Vibration Of Composite Plates Research Articles

INFLUENCE OF INTERLAYER HYBRIDITY, LAYING ANGLESON FREE VIBRATIONS ANDDEFORMATION CHARACTERISTICS

Natural frequencies and modes of vibration, the rigidity of solids, are the most important parameters taken into account when designing structural elements in order to take into account dynamic loading conditions. The article presents the results of calculating the natural frequencies of the first forms of bending vibrations of composite plates with interlayer hybridity. The dependences of the deflections of the rods under the action of a distributed load over the surface on the internal structure are revealed. The calculations were obtained by numerical and approximate methods. For numerical analysis software based on the finite element method (ANSYS) was used.

Modeling of aeroelastic composite plates vibrations based on asymptotic theory

The paper is devoted to solving the problem of aeroelastic deformation of multilayer thin composite plates. A theory of aeroelastic deformations of composite plates based on the application of the asymptotic averaging method and piston theory for modeling pressure on the body surface is proposed. The averaged equations of aeroelastic vibrations of composite plates are derived. An example of a numerical solution of the problem of one-dimensional bending vibrations of a composite plate based on the developed theory is given.

Nitsche-based isogeometric approach for free vibration analysis of laminated plate with multiple stiffeners and cutouts

On the basis of the first order shear deformation and Timoshenko beam theories, a general Nitsche-based isogeometric analysis (IGA) is developed for studying the free vibration behaviors of composite plates with/without stiffeners and cutouts. Firstly, the laminated plate with/without cutout is described by several non-overlapped NURBS patches. The stiffeners are placed on the common edges of adjacent patches and share the same control points with these sub-patch edges. Then, different patches are stuck together by the means of Nitsche method. Eventually, the proposed method is implemented for analyzing the free vibration of composite plates with/without stiffener and cutout. First of all, it avoids the discretization of the stiffener and the identification of plate elements where stiffener nodes are located at, that are required in finite element method and IGA. In addition, it can handle with laminated plate with multiple stiffeners and cutouts conveniently. At first, four meshing schemes with different element sizes are implemented to validate the good convergence and accuracy of the present method in case of laminated plate with stiffener. Then, rectangular, skew and elliptical plates without stiffener and cutout are considered and the obtained natural frequencies and mode shapes agree well with those reported in literature. Furthermore, results from composite plates with/without stiffener and cutout under different boundary conditions are analyzed by considering different lay-up numbers and orientations of fiber, shapes and numbers of cutout, orientation angles and numbers of stiffener.

Investigating the Instability of Parametric Vibrations of Composite Plates under Arbitrary Pulsating Loads Based on High-Order Plate Theories

Investigating the Instability of Parametric Vibrations of Composite Plates under Arbitrary Pulsating Loads Based on High-Order Plate Theories

A comparative study on the effect of SMAs and CNTs on the vibration of composite plates exposed to thermal environments

The main purpose of this study is to compare the effects of two advanced materials, namely shape memory alloys (SMAs) and carbon nanotubes (CNTs) on the fundamental natural frequencies of rectangular graphite fiber/epoxy (GF/EP) composite plates. The performance of each of these materials is evaluated for different geometric conditions and boundary conditions as well as operating temperatures. Moreover, the glass transition temperature is considered as a limiting factor in the study. The governing equations are derived based on first-order shear deformation theory (FSDT) and then solved by generalized differential quadrature (GDQ) technique. The effective thickness-to-width ratio and temperature ranges are determined for both SMA wires and CNTs. The results of this study show that in some conditions, the use of CNTs is preferable over SMA wires and vice versa. Moreover, unlike SMA wires, the positive effect of the CNTs is limited to a certain extent. Furthermore, the numerical results indicate that depending on the different parameters, the use of SMAs may have constructive or destructive effects on the structural vibrations. Interestingly, it is shown that in some circumstances, the co-incorporation of SMAs and CNTs leads to a significant enhancement in the natural frequencies of the structure.

