaction between these two modes of vibrations due to the parametric stiffness modulation. It is shown that such a parametric control can provide a significant shift of the first eigenfrequency of a controlled plate (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled plate. Heavy fluid loading conditions are accounted for as well as the energy dissipation in the material of a plate. It is demonstrated that although heavy fluid loading reduces resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases. Dynamics of an elementary two-degree-of-freedom model mechanical system is considered to illustrate the mechanism of modal interaction, which is involved in the suggested way of an active control of vibrations of sandwich plates.

Free vibration of sandwich plates with laminated faces

AbstractDescription is given of the development of a spline finite strip method for predicting the natural frequencies and modes of conventional rectangular sandwich plates. The faceplates are treated as being classically thin and may be of composite laminated construction. The core is modelled as a three‐dimensional body. Finite strip stiffness and mass properties are based on a displacement field which represents eight fundamental through‐thickness displacements as a series of products of longitudinal B‐spline functions and crosswise Lagrangian or Hermitian polynominal shape functions. The solution procedure utilizes the efficient superstrip concept in conjunction with the extended Sturm sequence‐bisection approach. A variety of applications of the developed analysis capability is described which demonstrates the nature of the convergence of the finite strip predictions of natural frequencies and the close comparison of these predictions with available results in the literature, and also the use of the capability in parametric studies. Copyright © 2002 John Wiley & Sons, Ltd.

Overall and local buckling of sandwich plates with laminated faceplates, Part I: Analysis

After discussion of related past work, a description is given of a B-spline finite strip method (FSM) for predicting the buckling stresses of rectangular sandwich plates. The core is represented as a three-dimensional solid in which the in-plane displacements vary quadratically through the thickness whilst the out-of-plane displacement varies linearly. The faceplates may in general be composite laminates which are represented, in turn, as either shear-deformable plates or classically-thin plates. The displacement field of a finite strip requires the representation of 12 (for shear-deformable faceplates) or eight (for thin faceplates) fundamental quantities over the strip plan area, with each quantity expressed as a summation of a series of products of longitudinal B-spline functions and crosswise shape functions. Full details are given of the development of elastic stiffness and geometric stiffness matrices. The nature of the solution of the buckling problem is described and this incorporates multi-level sub-structuring, through the use of superstrips. This allows the efficient prediction of buckling stresses for both overall modes and highly-localised, wrinkling-type modes, but description of applications of the developed capability is deferred to the companion Part II paper.

Overall and local buckling of sandwich plates with laminated faceplates, part II: Applications

In the companion Part I paper a description has been given of the development of a B-spline finite strip method for predicting the buckling stresses of rectangular sandwich plates which may have fibre-reinforced composite laminated faceplates. Such faceplates may be modelled in the context of classical plate theory or of first-order shear deformation plate theory. Here the use of the developed analysis capability in solving specific buckling problems is described. The convergence characteristics of the finite strip method are demonstrated, with respect to both the number of finite strips and the number of spline sections used. A wide range of applications is considered and this range embraces highly localised buckling, of the wrinkling type, as well as overall buckling.

NATURAL FREQUENCY FOR RECTANGULAR ORTHOTROPIC CORRUGATED-CORE SANDWICH PLATES WITH ALL EDGES SIMPLY-SUPPORTED

A simple approach to reduce the governing equations for orthotropic corrugated-core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.