A generalized element for the free vibration analysis of composite beams
TL;DR: In this article, a general finite element based on a first-order deformation theory is developed to study the free vibration characteristics of laminated composite beams, which accounts for bi-axial bending as well as torsion.
About: This article is published in Computers & Structures.The article was published on 1994-06-03. It has received 49 citations till now. The article focuses on the topics: Finite element method & Vibration.
Citations
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TL;DR: In this article, the vibrational behavior of pre-twisted composite space rods under isothermal conditions is theoretically investigated based on the Timoshenko beam theory, and the Poisson effect is incorporated in the formulation of the beam resultant constitutive equations.
40 citations
TL;DR: In this paper, the spectral element matrix is derived by rigorous use of the analytical solutions of the governing differential equations of the laminated beam in free vibration, which is demonstrated by adopting the Wittrick-Williams algorithm.
37 citations
TL;DR: In this article, the transfer matrix method is used for the numerical solution of both in-plane and out-of-plane free vibration problems of symmetric cross-ply laminated composite beams.
Abstract: The transfer matrix method is used for the numerical solution of both in-plane and out-of-plane free vibration problems of symmetric cross-ply laminated composite beams. The rotary inertia, and both shear and extensional deformation effects, are considered in the analysis. A distributed parameter model is used in the mathematical formulation of the free vibration problem. The overall transfer matrix of the beam is obtained making use of the series solution of a set of differential equations. All the effects of the boundary conditions, the slenderness ratio, the ratio of the height to the width of the rectangular cross-section, the number of plies, and material types on the free vibration frequencies are studied. Comparison of the exact natural frequencies obtained in this study with the existing results is quite good. Copyright © 1999 John Wiley & Sons, Ltd.
36 citations
TL;DR: A bibliographical review of the finite element methods applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given.
Abstract: Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
36 citations
TL;DR: In this paper, a model for the modal analysis of a rotating composite cantilever plate is presented, where a set of linear ordinary differential equations of motion for the plate is derived by using the assumed mode method.
35 citations
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Book•
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
TL;DR: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations is presented in this paper, where a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials.
Abstract: A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.
288 citations
TL;DR: In this paper, exact solutions for the free vibration of symmetrically laminated composite beams are presented for the first-order shear deformation and rotary inertia have been included in the analysis.
216 citations
TL;DR: In this article, a finite element model based on a higher-order shear deformation theory is developed to study the free vibration characteristics of laminated composite beams and the effects of in-plane inertia and rotary inertia are considered in the formulation of the mass matrix.
130 citations