Stochastic free vibration of composite plates with temperature-dependent properties under spatially varying stochastic high thermal gradient

The uncertainty of natural frequencies of composite plates due to the uncertainty of high-temperature distribution on the plate is investigated. Mechanical properties are assumed to be uncertain linear functions of temperature with assuming a stochastic linear dependency function (SLDF). The temperature gradient is assumed to be a Gaussian stochastic field with an exponential kernel. Assuming first-order shear deformation theory, the displacement field is defined. The stochastic assumed modes (SAM) method is proposed and discretized stochastic equations of motion are derived. The probability space is studied using an intrusive polynomial chaos approach. Stochastic simulations are verified using the stochastic finite element method (SFEM) based on the Monte Carlo approach. Results show the proposed semi-analytical method is an efficient alternative to time-consuming SFEM with resulting accurate statistical moments. Uncertainty in natural frequencies is quantified for symmetric and anti-symmetric composite plates with different side to thickness ratios. The applicability of linear dependency of composite material properties to the temperature is evaluated by uncertainty propagation in SLDF. Uncertainties in SLDF and temperature distribution have significant effects on predicted natural frequencies. Based on the results, the application of linear dependency of material properties to the temperature can lead to significant errors in predicted natural frequencies.

Hygrothermal environmental effect on free vibration of laminated plates using nth-order shear deformation theory

The formulation of the nth-order shear deformation theory was modified to discuss the hygrothermal response of free vibration of laminated composite plates. Current theory has four unknown variables. Besides, this theory does not require a shear correction factor and gives a parabolic distribution of shear stresses across the thickness of the plate. The properties of the plate are affected by temperature and humidity. The equations of motion are established from Hamilton’s principle. The Navier-type solution procedure is applied to determine analytical solutions for free vibration of simply-supported laminated plates. The numerical results obtained by the present analysis of the free vibrations of composite plates are discussed to present the influence of the temperature, humidity, proportion of the aspect, and the orientation of the fiber orient on the characteristics of the vibration of the laminated plate.

Free Vibration Analysis of Composite Plates and Cylindrical Shells Using Spline-Constrained Finite Strip Method

In this paper, free vibration of composite plates and cylindrical shells are investigated. The method of analysis is the spline-constrained finite strip method which is based on the full energy methods. This method is based on the energies including potential, kinetic and external work integrations. Using Layerwise spline functions for longitudinal shape functions in the finite strip method makes it possible to provide a detailed examination, with less degrees of freedom for convergence and easier application of boundary conditions, and allows the strips to be connected more easily and conveniently.

Uncertainty propagation analysis in free vibration of uncertain composite plate using stochastic finite element method

Material uncertainty is more widespread in composite material than the other engineering materials. This uncertainty makes response of these types of structures to be nondeterministic. In order to predict structural reliability, uncertainty in structural responses must be quantified. There is not a reported research in the literature studing free vibration of composite plate with spatially stochastic material properties. In this research, physical and mechanical properties of composite plate including tensile and shear modulus and density of the plate are modeled as stochastic Gaussian fields. Assuming exponential auto covariance kernels for aforementioned stochastic fields, they are discretized to two parts, including deterministic and stochastic parts employing Karhunen-Loeve theorem. Assuming linear form of strains, mechanical strains are defined applying first order shear deformation theory. Kinetic and potential energy of the composite plate is extracted using finite element formulation. Stochastic finite element formulation is derived employing Hamilton’s principle and Euler-Lagrange and equations are verified with the results in the literature for deterministic case. After verification of formulation, material uncertainty effects on uncertainty of natural frequencies are investigated using Monte Carlo simulation. Results show that there is a linear relation between coefficient of variation of uncertain properties and coefficient of variation of stochastic natural frequencies.

