Vibration Analysis of Shear-deformable Circular and Elliptical Laminated Composite Plates.

Use of two-dimensional orthogonal polynomials for vibration analysis of circular and elliptical plates

Natural frequencies of symmetrically laminated elliptical and circular plates

Hybrid isogeometric-based analysis and experimental investigation on the dynamic response characteristics of a clamped circular plate partially in contact with fluid

The composite materials are well known by their excellent combination of high structural stiffness and low weight. The main feature of these anisotropic materials is their ability to be tailored for specific applications by optimizing design parameters such as stacking sequence, ply orientation and performance targets. Finding free torsional vibrations characteristics of laminated composite beams is one of the bases for designing and modeling of industrial products. With these requirements, this work considers the free torsional vibrations for laminated composite beams of doubly symmetrical cross sections. The torsional vibrations of the laminated beams are analyzed analytically based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes due to fiber orientation of the laminated beams are neglected. Also, the torsional vibrations of the laminated beams analyzed by shear deformation theory in which the shear deformation effects are considered. Numerical analysis has been carried out using finite element method (FEM). The finite element software package ANSYS 10.0 is used to perform the numerical analyses using an eight-node layered shell element to describe the torsional vibration of the laminated beams. The rotary inertia and shear deformation effects of the element are taken. The influence of fiber directions and stacking sequences of laminates on torsional natural frequencies were investigated. Also, the effects of boundary conditions are demonstrated. Numerical results, obtained by the ANSYS 10.0, classical lamination theory, and shear deformation theory are presented to highlight the effects of fibers orientation and layers stacking sequence on torsional frequencies of the beams. The results obtained by ANSYS are compared against the classical lamination theory, as well as shear deformation theory.

A layerwise optimization approach, developed for the design of vibration of laminated rectangular plates, is extended to the symmetrically laminated, composite elliptical plates. There is little information available on the optimum lay-ups of such elliptical plates, including the special case of circular plates. The optimum design problem is formulated to maximize the critical buckling load and the lowest frequency, and fiber orientation angles in the layers are used as the design variables. A Ritz method is used to calculate eigenvalues (buckling load and frequency) of the elliptical plates and the convergence and comparison studies indicate accuracy of the calculated eigenvalues as the object function. A set of numerical results is given in tabular and graphical form, illustrating the optimum lay-ups of the laminated elliptical plates with respect to the fiber orientation angles.

This paper studies the effect of vibration mode on damping of fiber reinforced plastic composite plates. For this purpose, the free vibration analysis for the laminated plates is formulated by using the Ritz method, based on Classical Lamination Theory (CLT), First-order Shear Deformation Theory (FSDT) and Higher-order Shear Deformation Theory (HSDT), and then natural frequencies and specific damping capacities of the plates with different stacking sequences are calculated numerically assuming complex elastic modulus. On the other hands, experimental study is also carried out using experimental mode analysis. Finally not only the applicability of each analytical model for damping analysis but also the effect of vibration mode on damping are discussed from the comparisons of the numerical results and experimental results.

In the present paper, free vibration analysis of angle-ply laminated composite annular and circular plates is performed by numerical methods. First-order shear deformation plate theory is used for kinematic relations. The related governing equations of motion are discretized via differential quadrature and discrete singular convolution methods. Frequency values are obtained for different lamina scheme, thickness-to-radius ratio, and mode numbers. The advantages and accuracy of these two methods are also tested in detail.

The problem of free vibration of non‐linear structures is considered initially. It is shown that this problem can be represented as a non‐linear eigenvalue problem. Variational principles for non‐linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non‐linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non‐linear eigenvalue parameters can be used in modal expansion approximations for the non‐linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non‐linear circular plate are determined.

Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method

This paper studies the assumption of displacements employed in the vibration analysis of laminated composite plates. For this purpose, the maximum strain and kinetic energies of a cross-ply laminated plate are evaluated analytically based on the three-dimensional theory of elasticity. The displacements of the simply-supported rectangular plates are expanded into the polynomial forms with respect to a thickness coordinate, and then governing equations are formulated by using the Ritz's method. In the numerical calculations, natural frequencies and modal damping ratios are calculated for the plates with different stacking sequence and the thickness ratios. The validity of the assumption of displacements and the applicability of the other plate theories (e. g. Classical Lamination Theory, First-order Shear Deformation Theory and Higher-order Shear Deformation Theory) to the laminated thick plates are discussed by comparing the numerical results obtained by the present method with the CLT and the FSDT solutions.

This paper presents a free vibration analysis of functionally graded Reissner-Mindlin circular plates with various supported boundaries in thermal environments. A FGM consisting of metal and ceramic was considered in the study. Based on the geometric equation, physical equation and equilibrium equation of thick plate, taking into account the transverse shearing deformation, the free vibration equation of the axisymmetric FGM moderately thick circular plates was derived in terms of the middle surface angles of rotation and lateral displacement. The material properties of the plate were assumed to vary continuously in the thickness direction according a power law. By using shooting method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of FGM thick circular plates were obtained numerically. The effects of material gradient property, thickness ratio and boundary conditions on the natural frequencies were discussed in detail.

Free vibration of annular and circular asymmetric composite laminates

Fundamental frequencies of solid and annular elliptical plates were approximated using the static deflections by means of finite element method (FEM) without computing the eigenvalues. The problem was formulated within the framework of the first order shear deformation theory (FSDT). The effects of (i) the inner and outer boundary conditions, (ii) the size of the perforation, (iii) the aspect ratio, and (iv) the thickness of the plate on the performance of the method were examined via a large variety of numerical simulations. Convergence study was performed through h-refinement. Accuracy of the results was validated through comparison studies. The results reveal that the application of the Morley’s formula which does not require eigenvalue analysis approximates the fundamental frequency with finer mesh compared to the eigenvalue analysis. The method can be considered as a practical technique to approximate the fundamental frequency. However, the boundary conditions have dominant role on the accuracy of the solution particularly when the plate is perforated.

NATURAL FREQUENCIES OF TRANSVERSE VIBRATIONS OF NON-UNIFORM CIRCULAR AND ANNULAR PLATES

Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright © 2008 John Wiley & Sons, Ltd.