Sandwich Annular Plate Research Articles

Magneto Axisymmetric Vibration of FG-GPLs Reinforced Annular Sandwich Plates with an FG Porous Core Using DQM and a New Shear Deformation Theory

Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular plate is assumed to deform axisymmetrically and expose to a radial magnetic field. The Lorentz magnetic body force is deduced via Maxwell’s relations. The effective physical properties of the upper and lower layers of the sandwich plate are obtained by employing the Halpin–Tsai model. Our technique depends on a new four-unknown shear deformation theory to depict the displacements. In addition, the motion equations are established via Hamilton’s principle. The motion equations are solved by employing the DQP. In order to study the convergence of the DQ method, the minimum number of grid points needed for a converged solution is ascertained. In addition, the current theory’s outcomes are compared with those of previous higher-order theories. The effects of the porosity distribution type, porosity factor, GPLs distribution pattern, GPLs weight fraction, inner-to-outer radius ratio, outer radius-to-thickness ratio, magnetic field parameters, core thickness, and elastic substrate parameters on the nondimensional vibration frequencies are discussed.

Introducing hybrid deep neural networks to predict the transient vibrations of the sandwich systems reinforced by multi-phase nanocomposites

In advanced materials engineering, understanding transient vibrations in sandwich annular plates reinforced by multi-phase nanocomposites is essential. To adequately represent the geometry of these systems, a generic cylindrical coordination system is often used in modeling. The heterogeneous laminated plate is homogenized into an analogous uniform medium to facilitate analysis. In order to represent precise stress and strain distributions, taking into account rotating inertia and transverse shear deformation, a higher-order theory based on a hyperbolic function is used. The governing equations of motion are derived using Hamilton’s principle in polar coordinates, guaranteeing compliance with energy laws. The 2D generalized differential quadrature (GDQ) method effectively discretizes the governing equations for numerical solutions while retaining a high degree of accuracy in recording transient reactions. Furthermore, by solving the differential equations in the frequency domain, the Laplace transform approach sheds light on the dynamic behavior of the system. Using the deep neural networks (DNNs)-fuzzy approach improves the prediction of these composite structures’ vibrational activity. This hybrid approach uses fuzzy logic to control uncertainty and DNN for pattern identification. The DNN-fuzzy approach reliably predicts the intricate vibrational properties of multi-phase sandwich systems reinforced with nanocomposite using datasets from mathematical modeling. This combined use of mathematical techniques, theoretical models, and predictive algorithms improves our knowledge of complex composite structures’ transient vibrations and makes them more useful in a range of engineering domains.

Dynamic stability analysis of CFRP sandwich structure reinforced by advanced nanocomposites via both machine learning method and mathematical simulation

This work introduces a quasi-3D refined theory for assessing the transient dynamic reactions of a sandwich annular sector plate subjected to mechanical shock loading. The sandwich structure has two facesheets composed of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) and a core composed of carbon fiber reinforced polymer. The auxetic quality of the annular plates is mainly determined by the quantity of graphene and the level of folding in the GOri material. The elements are assessed layer by layer across the thickness of the plates. Micromechanical models supported by genetic programming may be used to predict the position-dependent Poisson’s ratio and other material parameters. The concept of Hamiltonian is used to deduce the governing equations of the structure. The equations of motion, which vary with time, are solved using the numerical solution process and the Laplace transform. A comprehensive parametric study is carried out to examine the influence of various geometric and physical parameters on the time-dependent behavior of annular sector plates. The current mathematical modeling results are being compared to the findings of previous works, as well as a machine learning technique. By using this machine learning methodology, it is feasible to computationally solve differential equations at a reduced expense, while simultaneously surmounting the challenge of formulation. To use machine learning techniques, a dependable dataset acquired from either experimental or numerical analysis is necessary. The dataset was created using the quantitative findings of the investigation. Furthermore, the machine learning technique demonstrates its capacity to provide very precise outcomes when predicting the transient behavior of the existing structure under novel loading and boundary circumstances.

