Vibration Analysis Of Composite Plates Research Articles

Free Vibration Analysis of Composite Plate Stiffened by Lattice Structures

Free vibration behavior of laminated composite plates stiffened by different lattice structures is considered. To simulate free vibration, finite element models were created with Ansys Parametric Design Language (APDL). In the models, SHELL181 and BEAM181 elements were used to model laminated composite and lattice structures, respectively. The influence of the different stiffeners lattice structures on natural frequencies of the composite plate is examined for the clamped-free-clamped-free boundary condition. The results showed that the frequency parameters of the stiffened composite structures made of the L2-type lattice are higher than those composed of other lattice types. This study provides an exciting opportunity to advance our knowledge of the usage of lattice structures as stiffener structures for composite plates.

Random vibration analysis of composite plate

Random vibration analysis is one of the major type of dynamic load which are having multiple amplitudes with multiple frequencies at a given particular time. The aerospace structure which contains Printed circuit board [PCB] fails frequently due to the high accelerations, high Stresses levels and high deformations under dynamic loads. So it is very important to analyse the PCB (Composite Plate) under dynamic load conditions. In the present research work, rectangular plate with composite materials which acts as PCB is analysed under random vibration load with different boundary conditions 2 faces fixed using Copper foil and Epoxy E Glass UD materials. The geometry of the rectangular plate is modelled in the FEA Software ANSYS. Proper fine mesh is done for the rectangular plate. Plate with [1/1], [2/2], [2/4] and [4/4] layups are designed in the Ansys ACP pre-module and later assigned the different properties of the composites to the rectangular plate and performed random vibration analysis by applying PSD G acceleration load to the fixed supports. A total number of 9 critical points are selected on the plate for calculating the PSD responses [Acceleration, displacement and normal stresses] to the random vibrations which are given to the rectangular plate. Based on the results, critical point is located and best material and best layup sequence is selected for the composite plate.

Transverse Vibration Analysis of Composite Plates with Multiple Distributed Composite Patches

Transverse vibration of rectangular composite plates with multiple distributed composite patches is analyzed in this paper. Because of the geometric discrepancy between the plate and patch, analytical solutions are usually hard to achieve. The present model is formulated by using the Rayleigh–Ritz method and adopting various types of modal shape functions of uniform beam as admissible functions for different boundary conditions. The total system energies are calculated by adding the energies of the substrate plate and the energies of the patches. By imposing the displacement-matching condition at the patch domains, the coordinate systems of the substrate plate and patches are coupled. By means of the present method, it is very convenient and efficient to build the system governing equations and solve the eigenvalue problem. For the composite patches, they are also assumed to be symmetrically layered and have the same layer stacking sequence with the substrate laminate. The effects of layer stacking sequence, modulus ratio, aspect ratio, and boundary conditions on the natural frequencies are investigated and discussed. The results are also compared with the existed benchmark solutions and FEM solutions for validation. The numerical results demonstrate that the proposed approach is computationally very efficient and accurate and can be used as a tool to solve transverse vibration problems of composite plate with multiple composite patches.

Uncertainty propagation in dynamics of composite plates: A semi-analytical non-sampling-based approach

In this study, the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method. The material properties including tensile modulus, shear modulus, and density of the plate were assumed to be spatially varying and uncertain. Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties. The stochastic fields were decomposed via application of the Karhunen-Loeve theorem. A first-order shear deformation theory was assumed, following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies. The stochastic equations of motion of the plate were obtained using the variational principle. The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies, and the corresponding mode shapes of the plate were determined using a polynomial chaos approach. The proposed method significantly reduced the size of the mathematical models of the structure, which is very useful for enhancing the computational efficiency of stochastic simulations. The methodology was verified using a stochastic finite element method and the available results in literature. The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated, and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.

A new C0 layerwise wavelet finite element formulation for the static and free vibration analysis of composite plates

In this paper, a new C0 layerwise wavelet finite element is proposed for the static and free vibration analysis of composite plates. The refined zigzag theory is adopted to introduce the zigzag effects in multilayered plate structures by using piecewise linear C0 continuous functions. Then the layerwise wavelet-based BSWI element is derived based on the higher-order plate theory by means of two-dimensional BSWI scaling functions. The proposed model satisfies the conditions of transverse shear stress continuity at the layer interfaces as well as yields to the stress-free boundary conditions on the surface of plate without a shear correction factor. What’s more, the layerwise wavelet-based BSWI element also possesses the advantages of high convergence, high accuracy and reliability with fewer degrees of freedom on account of the excellent approximation property of BSWI. The accuracy and effectiveness of proposed layerwise wavelet-based BSWI element is assessed for static and free vibration analysis of laminated composite and sandwich plates with available 3D elasticity solutions, finite element solutions and other referential solutions in published literatures.

