Free vibration of laminated composite rectangular plates
TL;DR: In this paper, the Ritz method with algebraic polynomial displacement functions is used to solve the vibration problem for laminated composite plates having different boundary conditions, and convergence studies are made which demonstrate that accurate results are obtained by using 64 displacement terms for symmetrically-luminated plates.
About: This article is published in International Journal of Solids and Structures.The article was published on 1991-01-01. It has received 59 citations till now. The article focuses on the topics: Ritz method & Normal mode.
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SIDI1
TL;DR: In this paper, the authors used the four variable refined plate theory for free vibration analysis of plates made of functionally graded materials with an arbitrary gradient, where the material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents with a given gradient.
Abstract: The novelty of this paper is the use of four variable refined plate theory for free vibration analysis of plates made of functionally graded materials with an arbitrary gradient. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents with an arbitrary gradient. The equation of motion for FG rectangular plates is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. In the case of FG clamped plates, the free vibration frequencies are obtained by applying the Ritz method where the four displacement components are assumed as the series of simple algebraic polynomials. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of FG plates. Illustrative examples are given also to show the effects of varying gradients, aspect ratios, and thickness to length ratios on the free vibration of the FG plates.
183 citations
SIDI1
TL;DR: In this paper, the authors used the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates, which is variationally consistent and strongly similar to the classical plate theory in many aspects.
Abstract: This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.
95 citations
TL;DR: In this paper, a meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates, where the essential boundary conditions are enforced by a singular kernel method.
88 citations
TL;DR: In this article, a 3D finite element model of delaminated fiber-reinforced composite plates is developed to analyze their dynamics, including natural frequencies and modal displacements.
87 citations
TL;DR: In this paper, a discrete singular convolution (DSC) method was developed for static analysis of symmetric cross-ply laminated composite plates based on the first-order shear deformation.
Abstract: A new numerical technique, the discrete singular convolution (DSC) method, is developed for static analysis of thick symmetric cross-ply laminated composite plates based on the first-order shear de...
77 citations
References
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28 Feb 1986TL;DR: In this paper, the authors introduce the concept of anisotropic elasticity and composite Laminate Theory for composite materials, and present a test standard for polymer matrix composites.
Abstract: Preface to the Second Edition. Preface to the First Edition. 1. Introduction to Composite Materials. 2. Anisotropic Elasticity and Composite Laminate Theory. 3. Plates and Panels of Composite Materials. 4. Beams, Columns and Rods of Composite Materials. 5. Composite Material Shells. 6. Energy Methods For Composite Material Structures. 7. Strength and Failure Theories. 8. Joining of Composite Material Structures. 9. Introduction to Composite Design. Appendices: A-1. Micromechanics. A-2. Test Standards for Polymer Matrix Composites. A-3. Properties of Various Polymer Composites. Author Index. Subject Index.
1,144 citations
147 citations
TL;DR: In this article, an exact solution and numerical results for simply supported plates that are laminated unsymmetrically about their middle surface are presented for common composite materials such as boron or epoxy and graphite/epoxy, where the coupling between bending and extension induced by the lamination asymmetry substantially decreases buckling loads and vibration frequencies.
Abstract: An exact solution and numerical results are presented for simply supported plates that are laminated unsymmetrically about their middle surface. The coupling between bending and extension induced by the lamination asymmetry substantially decreases buckling loads and vibration frequencies for common composite materials such as boron/epoxy and graphite/epoxy. For antisymmetric laminates, the effect of the coupling dies out rapidly as the number of layers is increased. For generally unsymmetric laminates, however, the effect of coupling dies out very slowly as the number of layers increases. That is, having a large number of layers is no guarantee that coupling will not seriously degrade buckling resistance and vibration frequencies. Thus, designers must include coupling between bending and extension in all analyses of unsymmetrically laminated plates.
110 citations
TL;DR: In this paper, the Ritz method with algebraic polynomial displacement functions is used to analyze free vibrations of thin cantilevered laminated plates and shallow shells having rectangular planforms.
109 citations