Free vibration analysis of the sandwich structured composite annular plates: Numerical and experimental investigation

Sandwich structures are interesting structural elements due to their high stiffness-to-weight ratio, high fatigue resistance, and excellent vibration characteristics. The aerospace industry relies heavily on these types of structures considering the different optimized materials and shapes available for sandwich construction. In the present study, vibration aspects of annular sandwich structures with composite laminates and a 3D printed honeycomb core are investigated in both the numerical and experimental methods. Amongst the various shapes of sandwich structures, annular sector plates are predominantly used in the construction of modern bridges, aircrafts, and automobile parts. Furthermore, the investigation of annular sandwich plates featuring GFRP facesheet and 3D printed PLA cores are studied in a very limited extent. In order to obtain the sector plates experimentally, Glass Fiber Reinforced Polymer (GFRP) laminates are fabricated by hand layup techniques, and the 3D printing Poly-lactic Acid (PLA) honeycomb core is manufactured using Fused Deposition Modelling (FDM). The material properties of honeycomb core and composite skins are estimated with the help of Gibson formulation and rule of mixture, respectively. Based on available literature, the analysis approach is validated through numerical analysis using ANSYS Finite Element (FE) software. Also, the frequency responses of annular sandwich plate were measured in both experimental and numerical analysis and the results showed good agreement. However, in order to describe the effectiveness of annular composite sandwich plates, parametric studies are carried out in terms of natural frequencies and mode shapes with different configurations of core geometry, ply orientation, boundary constraints, and inner to outer radius ratio. The research outcome highlights that the optimum angle ply orientation, core height of 12.5 mm with clamped–clamped condition and inner to outer radius of 0.75 mm yields better structural stiffness.

The exact solution of annular sandwich plate undercoated with radial-FGM subjected to radial pressure or transverse load

This study aims to derive the exact stretching and bending solutions of the radially FGM annular sandwich plate subjected to either radial pressure or transverse load. The radially FGM annular sandwich plate consists of two homogeneous rings and an FGM-undercoated layer with uniform Poisson’s ratio and radially graded Young’s modulus based on the power function. Although the radially FGM annular sandwich plate is nonhomogeneous, the stretching and bending problems can be analyzed separately based on the elastic plate theory. Then the exact solution corresponding to the power-law graded FGM can be evaluated by solving the simultaneous equations of the boundary and continuous conditions. The theoretical results are validated through the comparison with the finite element solutions. When degenerated, our results coincide with those of the homogeneous annular plate in the literature, making the obtained solutions reliable. Using the radial-FGM as the undercoated layer makes the strains and stresses smoothly continuous at the interfaces of the layers. The effects of the material index on mechanical behavior are under investigation.

Axisymmetric Free Vibration Analysis of Functionally Graded Sandwich Annular Plates: A Quasi-3D Shear and Normal Deformable Model

This paper concentrates on axisymmetric free vibration of functionally graded (FG) sandwich annular plates obtained using a quasi-3D plate theory. Motion equations and corresponding boundary conditions are established via the mentioned plate theory which takes into consideration the non-uniform shear strains across the thickness and also stretching trough the thickness. Generalized differential quadrature method (GDQM) is applied to discrete the annular sandwich plate governing equations. The results of this study are applicable for optional thick plates since the adopted theory considers the shear and normal strains across the thickness direction. Outcoming results are verified on the basis of information accessible in the open literature. To investigate the influences of power law index of functionally graded materials (FGMs) and dimensions of the sandwich annular plate layers, parametric studies are presented. It was well demonstrated that the applied theory precisely predicts the natural frequencies of FG annular sandwich plates with arbitrary thickness.

Free Vibration Analysis of Spinning Sandwich Annular Plates with Functionally Graded Graphene Nanoplatelet Reinforced Porous Core.

This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young’s modulus, Poisson’s ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange’s equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail.

Vibration analysis of thick annular sandwich plates based on Reddy’s theory

Free axisymmetric vibrations of uniform annular sandwich plates with relatively stiff core and membrane facings have been studied on the basis of Reddy’s higher-order shear deformation theory. The core and facings are considered to be made up of isotropic materials. The governing equations of motion and natural boundary conditions are developed using Hamilton’s principle. Chebyshev collocation technique is employed to obtain the frequency equations for clamped-clamped, clamped-simply supported and clamped-free edge conditions. The lowest three roots of these equations have been computed and reported as the values of frequency parameters for the first three modes of vibration. After validating the results of the proposed approach, detailed numerical results are given to analyze the effects of thickness of the core, face thickness and radii ratio on the natural frequencies. The results obtained for various plate parameters are compared numerically and graphically with those available in the literature. It also shows that the application of first-order theory is inappropriate for analyzing the vibration of annular sandwich plates with thick core. Three-dimensional mode shapes for a specified plate for all the three boundary conditions have been plotted.

