Composite Annular Plates Research Articles

Analysis of Vibration Characteristics for Rotating Braided Fiber-Reinforced Composite Annular Plates with Perforations

In the current study, a comprehensive numerical model for analyzing the vibrational characteristics of braided fiber-reinforced composite (BFRC) rotating annular plate with perforations under diverse boundary constraints was introduced. This model employs the differential quadrature finite element method (DQFEM), which was developed based on the first-order shear deformation theory (FSDT) and coordinate transformation approach. The BFRC material, specifically a two-dimensional biaxial orthogonal fabric, was utilized to fabricate the annular plate with two distinct types of holes: circular and sector-shaped. The model’s convergence, accuracy, numerical stability, and reliability were confirmed through comparative assessments utilizing data from the literature, from ABAQUS software, and from experimental findings. The analysis focuses on studying the influences of structural properties, material parameters, and boundary restraints on the frequencies of vibration for BFRC rotating annular plates with holes. This theoretical model helps provide scientific basis and technical guidance for the stability and lightweight design of rotating annular plates, such as rotor structures in aircraft engines.

Theoretical and numerical analysis of free vibrations of piezoelectric circular plate reinforced with boron nitride

PurposeThe purpose of this research is to extract the natural frequencies of a circular plate containing a central hole reinforced with boron nitride nanotubes (BNNTs) and containing piezoelectric layers.Design/methodology/approachA unit cell shall be taken into account for the simulation of BNNT's volume fraction. A rectangular micromechanical model is used to obtain the mechanical properties of unit cell of piezoelectric fiber-reinforced composite (PFRC). The three-dimensional (3D) elasticity method is presented to provide the relationship between displacements and stresses. The one-dimensional differential quadrature method (1D-DQM) and the state-space methodology are combined to create the semi-analytical technique. The state-space approach is utilized to implement an analytical resolution in the thickness direction, and 1D-DQM is used to implement an approximation solution in the radial direction. The composite consists of a polyvinylidene fluoride (PVDF) matrix and BNNTs as reinforcement.FindingsA study on the PFRC is carried, likewise, the coefficients of its properties are obtained using a micro-electromechanical model known as the rectangular model. To implement the DQM, the plate was radially divided into sample points, each with eight state variables. The boundary situation and DQM are used to discretize the state-space equations, and the top and bottom application surface conditions are used to determine the natural frequencies of the plate. The model's convergence is assessed. Additionally, the dimensionless frequency is compared to earlier works and ABAQUS simulation in order to validate the model. Finally, the effects of the thickness, lateral wavenumber, boundary conditions and BNNT volume fraction on the annular plate's free vibration are investigated. The important achievements are that increasing the volume fraction of BNNTs increases the natural frequency.Originality/valueThe micromechanical “XY rectangle” model in PFRC along with the three-dimensional elasticity model is used in this literature to assess how the piezoelectric capabilities of BNNTs affect the free vibration of polymer-based composite annular plates under various boundary conditions.

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.

Symmetric and asymmetric vibrations of rotating GPLRC annular plate

The present paper discusses the symmetric and asymmetric free and forced vibrations of a rotating graphene-platelets-reinforced composite annular plate subjected to the complex external excitation in thermal environment, where the aerodynamic force is considered. Displacement components are able to vary along the radial and circumferential directions and von Kármán’s geometrical nonlinearity is taken into account. The free vibration analysis is conducted first. Then the forced vibration equations are discretized by utilizing the Galerkin method with the aid of vibration mode. The incremental harmonic balance method and pseudo-arclength continuation algorithm are employed in combination to solve these equations. The effects of plate dimensions, graphene-platelets-reinforced composite (GPLRC) parameters, temperature rise, rotational motion, and external excitation on the symmetric and asymmetric vibration are studied by the parameter analysis for annular plate. Results implicate that temperature rise would affect the order in which the symmetric and asymmetric vibrations appear whereas the other factors not. Asymmetrical material properties along the thickness direction leads to that the periodic motion is asymmetric with respect to mid-plane. Under the complex external excitation, the dominant role of deformation shifts from symmetric vibration to asymmetric vibration as the frequency increases.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

Axisymmetric Postbuckling of Functionally Graded Graphene Platelets Reinforced Composite Annular Plate on Nonlinear Elastic Medium in Thermal Environment

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including [Formula: see text]-pattern, [Formula: see text]-pattern, [Formula: see text]-pattern, [Formula: see text]-pattern, and [Formula: see text]-pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium’s parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs.