Free vibration of a composite plate with spatially varying Gaussian properties under uncertain thermal field using assumed mode method

The stochastic assumed mode (SAM) method is developed for vibration analysis of composite plates with spatially varying stochastic properties. Temperature distribution in the plate is considered as Gaussian random field. To keep the generality, material properties of the composite plate such as tensile modulus, shear modulus, and thermal expansion coefficient are also assumed to be Gaussian random fields. Considering exponential autocovariance and employing the Karhunen–Loeve theorem, Gaussian random fields are decomposed. Hamilton principle and Euler–Lagrange equations are employed to derive stochastic equations of motion. The effects of uncertainties in mechanical properties as well as stochastic thermal preload on the natural frequencies are studied utilizing the Monte Carlo approach. Results show the proposed method can span probability space without a reduction in accuracy of the statistical moments in the case of plates with spatially stochastic properties. A significant decrease in computational cost in comparison with the intrusive stochastic finite element method (SFEM) is achieved.

Stochastic meshless method for nonlinear vibration analysis of composite plate reinforced with carbon fibers

With the aid of an efficient meshless numerical solution and the reproducing kernel particle method, the feasibility for investigating the nonlinear vibrations of the carbon fiber reinforced composite rectangular plate with the random material properties is studied in this paper. A geometrically nonlinear mathematical model is established based on the classical plate theory. According to the derived governing equation of motion by using the principle of virtual displacement, the nonlinear vibration behaviors of the carbon fiber reinforced composite plates with various edge supports are investigated. The linear and nonlinear eigenvalues and corresponding eigenvectors are calculated iteratively by using the dimensionless amplitude. The stochastic meshless method is proved to have a good computational accuracy for the composite plate, and exhibits an optimal choice for the shape function and constraint of the essential boundary conditions. The useful conclusions are obtained regarding the effect of the material and geometrical parameters including the boundary condition, length-width ratio, plate length and carbon fiber content on the nonlinear responses in the framework of the meshless method.

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.

Influence of Mechanical Properties on Modal Analysis of Natural Fiber Reinforced Laminated Composite Trapezoidal Plates

ABSTRACT Present work concentrates on modal parameters of laminated composite plates composed of natural fibers reinforced with unsaturated polyester resin. The selected jute and ramie fibers underwent alkaline treatment to improve mechanical properties. Upon compression molding, the laminated composite plates such as ramie/polyester (R plate), jute/polyester (J plate) and combination of ramie and jute (RJ plate) are fabricated. The physical, mechanical and elastic properties are calculated as per ASTM standards. Using obtained elastic properties, the free undamped vibration analysis of composite plates are computed using finite element software ANSYS 18.1 for trapezoidal plates, with respect to a/b = 1 and 2, c/b = 0.25 to 1 and a/h = 50. The natural frequency and mode shape of the plates are obtained for various boundary conditions such as CFFF, CFCF, CCCC, SFSF and SSSS (C-Clamped, F-Free and S-Simply supported). The dimensionless frequency and mode shapes of R, J and RJ plates are compared with literatures which are in good agreement.

Thermal buckling and vibration of laminated composite plates with temperature dependent properties by an asymptotic numerical method

The objective of this work is the elaboration of analytical and numerical procedures to investigate thermal buckling and vibration analyses of composite plates with thermal dependent material properties. Based on the homotopy and an asymptotic numerical method, a mathematical formulation that may account for various temperature dependent models is elaborated. Power series expansions of the displacement and the temperature are developed, and the finite element method is used for numerical solution. The effects of temperature dependent properties, structural geometry and boundary conditions on the thermal buckling and vibration are analyzed.

Free vibration analysis of composite plates based on a variable separation method

This work deals with the free vibration analysis of laminated composite plates through a variable separation approach. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x,y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterative process. That consists of solving a 2D and 1D eigenvalue problem successively. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used.A wide range of numerical tests involving several representative laminated and sandwich plates is addressed to show the accuracy of the present LayerWise (LW) method. Different slenderness ratios and boundary conditions are also considered. By comparing with exact or 3D FEM solutions, it is shown that it can provide accurate results less costly than classical LW computations.

Free vibration analysis of composite plates using indirect quadrature technique

This work concerns with free vibration analysis of composite plate materials. Based on a transvers shear theory, the governing equations of the problem are derived. An indirect technique of moving least-square differential quadrature method is developed and employed to reduce the problem to that of eigen-value one. Natural frequencies and mode shape functions of the composite are obtained. Validity of the developed technique is examined for regular and irregular plates with different boundary conditions. Accuracy and efficiency of the obtained results are achieved by comparing them with the previous exact and numerical ones. Further, a parametric study is introduced to investigate the effects of elastic and geometric properties on values of vibration field quantities.

Strong and weak formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells: Convergence and accuracy

The aim of this work is to investigate and compare the accuracy and convergence behavior of two different numerical approaches based on Differential Quadrature (DQ) and Integral Quadrature (IQ) methods, respectively, when applied to the free vibration analysis of laminated plates and shells. The numerical methods at issue allow to solve the strong and the weak forms of the governing equations of these structural elements. A completely general approach is presented to evaluate numerically derivatives and integrals by using several basis functions (polynomial approximation) and grid distributions (discretization). The convergence analyses are performed for three different approaches: Strong Formulation (SF), Weak Formulation (WF) with C1 continuity conditions, and Weak Formulation (WF) with C0 continuity conditions. For each approach, a set of convergence graphs is shown, by varying both basis functions and discrete grids, in order to define the combinations that provide the best accuracy with reference to the exact solutions available in the literature.