Response Suppression of FGM Plate Using Piezoelectric Layers Under Parametric Uncertainty Conditions with Markovian Jump Approach

It should be noted that in addition to the geometry, constituent material also affects the strength and rigidity of the cylindrical shell, some factors that determine the transient response are its geometry and the constituent material. The capability of piezoelectric materials to adept their properties in reaction to environmental factors including electricity and loading is one of the major reasons for using in this work. Therefore, in this study, the transient response of a symmetric annular sandwich plate incorporating functionally graded core and piezoelectric layers under external harmonic force and electrical voltage is investigated. The properties of the core material vary along its thickness according to a power law model. The displacement field is represented by the third-order shear deformation theory. With the aid of Hamilton’s principle, the structural equations are obtained in terms of displacement components, then solved using the differential quadrature method. In addition, the time response is evaluated with respect to effective parameters including the internal radius, power law index, core thickness, and external voltage. According to the simulation results, the oscillation amplitude decreases as the internal radius of the plate increases over the desired time interval. Also, a higher index parameter is associated with a wider time response range. Moreover, the stability analysis of a piezoelectric system with [Formula: see text] performance is considered based on the theory of Markovian jump systems. To this end, a Markovian jump state-space model of the piezoelectric system obtained using system identification under the effect of external disturbance is presented. The [Formula: see text] stability index is selected based on a candidate Lyapunov function that leads to a set of linear matrix inequalities for each region. The uncontrolled and controlled transient responses of the coupled system under external disturbance are calculated and compared, indicating the satisfactory controller performance in the presence of external disturbance and jump in the sensor and system dynamics.

Vibration and symmetric thermal buckling of asymmetric annular sandwich plates with piezoelectric/GPLRC layers rested on foundation

The investigation of thermal load on the graphene-platelets-reinforced composite (GPLRC) is an important issue for developing composite structures in aerospace applications like the spacecraft in near-Sun missions. This paper presents vibration and symmetric thermal buckling behaviors of an annular sandwich plate that consists of two asymmetric piezoelectric surface layers and one GPLRC core layer. The plate is rested on Pasternak foundation. Modified Halpin-Tsai micromechanical model and the rule of mixtures are utilized to calculate the effective material properties. Basic equations are obtained according to the first-order shear deformation theory in which von Kármán's nonlinearity is considered. Then governing equations are derived based on Hamilton's principle and Maxwell static electricity equation. The differential quadrature method is introduced to solve these governing equations under different boundary conditions. Effects of the geometrical sizes, dispersion patterns and weight fractions of graphene-platelets, asymmetric laying of piezoelectric layers, and temperature variation on natural frequencies and critical buckling temperatures of the annular plate are discussed. Results reveal that adding graphene-platelets into the matrix can increase the fundamental natural frequency, while decline the thermal buckling temperature. The combined action of asymmetric configuration of piezoelectric layers and distribution patterns of graphene-platelets has a significant influence on the vibration and thermal buckling.

Free Vibration and Transient Response of Heterogeneous Piezoelectric Sandwich Annular Plate Using Third-Order Shear Deformation Assumption

Based on the third-order shear deformation theory (TSDT), this paper numerically investigates the natural frequencies and time response of three-layered annular plate with functionally graded materials (FGMs) sheet core and piezoelectric face sheets, under initial external electric voltage. The impressive material specifications of FGM core are assumed to vary continuously across the plate thickness utilizing a power law distribution. The equilibrium equations are obtained employing Hamilton’s method and then solved applying differential quadrature method (DQM) in conjunction with Newmark-β. Numerical studies are carried out to express the influences of the external electric voltage, aspect ratio, and material gradient on the variations of the natural frequencies and time response curves of FGM piezoelectric sandwich annular plate. It is precisely shown that these parameters have considerable effects on the free vibration and transient response.