Static Stability of Composite Annular Plates with Auxetic Properties.

This paper presents an evaluation of the static stability of complex, composite annular plates with layers having auxetic properties. The main objective of the numerical investigations is the development of a plate model, which uses an approximate solution based on orthogonalization and finite difference methods. The three-layered plate is composed of auxetic facings and a soft, foam core. The material properties of the facings are characterized by Poisson’s ratio, the values of which are variously positive and negative. The results obtained for an auxetic plate were compared on the basis of the results for a plate with traditional facings and a plate model built of finite elements. Additionally, in order to verify the calculation results, an analysis of the homogeneous plate was performed. Two plate models built of finite differences and finite elements were compared. The wide image of buckling responses of the examined plates was created on the basis of the calculation results of both compressed and radially stretched plates. An increase in the values of the critical static loads with increasing absolute value of Poisson’s ratio of auxetic facings is one of the observations.

Symmetric and asymmetric thermo-induced buckling and postbuckling of rotating GPLRC annular plates rested on elastic foundation

Investigating the instability of annular plate which revolves on its axis in thermal environment is a valuable subject in vehicle engineering and aerospace industry, for instance, extending the service life of engine bearing. The symmetric and asymmetric buckling and postbuckling induced by the temperature rise of a rotating graphene-platelets-reinforced composite annular plate rested on Pasternak foundation are studied in present paper. Asymmetric deformation forms are captured by adopting the first-order shear deformation theory. Introducing von Kármán’s nonlinearity ensures the accuracy of postbuckling equilibrium paths. Highly coupled governing equations are solved by using the differential quadrature method and postbuckling paths are traced by utilizing the pseudo-arclength continuation algorithm. Parametric studies are conducted to discuss the influences of the dispersion patterns, weight fraction, and dimensions of GPLs, annular plate sizes, elastic foundation, and rotation motion on buckling and postbuckling. Results indicate that the sequence in which symmetric and asymmetric buckling modes appear is inextricably linked to the radial wave number of buckling configuration. Both adding GPLs and adjusting the foundation parameters appropriately can improve the ability to resist symmetric and asymmetric deformation of annular plate. The effect of rotation motion shows a transitional change along with the temperature rise.

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

This research is based on higher-order shear deformation theory to analyse the free vibration of composite annular circular plates using the spline approximation technique. Equilibrium equations are derived, and differential equations in terms of displacement and rotational functions are obtained. Cubic or quantic spline is used to approximate the displacement and rotational functions depending upon the order of these functions. A generalized eigenvalue problem is obtained and solved numerically for eigenfrequency parameter and associated eigenvector of spline coefficients. Frequency of annular circular plates with different numbers of layers with each layer consisting of different materials is analysed. The effect of geometric and material parameters on frequency value is investigated for simply supported condition. A comparative study with existing results narrates the validity of the present results. Graphs and tables depict the obtained results. Some figures and graphs are drawn by using Autodesk Maya and Matlab software.

Tuned deep neural network for computer simulation of chaotic performance of the electromechanical annular system coupled with a piezoelectric patch

In this paper, an attempt is made to extend a nonlinear two-dimensional model for large oscillation and chaotic characteristics of the annular plate coupled with a piezoelectric patch subject to external excitation. For improving the mechanical properties, the core of the electrically structure is reinforced with graphene nanoplatelets. Von-Karman nonlinear theory and Hamilton’s principle are taken into consideration for the exact derivation of the general nonlinear governing equations and boundary conditions of the axisymmetric annular plate coupled with a piezoelectric patch. For developing a precise solution approach, the generalized differential quadrature element method, and Multiple scales technique, are eventually used. The results demonstrate that radius ratio, applied voltage, thickness to radius ratio, and harmonic load have an important role in the nonlinear large oscillation, and chaotic motion of the graphene platelets reinforced composite (GPLRC) annular plate coupled with a piezoelectric patch. The golden and fundamental result of the current research is that, as the thickness of the piezoelectric patch increases, the system's nonlinear frequency decreases, and the area of instability in responses and maximum amplitude or the peak point of the backbone curve of the smart annular plate increases.