Buckling analysis of composite plates using moving least squares differential quadrature method

ABSTRACTThis work concerns with buckling and vibration analysis of composite plates based on a transverse shear theory. A numerical scheme is introduced to determine the angular frequencies and critical buckling loads of such plates. Moving least square differential quadrature method is employed to reduce the problem to that of eigen value problem. The accuracy and efficiency of the proposed scheme is examined with different computational characteristics, (radius of support domain, basis completeness order, and scaling factors). The obtained results agreed, at less execution time, with the previous ones. Further, a parametric study is introduced to investigate the influence of elastic and geometric characteristics, (Young's modulus gradation ratio, shear modulus gradation ratio, Poisson's ratio, loading parameter, and aspect ratio), of the composite on the values of critical buckling load, natural frequencies, and behavior of mode shape functions.

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.

An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part II: Applications

An exact spectral-dynamic stiffness method (S-DSM) for free vibration analysis of composite plates and plate assemblies has been proposed in Part I of this two-part paper. The main purpose of this Part II paper is twofold: (i) To validate and demonstrate the superiority of the proposed S-DSM and (ii) To establish exact benchmark solutions for free vibration of composite plate-like structures. The S-DSM is applied to a number of problems covering orthotropic composite plates and plate assemblies. It is demonstrated that the S-DSM gives exact solutions with high computational efficiency within low as well as high frequency ranges. The applications are completely general and the new development can handle complex plate shapes with any boundary conditions.

Free vibration analysis of composite plates by higher-order 1D dynamic stiffness elements and experiments

A novel approach for free vibration analysis of composite plate-like structures is introduced in this paper. Refined beam theories are formulated by making use of the Carrera Unified Formulation (CUF). By exploiting the hierarchical characteristics of CUF, the differential equations of motions and the natural boundary conditions are written in a compact and concise form in terms of fundamental nuclei, whose formal mathematical expressions do not depend on the order of the theory N. After the closed form solution of the N-th order beam model is sought, a general procedure to derive the exact Dynamic Stiffness (DS) matrix is devised by relating the amplitudes of the harmonically varying loads to those of the responses. The global DS matrices of composite laminated plates are then used with reference to the algorithm of Wittrick and Williams to carry out free vibration analyses. The accuracy of the proposed methodology is verified through published literature, finite element solutions from the commercial code MSC/Nastran and experimental tests.

Analysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques

The static bending and the free vibration analysis of composite plates are performed with Carrera’s Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4-noded mixed interpolation of tensorial components approach (MITC4). The smoothing method is used for the approximation of the bending strains, whilst the mixed interpolation allows the calculation of the shear transverse stress in a different manner. With a few numerical examples, the accuracy and the efficiency of the approach is demonstrated. The insensitiveness to shear locking is also demonstrated.

Meshless natural neighbor Galerkin method for the bending and vibration analysis of composite plates

In the present work we present a meshless natural neighbor Galerkin method for the bending and vibration analysis of plates and laminates. The method has distinct advantages of geometric flexibility of meshless method. The compact support and the connectivity between the nodes forming the compact support are performed dynamically at the run time using the natural neighbor concept. By this method the nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the computational effort in construction of the shape functions. Smooth non-polynomial type interpolation functions are used for the approximation of inplane and out of plane primary variables. The use of non-polynomial type interpolants has distinct advantage that the order of interpolation can be easily elevated through a degree elevation algorithm, thereby making them suitable also for higher order shear deformation theories. The evaluation of the integrals is made by use of Gaussian quadrature defined on background integration cells. The plate formulation is based on first order shear deformation plate theory. The application of natural neighbor Galerkin method formulation has been made for the bending and free vibration analysis of plates and laminates. Numerical examples are presented to demonstrate the efficacy of the present numerical method in calculating deflections, stresses and natural frequencies in comparison to the Finite element method, analytical methods and other meshless methods available in the literature.

Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip procedures

This research describes spectral finite element formulation for vibration analysis of rectangular symmetric cross-ply laminated composite plates of Levy-type based on classical lamination plate theory (CLPT). Formulation based on SFEM includes partial differential equations of motion, spectral displacement field, dynamic shape functions, and spectral element stiffness matrix (SESM). In this paper, vibration analysis of composite plate is investigated in two sections: free vibrations and forced vibrations. In free vibrations, natural frequencies are calculated for different Young’s moduli ratios and boundary conditions. In forced vibrations, plate vibrations are investigated under high-frequency concentrated impulsive loads. The resulting responses due to spectral element formulation are compared with those of (time-domain) finite element and analytical formulations, whenever available. The results demonstrate the superiority of SFEM with respect to FEM, in reducing computational burden, simultaneously increasing numerical accuracy, specifically for excitations of high-frequency content. By reducing the time duration of impulsive loads, and consequently increasing the modal contribution of higher modes in the transient response of plate, the accuracy of FEM responses decreases substantially accompanied with a high volume of computations, while the accuracy of the SFEM response results is very high and simultaneously, with a low computational burden. Practically, SFEM follows very closely exact analytical solutions.