Free axisymmetric vibrations of composite annular sandwich plates by higher-order theory using Chebyshev collocation technique

Abstract Free axisymmetric vibrations of composite annular sandwich plates with thick isotropic core and orthotropic facings have been studied using Reddy's higher-order shear deformation theory. Core is assumed to be of uniform thickness while the face sheets are treated as membranes. Equations of motion and natural boundary conditions are developed using Hamilton's principle. Chebyshev collocation technique has been applied to get the frequency equations for clamped-clamped, clamped-simply supported and clamped-free edge conditions. Obtained equations are solved numerically for the lowest three roots and reported as the frequency parameters for the first three modes of vibration. Results obtained from the proposed approach are validated by comparing them numerically and graphically with their counterparts available in the literature. Detailed numerical results are given to analyze the effects of core thickness, thickness of faces and radii ratios on the frequency parameter. It is also shown that the published analysis based on first-order theory is not suitable for estimation of natural frequency of annular sandwich plate with thick core. Three dimensional mode shapes have been plotted for a specified plate for all the three boundary conditions.

Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

Shear actuation mechanism and shear-based actuation capability of an obliquely reinforced piezoelectric fibre composite in active control of annular plates

In this work, the mechanism of shear actuation and the shear mode actuation capability of an obliquely reinforced piezoelectric fibre composite are investigated in active control of annular plates. This piezoelectric fibre composite is capable of providing extensional and shear actuation forces in a transverse plane of its Cartesian material coordinate system, and these actuation forces are utilized for shear-based actuation of an annular plate by embedding the piezoelectric fibre composite patches at the core of the plate. First, the mechanism of shear actuation of the annular sandwich plate is analysed, and it mainly reveals an adverse effect of the coupling between the transverse normal strain and shear stresses on the shear actuation forces, even though a good shear-actuated bending deformation of the annular plate is observed. So, next, the effectiveness of the piezoelectric fibre composite patches in shear mode active control of flexural vibration of the annular sandwich plate is investigated, where a shear-based feedback control arrangement is proposed for effective active control of the plate according to the velocity feedback control law. The analysis reveals an indicative shear actuation capability of this obliquely reinforced piezoelectric fibre composite, and thus it may be a potential material for shear-based active control of vibration of annular plates.

Shear-based vibration control of annular sandwich plates using different piezoelectric fiber composites: A comparative study

This work presents the shear-based attenuation of vibration of an annular sandwich plate using two different shear mode piezoelectric fiber composite (PFC) actuators namely Shear Actuated Fiber Composite (SAFC) and Balanced Laminate of PFC (BL-PFC). A conventional shear mode monolithic piezoelectric (PZT5H) actuator is also used, and a comparative study on the shear actuation capabilities of all three shear actuators is performed to address the best one for shear-based control of the annular sandwich plate. Every actuator is used in the form of an actuator laminate that is inserted at the core of the sandwich plate in the form of the patches, where a fruitful arrangement of the patches and a shear-based control strategy are presented for effective attenuation of vibration of the sandwich plate according to the velocity feedback control law. First, the effective properties of the actuator laminate are determined using the Uniform Field Method. Next, a closed-loop finite element model of the sandwich plate is developed based on the layer-wise shear deformation theory. Subsequently, the suitability of the present arrangement of shear actuator patches and the shear-based control strategy are substantiated. This arrangement of the actuator patches is further optimized for every shear actuator, and the corresponding shear actuated resonant displacement-amplitudes of the sandwich plate are evaluated. These results reveal lesser actuation capability of the SAFC than that of the PZT5H while the BL-PFC is the best one for shear-based attenuation of vibration of the annular sandwich plate.

Effect of radially graded porosity on the free vibration behavior of circular and annular sandwich plates

Porous materials with functionally graded porosity are achieved by tailoring the size and density of the internal pores in one or more directions that leads the desired mechanical properties. Thus, due to the promotion of porous materials in engineering applications such as the foam core in sandwich plates, the compact heat exchangers, lightweight structures, biomedical systems and separation processes, in this paper, the free vibration of sandwich circular and annular plates with a core made of materials with functionally graded porosity are investigated. Different porosity distributions through the radial direction are introduced for the core of the plate. The governing equations of motion for the free vibration of a plate are obtained based on the first order shear deformation plate theory (FSDT). Clamped and simply supported edges are assumed for the plates. The collocation version of spectral method called the pseudo-spectral (PS) method using Chebyshev polynomials as the basis function is adopted to solve the equations of motion. Validation studies are also done to demonstrate the accuracy of the results. The natural frequencies of the clamped and simply-supported sandwich circular and annular plates with a porous core are calculated. The effects of different porosity distributions, porosity parameter, core thickness and geometric parameters on the results are investigated.

