Sandwich Annular Plate Research Articles

3-D Vibration analysis of FG-MWCNTs/Phenolic sandwich sectorial plates

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of twodimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM

ABSTRACTThe purpose of this paper is to investigate the bending, buckling, vibration analyses of microcomposite circular-annular sandwich plate with CNT reinforced composite facesheets under hydro-thermo-magneto-mechanical loadings are presented using first order shear deformation theory (FSDT) and modified strain gradient theory (MSGT) that includes three material length scale parameters. Also, an isotropic homogeneous core is considered for microcomposite circular-annular sandwich plate. The generalized rule of mixture is employed to predict mechanical, moisture and thermal properties of microcomposite sandwich plate. By using Hamilton’s principle, governing equations are solved by differential quadrature method (DQM) for a circular annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the FGM plates by modified couple stress theory (MCST). The obtained results are given to indicate the influence of the material length scale parameter, core- to-facesheet thickness ratios, magnetic effect, thermal and moisture effects on the dimensionless deflection, critical buckling load, and natural frequency of microcomposite circular sandwich plate. The results can be employed in solid-state physics, materials science, nano-electronics, and nano electro-mechanical devices such as microactuators, and microsensor.

Axisymmetric bending of circular and annular sandwich plates with nonlinear elastic core material

This paper compares the analytical model of the axisymmetric bending of a circular sandwich plate with the finite element method (FEM) based numerical model. The differential equations of the bending of circular symmetrical sandwich plates with isotropic face sheets and a nonlinear elastic core material are obtained. The perturbation method of a small parameter is used to represent the nonlinear differential equations as a sequence of linear equations specifying each other. The linear differential equations are solved by reducing them to the Bessel equation. The results of the calculations with the use of the analytical and FEM models are compared with the results obtained by other authors by the example of the following problems: (1) axisymmetric transverse bending of a circular sandwich plate; (2) axisymmetric transverse bending of an annular sandwich plate. The effect of the nonlinear elasticity of the core material on the strained state of the sandwich plate is described.

Vibration Characteristic Analysis of Polar Orthotropic Sandwich Annular Plate with Tunable MR Elastomer Treatment

Vibration analysis of polar orthotropic sandwich annular plate with magnetorheological (MR) elastomer is considered. The effects of thickness of the MR elastomer, applied magnetic fields on the sandwich system are discussed. The characteristics of the sandwich plate system can be controlled and changed by the applied magnetic fields. The core layer of MR elastomer has significant effects on the damping behavior of the sandwich plate system according to the numerical results.

Analytical and experimental free vibration analysis of multi-layer MR-fluid circular plates under varying magnetic flux

Free vibration characteristics of sandwich annular circular plates comprising magneto-rheological (MR) fluid as the core layer are evaluated analytically and experimentally. An analytical model of the sandwich annular plate was formulated using Ritz method based on the classical plate theory. The numerical analyses were performed to study the free vibration responses of the sandwich plate in terms of resonant frequencies and loss factors considering variations in the magnetic flux and boundary conditions. The experiments were conducted on a free-free sandwich circular plate comprising two PETG (Polyethylene Terephthalate Glycol) face layers constraining the MR fluid core layer. A hollow-core electromagnet was developed for inducing variable magnetic flux over the structure. The free vibration properties of the sandwich plate were measured using MEscop VES modal analyzer. The measured data were analyzed to determine natural frequencies of the MR sandwich plate under different levels of the magnetic flux, which were subsequently used to examine validity of the analytical model. Furthermore, the effects of plate parameters on the natural frequencies and damping of the structure were investigated. The results suggested that increasing the flexibility of the face layers yields more pronounced effect of magnetic flux on the structure stiffness properties.

Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation

In practical applications, sandwich plates are often connected to other members, supported by damaged clamped/simply supported boundary conditions or supported by elastic restraints. Therefore, the mentioned structures may not always be simulated by the classical boundary conditions, i.e., ideal simply supported, clamped and free edges. Also, these structures may be subjected to various loads. In this study, for the first time, a novel economical analytical solution procedure is presented for axisymmetric static analysis of sandwich annular plates, by using the layerwise and 3D elasticity theories. Based on the proposed approach, functionally graded sandwich annular plates with various elastically restrained edges under arbitrary distributed loads may be analyzed and all of the displacements and stresses components may be exactly achieved. Also, imposed loads at the boundaries may be evaluated. Transverse shear and normal stresses boundary conditions on the top and bottom of the sandwich plate and the interlaminar continuity conditions of the in-plane displacement, transverse shear and normal stresses are exactly satisfied. Accuracy and efficiency of the presented solution procedure are demonstrated by comparing the obtained results for sandwich plates with the classical edge conditions as some special cases of the elastic supports with results of the three-dimensional theory of elasticity.

Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton’s principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin’s method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer.

Thermo elasticity solution of sandwich circular plate with functionally graded core using generalized differential quadrature method

Bending analysis of sandwich circular plate with functionally grade core layer subjected to thermo-mechanical load is carried out using generalized differential quadrature (GDQ) method. The facing layers are made by metal and ceramic whereas the core layer is functionally graded materials composed of metal and ceramic material with distribution according to exponential function. Sandwich plate has various edges boundary conditions. Temperature distribution in three dimensions is obtained by solving heat conduction governing equation analytically. From combination of three dimensional governing equilibrium equations and constitutive relations, state space equations are derived. Applying GDQ method to the state space equations along the radial direction, semi-analytical solution can be obtained. After checking the convergence of the present approach, validation is carried out by comparing numerical results with the available results in open literature. Moreover, parametric study is presented to show the effects of the gradient direction, outer radius to thickness ratio, edges boundary conditions on the thermoelastic behavior of sandwich annular plates.

Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores

In the present research, free vibration of circular and annular sandwich plates with auxetic (negative Poisson’s ratio) cores and isotropic/orthotropic face sheets is investigated for different combinations of the boundary conditions. To ensure that the results are accurate and reliable, a global–local layerwise plate theory is employed instead of the traditional equivalent single-layer theories. The governing equations are derived based on Hamilton’s principle and solved using a Taylor transform whose center is located at the outer radius of the plate. Due to this hint, the resulting semi-analytical solution can be employed for both circular and annular sandwich plates. After investigation of vibration behavior of a single-layer annular auxetic plate, a comprehensive parametric study including evaluation of effects of the auxeticity for sandwich plates with isotropic and orthotropic face sheets, symmetric and asymmetric layups, different core to sheet thickness, radius to thickness, and inner to outer radius ratios, and various boundary conditions, is carried out. Results show that unlike the single-layer auxetic plates that exhibit a transition state, the auxeticity may considerably increase the natural frequencies and rigidities of the circular/annular sandwich plates, especially when the boundary conditions induce higher rigidity in the plate or when the fibers are along the radial direction. Accuracy of results of the employed layerwise theory and the proposed semi-analytical solution is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS software.

Dynamic relaxation analysis of composite sandwich annular sector plate with viscoelastic core

The three-layer annular composite sandwich sector plate is investigated numerically using the dynamic relaxation method. The upper and lower faces consist of un-symmetrical rectangular orthotropic laminates, and the core is based on viscoelastic material. The non-linear governing equations are considered using the first-order shear deformation theory and large deflection type of deformation. The constitutive relations of sandwich are presented for laminated faces, and the linear viscoelastic core is considered for the Boltzmann superposition principle. The dynamic relaxation iterative procedure in conjunction with finite-difference discretization is performed for the solution of the governing equations. Under uniform lateral pressure as well as clamped and simply supported edged constraints, the plate deformation is predicted for different times. In order to verify the dynamic relaxation algorithm, the elastic sector plate is compared with finite element solutions, and it is established that the correlations are very satisfactory. The dimensionless deflections, stress resultants, and stress couples of sandwich plates with viscoelastic core are illustrated to show the creep behavior of the plate with an increase in time.

On radially symmetric vibrations of non-uniform annular sandwich plates

Analysis and numerical results for the axisymmetric vibrations of annular sandwich plates with relatively stiff core of non-uniform thickness have been investigated using a refined theory. The face sheets are treated as membranes of constant thickness and the core is assumed to be solid as well as moderately thick of parabolically varying thickness. Due to this-type of variation in the thickness of the core, the face sheets take the shape of paraboloid of revolution and because of this, the face sheets membrane forces contribute to the bending and transverse shear stresses of the core of the plate. The equations of motion for such a plate have been derived using Hamilton’s energy principle. The frequency equations for three different combinations of boundary conditions; clamped at the inner edge and clamped or simply supported or free at the outer edge are obtained employing differential quadrature method. The lowest three roots of these frequency equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as radii ratio, taper parameter, thickness of the facings and core at the centre on the natural frequencies has been studied. Three-dimensional mode shapes for the specified plates have been illustrated. A comparison of the results with published work has been made.