Temperature Effect on Stability of Clamped-Clamped Composite Annular Plate with Damages.

The paper presents the response of a three-layered annular plate with different damaged laminate facings to the action of the static or dynamic temperature field model. Various damages of laminate, composite facings change the plate structure reaction under the temperature fields. Obtained results indicate practical meaning of analyses in failure diagnostic process. The thermal sensitivity of two kinds of plate structures, undamaged and damaged, offers both new practical and scientific possibilities in evaluation of the plate behavior. The relations between macro-damage, i.e., the buckling of the plate structure and micro-damages of plate layers subjected to temperature gradient, are shown. The numerical solution is proposed as the most effective in examinations of the various transversally symmetrical and asymmetrical plate structures with a different rate of damages. The graphical distribution of changes in values of static and dynamic critical loads illustrate the process of structural damaging during its exploitation. They have practical importance in the evaluation of the structure capacity. The knowledge of the effect of laminate degradation process on plate buckling phenomenon located in thermal environment complements previous investigations and designates complex, multi-parameter problems as having scientifically new elements.

On the Large Amplitude Forced Vibration Analysis of Composite Sectorial Plates

The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinematics of first-order shear deformation theory (FSDT) and employing Hamilton’s principle. The governing equations of motion have been solved in a time domain using a modified shooting method and arc-length/pseudo-arc length continuation technique. The influence of the boundary condition, sector angle, and annularity ratio on the linear as well as nonlinear steady state forced vibration response has been investigated. The strain/stress variation across the thickness of the annular sector plate is presented to explain the reason for a decrease/increase in hardening nonlinear behaviour. The periodic variation of the non-linear steady state stress has also been obtained to throw light into the factors influencing the unequal stress half cycles and multiple cyclic stress reversals, which is detrimental to the fatigue design of laminated composite annular sectorial plates. The frequency spectra of the steady state stress reveals large even and odd higher harmonic contributions for different cases due to changes in the restoring force dynamics. The modal interaction/exchange during a cycle is demonstrated using a deformed configuration of the laminated annular sector plate.

On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation

In this study, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the graphene nanoplatelets (GPLs)-reinforced composite (GPLRC) annular plate subject to an external harmonic load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the annular plate subject to a harmonic excitation. The fundamental and golden results of this paper could be that the chaotic motion and nonlinear frequency of the annular plate are hardly dependent on the value of the length to thickness ratio (lGPL/wGPL) of the GPLs. Moreover, utilizing GPLs in the shapes close to square (lGPL/wGPL = 1) presents higher frequency of the annular plate. Also, increase in lGPL/tGPL indicates that using GPLs with lower thickness relative to its length provides better frequency response

Dynamic buckling of functionally graded multilayer graphene nanocomposite annular plate under different boundary conditions in thermal environment

This paper deals with dynamic stability of functionally graded (FG) nanocomposite annular plate reinforced with graphene platelets (GPLs) subjected to a periodic radial compressive load in thermal environment. On the basis of modified Halpin–Tsai micromechanics model, the effective elastic modulus of structure is estimated. Taking into consideration of the first-order shear deformation theory, the governing motion equations are obtained via the Hamilton’s principle. Afterward, the partial differential motion equations are discretized into a system of Mathieu–Hill equations by utilizing generalized differential quadrature method. Furthermore, the Bolotin’s technique is applied to determine the principle unstable zone of functionally graded graphene platelet reinforced composite (FG-GPLRC) annular plate. The accuracy and validity of current study are examined by comparing the fundamental natural frequencies of structure with those published in available literature. Eventually, to investigate the influences of number of layers, GPLs patterns and their geometric, boundary conditions, geometrical parameters of structure, static load factor, and temperature change on the DIRs of FG-GPLRC multilayer annular plate, different parametric studies are performed.

Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings

For the first time, the nonlinear forced vibration analysis of graphene nanoplatelets reinforced composite (GPLRC) annular plate under hygro-thermal environment and subjected to mechanical loading is presented. The GPLRC imperfect annular plate’s displacement fields are determined using third-order shear deformation theory (third-order SDT) and nonlinearity of vibration behavior of this structure is taken into account considering von Karman nonlinear shell model. Energy method known as Hamilton principle is applied to create the motion equations governed to the shell structures, while they are solved using generalized differential quadrature method (GDQM) as well as perturbation method (PM). Ultimately, the research’s outcomes reveal that increasing the value of the moisture change () and orientation angle parameter (), and the rigidity of the boundary conditions lead to an increase in the structure’s frequency. Besides, whenever the values of the nonlinear parameter () are positive and negative, the dynamic behavior of the plate tends to have hardening and softening behaviors, respectively, and could not be seen any effects from parameter on the maximum amplitudes of resonant vibration of the GPLRC imperfect annular plate. Last but not the list by decreasing the structure’s flexibility, the plate can be susceptible to have unstable responses.

Static, dynamic and natural frequency analyses of functionally graded carbon nanotube annular sector plates resting on viscoelastic foundation

In this paper, static, dynamic and natural frequency responses of composite annular sector plate with carbon nanotubes (CNTs) reinforcements resting on viscoelastic foundation are investigated. The carbon nanotubes are considered to have uniform or functionally graded pattern in the plate thickness. Kelvin-voight model is used to model the viscoelastic foundation. To model the problem, Hamilton principle based on first shear deformation plate theory and finite element method are applied. The mechanical properties of annular sector plate composed of CNTs and polymer matrix are evaluated by using the rule of mixtures. The numerical results are obtained for investigating the effect of various factors such as distribution and volume fraction of CNTs, boundary conditions, stiffness and damping coefficients of viscoelastic foundation and sector angles on natural frequency, static and dynamic transient responses of the plate.

Analysis of 3D-reinforced composite annular plate subjected to concentrated forces

This paper is dedicated to the solution of the problem about 3D-reinforced composite annular plate compressed by concentrated forces. 3D-reinforced composite materials, including high-temperature composites, are widely used in modern space industry, while their properties are insufficiently studied. Analytical solution of considered problem about annular plate compression will be a foundation for a method of determination of anisotropic composite materials stress-strain properties needed when conducting structural analysis: elastic and shear moduli, and Poisson’s ratio. Transverse shear deformations and changes in annular plate metrics during deformation are taken into account in the process of finding analytical solution of the problem. The analytical solution of the problem about annular plate compression was obtained by the authors. This solution is used to find relations between required properties of annular plate and radial displacements of annular plate characteristic points.

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.

Thermal and Mechanical Buckling and Vibration Analysis of FG-GPLRC Annular Plate Using Higher Order Shear Deformation Theory and Generalized Differential Quadrature Method

This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic substrate besides describing the kinematics on the basis of HSDT makes the results closer to real condition. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the plate and geometric dimensions of GPLs on the response of the structure. This study provides essential information to engineers seeking innovative ways to promote the composite structures in a practical way.

Vibration analysis of FG-GPLRC annular plate in a thermal environment

In this article, the thermal vibration of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plate resting on an elastic foundation under the mechanical load framework of higher order shear deformation theory (HSDT) is analyzed. Governing equations and boundary conditions are established by employing Hamilton’s principle. A generalized differential quadrature method (GDQM) is applied to obtain a numerical solution. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the annular plate, and geometric dimensions of GPLs on the response of the structure. The results revealed that applying sinusoidal temperature rise and locating more square-shaped GPLs in the vicinity of the top and bottom surface result in the highest natural frequency.