Mechanical buckling analyses of sandwich annular plates with functionally graded carbon nanotube-reinforced composite face sheets resting on elastic foundation based on the higher-order shear deformation plate theory

The main objective of this article is to analyze the buckling of sandwich annular plates with carbon nanotube-reinforced face sheets subjected to in-plane mechanical loading resting on the elastic foundation. It is assumed that the sandwich plate is composed of the homogeneous core layer and two functionally graded carbon nanotube-reinforced composite face sheets. The effective material properties of the functionally graded carbon nanotube-reinforced composite face sheets are estimated using the modified rule of mixture method. The higher-order shear deformation theory along with the variational differential quadrature method is employed to derive the governing equations. To this end, the quadratic form of energy functional of the structure is derived based on higher-order shear deformation theory which is directly discretized using numerical differential and integral operators. The validity of the proposed numerical approach is first shown and the effects of various parameters are then investigated on the buckling of sandwich annular plates. It was found that the elastic foundation coefficients, type of distribution of carbon nanotubes, inner-to-outer radius ratio and core-to-face sheet thickness ratio play important roles in the stability of the structure. Furthermore, the numerical results of the higher- and first-order shear deformation theories are compared.

Dynamic stability analysis of microcomposite annular sandwich plate with carbon nanotube reinforced composite facesheets based on modified strain gradient theory

In this article, dynamic stability of annular sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core are presented based on first-order shear deformation theory and modified strain gradient theory. The generalized rule of mixture is employed to predict mechanical properties of microcomposite sandwich plate. The equations of motion are derived from Hamilton’s principle and solved by differential quadrature method. The fast rate of convergence of the method is shown and the results are compared against existing results in the literature. The results indicate that volume fraction of carbon nanotubes in facesheets and dimensionless length scale parameter has significant effects on the dynamic stability region and the parametric resonance. Dynamic stability region increases with considering of dimensionless length scale parameter, increasing of volume fraction of carbon nanotubes, and static load factor. Also, the influence of inner-to-outer radius ratios, radius-to-thickness ratios, and core-to-facesheets ratios are considered. The results can be employed for design of materials science, in junction high pressure micropipe connections, solid-state physics, micro-electro-mechanical systems, and nano electromechanical systems such as microactuators and microsensor.

Bending and buckling analysis of functionally graded annular microplate integrated with piezoelectric layers based on layerwise theory using DQM

In present paper, bending and buckling analysis of functionally graded material (FGM) annular microplate integrated with piezoelectric layers is investigated. The annular sandwich microplate is subjected to radial compressive and uniform transverse load. Considering the nonlocal elasticity theory for small scale effect is developed. In order to mathematical modeling of annular sandwich microplate, layerwise theory, is employed. Furthermore, the surrounding elastic medium is simulated by Pasternak foundation model, in which both compression and tension are assumed. The material properties of FGM annular microplate are supposed to vary through the thickness according to power law. Using energy method and principle of minimum potential energy, the size dependent governing motion equations are derived. In this study, the governing motion equations are solved numerically using differential quadrature (DQ) method. The present numerical solutions are validated through comparisons against those available in open literature for the reduced cases. Also, different boundary conditions at the edges of the annular sandwich microplate are considered. A parametric study is conducted to examine the effects such as elastic foundation, small scale effect, various boundary conditions, number of grid point, external voltages of piezoelectric layers, outer–inner radius ratio on the critical buckling load, are developed. The results clarify that external voltages are effective parameter on the critical buckling load and the bending behavior of the system. In addition, the effects of elastic foundation is very remarkable on the buckling and deflection of the annular sandwich plate.

Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory

In this paper, a comprehensive numerical study is presented on the large-amplitude free vibration of sandwich annular plates integrated with functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets resting on elastic foundation. The sandwich plate is made of a homogeneous core and two FG-CNTRC face sheets whose material properties are estimated through a micromechanical model. Since the fundamental vibrational mode shapes of annular plates are axisymmetric, the governing equations are derived assuming the axisymmetric formulation. For this purpose, the quadratic form of total potential energy of the structure is presented based on the higher-order shear deformation theory (HSDT) of plates along with von-Karman nonlinear kinematic relations. The numerical differential and integral operators are then employed to discretize the energy functional in space and time domains. Finally, using the response of linear analysis and applying the pseudo-arc length continuation method, the nonlinear frequencies are obtained. After validating the results of proposed approach, detailed numerical results are given to analyze the effects of geometrical and material parameters on the nonlinear vibration of FG-CNTRC sandwich annular plates.