Axisymmetric vibrations of composite annular sandwich plates of quadratically varying thickness by harmonic differential quadrature method

In the present paper, axisymmetric vibrations of annular sandwich plates with isotropic core and orthotropic face sheets have been studied using the harmonic differential quadrature (HDQ) method. The thickness of the core is assumed to vary quadratically in the radial direction, and the face sheets are treated as membranes of constant thickness. The effect of shear deformation and rotatory inertia in the core has been taken into account, and the mathematical analysis of the model is based upon first-order shear deformation theory. The governing differential equations of motion have been obtained using Hamilton’s energy principle. In the resulting equations, the HDQ method is employed to obtain the frequency equations for the three edge conditions, namely CC, i.e., clamped at both the inner and outer edges, CS, i.e., clamped at the inner edge and simply supported at the outer edge, and CF, i.e., clamped at the inner edge and free at the outer edge. The lowest three roots of these equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, core thickness at the center, facing thickness and radii ratio on the natural frequencies has been studied. Three-dimensional mode shapes for the specified plates have been illustrated. To check the validity of the present considerations and the technique, a frequency parameter has been compared in particular cases.

Axisymmetric dynamic instability of polar orthotropic sandwich annular plate with ER damping treatment

The axisymmetric dynamic instability of polar orthotropic sandwich annular plate combined with electrorheological (ER) fluid core layer and constraining layer are studied in this paper. And, the ER core layer and constraining layer are used to improve the stability of the annular plate system. The boundaries of instability regions for the polar orthotropic sandwich annular plate system are obtained by discrete layer annular finite element and the harmonic balance method. The rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be controlled by applying different electric field strength. Thus, the damping characteristics of the sandwich system are more effective when the electric field is applied on the sandwich structure. Additionally, variations of the instability regions for the polar orthotropic sandwich annular plate with different applying electric field strength, thickness of ER layer and some designed parameters are investigated and discussed in this study.

Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

An analysis and numerical results of radially symmetric vibrations of annular sandwich plates with core of linearly varying thickness are presented. The face sheets are treated as membranes of constant thickness, and the core is assumed to be solid as well as moderately thick. Due to linear thickness variation in the core, the face sheets take the shape of a truncated conical shell and because of this the face sheets membrane forces contribute to the bending and transverse shear of the core of the sandwich plate. Keeping this in view, the equations of motion for such a plate are developed by Hamilton’s energy principle. The frequency equations for three different combinations of boundary conditions, namely clamped at the inner edge and clamped or simply supported or free at the outer edge, are obtained by employing the differential quadrature method. The lowest three roots of these frequency equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness, and radii ratio on the natural frequencies has been analyzed. Three-dimensional mode shapes for a specified plate for all the three boundary conditions are illustrated. A comparison of results is presented.

Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory

Present paper is devoted to stress and deformation analysis of functionally graded annular sandwich plates subjected to non-uniform normal and/or shear tractions. In spite of its wide applications, analytical stress analysis of plates under shear or combinations of normal and shear tractions has not been performed so far, especially for the sandwich plates. Furthermore, it is the first time that a power solution is developed for the annular functionally graded sandwich plates. The governing equations are derived based on principle of minimum potential energy and a double superposition zigzag theory. The transverse shear stresses are determined based on the three-dimensional theory of elasticity. The resulting governing equations may cover symmetric and asymmetric layups, various boundary conditions, and arbitrary non-uniform tractions on the top and bottom face sheets. The obtained results are verified by comparing them with results of the three-dimensional theory of elasticity. While the present approach is accurate, it is computationally more economic than the three-dimensional elasticity approach. Finally, a parametric study including evaluating effects of various parameters on the stress and displacement distributions of the annular sandwich FGM plates is accomplished.

Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates

In the present research, transient and forced dynamic responses of annular sandwich plates with functionally graded face sheets or cores are investigated by an analytical zigzag-elasticity approach, for the first time. The time-dependent partial differential governing equations are obtained based on principle of minimum total potential energy and solved through replacing the spatial derivatives by means of a series solution whose center is located at the outer radius of the plate and discretizing the time domain by the fourth-order Runge–Kutta numerical time integration scheme. The interlaminar continuity condition of the transverse shear stresses is satisfied a priori. The zigzag plate theory serves as a predictor approach and the three-dimensional theory of elasticity as a corrector technique. Since for the subject under investigation exact elasticity solutions do not exist, accuracy and efficiency of the proposed modeling and solution procedures are verified by comparing present results with high-fidelity finite element solutions obtained using the ABAQUS commercial code. Results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-thickness stress distributions and removing the interlaminar jumps in the transverse distribution of the radial stresses. Consequently, some of the failure modes may be prevented at the interfaces between the layers.

An analytical global–local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations

Free vibration of functionally graded annular sandwich plates resting on Winkler-type elastic foundations is investigated based on a zigzag global–local plate theory and a finite Taylor's transform whose center is located at the outer edge. Material properties of each layer may be graded in the transverse direction according to a power law. It is the first time that a global–local theory is combined with a layerwise analytical solution for analysis of the annular functionally graded sandwich plates. Various edge conditions are considered for the inner and outer edges. A parametric study including evaluating effects of the material properties distributions of the core and face sheets, symmetric and asymmetric layups, thickness to radius ratio of the plate, inner to outer radius ratio, coefficient of the elastic foundation, and the edge conditions on vibration behavior of the annular plate is carried out. Accuracy of the employed sandwich plate theory and the presented analytical solution are verified by comparing present results with those of the three-dimensional theory of elasticity extracted from ABAQUS software.

Parametric resonance of axisymmetric sandwich annular plate with ER core layer and constraining layer

The parametric resonance problems of axisymmetric sandwich annular plate with an electrorheological (ER) fluid core and constraining layer are investigated. The annular plate is covered an electrorheological fluid core layer and a constraining layer to improve the stability of the system. The discrete layer annular finite element and the harmonic balance method are adopted to calculate the boundary of instability regions for the sandwich annular plate system. Besides, the rheological property of an electrorheological material, such as viscosity, plasticity, and elasticity can be changed when applying an electric field. When the electric field is applied on the sandwich structure, the damping of the sandwich system is more effective. Thus, variations of the instability regions for the sandwich annular plate with different applying electric fields, thickness of ER layer, and some designed parameters are presented and discussed in this study. The ER fluid core is found to have a significant effect on the location of the boundaries of the instability regions.

Free vibration analysis of rotating polar orthotropic annular plate with ER damping treatment

The free vibration analysis of rotating polar orthotropic sandwich annular plate with electrorheological (ER) fluid core layer is studied in this study. By using discrete layer annular finite element method, the equation of motion for the rotating polar orthotropic sandwich system is derived. The ER fluid is utilized to control the vibration and damping characteristics of the rotating polar orthotropic sandwich annular plate system. Additionally, the extensional and shear modulus of ER fluid are described by complex quantities. And, the natural frequencies and loss factors of the system are obtained by solving the complex eigenvalues of the system. Natural frequency and modal loss of the rotating polar orthotropic sandwich annular plate with different designed parameters are calculated and discussed in this study.

Vibration and damping characteristics analysis of a rotating annular plate withelectrorheological treatment

In this paper, the vibration and damping analysis of a rotating sandwich annular plate withan electrorheological (ER) fluid core layer is studied. The equation of motion for therotating sandwich system is derived and calculated by the discrete layer annular finiteelement method. The rheological properties of ER fluid materials, such as viscosity,plasticity, and elasticity can be changed by applying different electric fields, so ER fluidis adopted to control the vibration and damping characteristics of the rotatingsandwich annular plate system. Besides, the extensional and shear modulus of ERfluid are described by complex quantities and the complex eigenvalues of thesystem are calculated numerically, and from these, natural frequencies and lossfactors are extracted. Natural frequency and modal loss of the rotating sandwichannular plate with different rotational speeds, applied electric fields, thickness of ERlayer, and some designed parameters are also presented and discussed in thisstudy.