Free Vibration Analysis of Graphene Platelets–Reinforced Composites Plates in Thermal Environment Based on Higher-Order Shear Deformation Plate Theory

As a first endeavor, this article presents the free vibration of composite plates reinforced with graphene platelets (GPLs) based on the higher-order shear deformation plate theory. Moreover, it is assumed that the material properties are temperature dependent and are graded in the thickness direction. It is assumed that GPLs randomly spread out in each individual composite layer reinforced with graphene platelets. The theoretical formulation is derived based on higher-order shear deformation plate theory and the initial thermal stresses are evaluated by solving the thermo-elastic equilibrium equations. The Halpin–Tsai micromechanical model is used to evaluate the effective material properties of every layer of composite plates reinforced GPLs. Further, the Navier solution has been used to derive the governing equations of motion and evaluate the natural frequencies and dynamic response of simply supported graphene platelet reinforced composite plates. Four different GPL distribution pattern is modeled to find out its effect on the frequency of the plate and the other parameters. The result asserted that subjoining GPL to composite plates has a significant reinforcing effect on the free vibration of Graphene platelet reinforced composite (GPLRC) plates.

Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions

This study aimed to develop a high-order shear deformation theory to predict the free vibration of hybrid cross-ply laminated plates under different boundary conditions. The equations of motion for laminated hybrid rectangular plates are derived and obtained by using Hamilton\'s principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained by using Navier\'s solution. To assess the validity of our method, we used the finite element method. Firstly, the analytical and the numerical implementations were validated for an antisymmetric cross-ply square laminated with available results in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for different combinations of boundary conditions of hybrid composite plates are investigated. The comparison of the analytical solutions with the corresponding finite element simulations shows the good accuracy of the proposed analytical closed form solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates under different boundary conditions.

Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation

This work examines vibration and bending response of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation. Four types of distributions of uni-axially aligned single-walled carbon nanotubes are considered to reinforce the plates. Analytical solutions determined from mathematical formulation based on hyperbolic shear deformation plate theory are presented in this study. An accuracy of the proposed theory is validated numerically by comparing the obtained results with some available ones in the literature. Various considerable parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are considered in the present investigation. According to the numerical examples, it is revealed that the vertical displacement of the plates is found to diminish as the increase of foundation parameters; while, the natural frequency increase as the increment of the parameters for every type of plate.

Predictions of the frequencies of bending-torsion coupled laminated composite plates with discontinuities: Novel analytical modeling and experimental validation

A novel analytical model that accurately represents the free vibration response of intact/damaged composite plates accounting for the bending-torsional coupling is developed. Unlike the existing models for the bending-torsion vibrations of composite plates, in the present model, the equations of motion are derived in an uncoupled form. It is then easier to derive analytical solutions for composite plates under coupled bending-torsion vibrations. In addition, for the first time, analytical solutions for the free bending and torsional vibrations of cantilever and clamped-clamped laminated composite plates with discontinuities including circular holes, rectangular holes, notches, and internal and edge cracks are easily obtained. Shifts in the natural frequencies due to discontinuities are modeled where the reductions in the plate stiffnesses are related to the amount of the energy release rate due to a defect formation. In order to verify the accuracy of the proposed model and the derived solutions, the proposed model is compared to the available conventional models. Moreover, experimental measurements of the free bending and torsional vibrations of carbon-fiber-laminated composite plates with circular holes is performed. A set of finite element analyses are carried out and compared to the experimental and the proposed model results. Then, a parametric study is presented in order to investigate the effects of the discontinuity size and location on the bending and torsional natural frequencies of laminated composite plates with various forms of discontinuities. The performed analyses demonstrate the accuracy of the proposed models to represent the free vibrations of laminated composite plates with discontinuities.

Termal Ortamda Elastik Tabandaki Kompozit Plakaların Doğrusal Olmayan Titreşim Analizi

Nonlinear vibrations of composite plates on an elastic foundation in thermal environments are presented in this study. Graphite/epoxy is selected as the plate material. The properties of composite material are assumed to be temperature-dependent. Nonlinear free vibrations of laminated composite plates are investigated in the fully clamped boundary conditions. The classical finite element method is used and a specially prepared computer code is written in the Matlab software. Vibrations of the spring supported laminated composite plate are directly influenced by the boundary conditions and dimensions of plate.In this study, generated graphical values reveal that foundation stiffness and temperature have significant effects on the linear and nonlinear frequencies of composite plates.

An efficient plate element for the vibration of composite plates

An element is presented for the free vibration analysis of composite plates. The element is capable of representing high orders of displacement using very few degrees of freedom. Hierarchy in the orders of deflection, rotation, moment and shear has been preserved in the element through scrupulous choice of field variables. The effect of rotary inertia has been considered through an innovative scheme for inclusion into mass lumping procedures. Performance of the element has been tested in a wide range of problems which indicate that free vibration analysis of plates with the help of the present element can reach a high level of accuracy at reduced computation cost, compared to standard elements in literature.

Asymptotic theory for vibrations of composite plates

Asymptotic theory for vibrations of composite plates

Modal Analysis of Woven Fiber Composite Plates with Different Boundary Conditions

Most of the work done for the vibration of composite plates published in the literature is either analytical or numerical studies with few experimental results available on composites with unidirectional fibers. The present study involves extensive experimental works to investigate the free vibration of industry driven woven fiber glass/epoxy composite plates with different boundary conditions including free–free cases. The modern modal testing and subsequent analysis with powerful computer and digital analysis system is an important tool for prediction of behavior of structures. The specimens of woven glass fiber and epoxy matrix composite plates are manufactured by the hand-layup technique. Elastic parameters of the plate are also determined experimentally by tensile testing of specimens using INSTRON 1195. An experimental investigation is carried out using modal analysis technique with Fast Fourier Transform Analyzer, PULSE lab shop, impact hammer and contact accelerometer to obtain the frequency response functions. The computational results are compared with results of previous studies in literature wherever available. The experimental results are also compared with the FEM numerical analysis based on first-order shear deformation theory. The effects of different geometrical parameters including number of layers, aspect ratio, fiber orientation and different boundary conditions of woven fiber composite plates are studied in detail. It is observed that comparisons performed between numerical predictions and experimental tests have a good correlation. The natural frequency is very less for cantilever than simply supported and fully clamped boundary conditions. The prediction of dynamic behavior of laminated composite plates plays a significant role in the future applications of structural composites.

The effect of hybridization and boundary conditions on damping and free vibration of composite plates

Abstract In this study, the influence of hybridization on natural frequency and damping properties of laminated composite plates consisting of various combinations of fibers and boundary conditions are examined. Carbon (C), Kevlar® (K), and S-glass fibers are used as reinforcement with epoxy resin for hybridization. Experiments are conducted on hybrid composites under the combinations of clamped, free, and simply supported boundary conditions. Natural frequency analyses of hybrid composites are performed using finite element analysis software ANSYS. Vibration test results obtained from experimental and numerical studies are compared with each other. Results show that hybridizations with three different fibers and their substitutions in the layers have strongly effected the damping and vibration characteristics of composite plates.

Force Vibration of Laminated Plates with Various Shapes Subjected to Low-velocity Impact

In this paper, force vibration of composite laminate plates subjected to low-velocity impacts are investigated semi-analytically and analytically. Symmetrically angle-ply laminated rectangular, circular and elliptical plates are considered. The simply supported edges boundary condition is considered. Plates were studied based on small deflection thin plate theory. A Hertz Contact Theory models the contact forces between the rigid projectile and the laminated plate. A simple and improved model was developed to calculate force vibration of composite plates. A semi-analytical model was obtained for force vibration of composite laminated plates by the method of Rayleigh-Ritz and modal expansion. Calculations of the impact response in composite material structures are important in damage-tolerant design. The results were compared with the results from the available literature and found to be in good agreement.

Effects of In-Plane Loading on Vibration of Composite Plates

This paper deals with the dynamic analysis of pre-stressed laminated composite plates. Particular emphasis is devoted to the case of in-plane mono-axial, biaxial, shear and combined loadings. Both equivalent single layer and layer-wise plate kinematic description are addressed, according to the hierarchical approach proposed by the Carrera's unified formulation. The different kinematic approaches are compared in order to identify the appropriate modeling for laminated composite plates subjected to combined loadings. The principle of virtual displacement is applied in order to obtain governing equations and the corresponding problem is solved through the finite element method. When possible, assessments/comparisons with exact solutions are proposed. Moreover, the effects of different stacking sequences, boundary conditions, geometries and materials on plate natural frequencies are illustrated.