Analytical solutions to vibration of generally layered composite beams
TL;DR: In this paper, the free vibration problem of clamped-clamped and clampedsupported composite beams is formulated as a constrained variational problem, the constraints being imposed through Lagrange multipliers.
About: This article is published in Journal of Sound and Vibration.The article was published on 1992-11-22. It has received 99 citations till now. The article focuses on the topics: Hamilton's principle & Rotary inertia.
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TL;DR: In this paper, the authors review most of the research done in recent years (1989-2012) on the vibration analysis of composite beams, with emphasis given to the theory being applied (thin, thick, layerwise), methods for solving equations (finite element analysis, differential transform and others) experimental methods, smart beams (piezoelectric or shape memory), complicating effects in both material and structure, and other areas that have been considered in research.
153 citations
TL;DR: In this article, the vibration analysis of cross-ply laminated beams subjected to different sets of boundary conditions is studied, and the analysis is based on a three-degree-of-freedom shear deformable beam theory.
116 citations
TL;DR: In this paper, a new method of state-space-based differential quadrature is presented for free vibration of generally laminated beams, which is validated by comparing numerical results with that available in the literature.
115 citations
TL;DR: Within the displacement field of a layerwise theory, two laminated beam theories for beams with general lamination are developed in this paper, and analytical solutions for static bending and free vibration are developed and compared with those of an existing threedimensional elasticity solution of cross-ply laminates in cylindrical bending and with the three-dimensional finite element analysis for angle-ply Laminates.
95 citations
TL;DR: In this article, a triply coupled vibration and buckling analysis of composite beams with arbitrary lay-ups using refined shear deformation theory is presented, which accounts for the parabolical variation of shear strains through the depth of beam.
72 citations
Cites result from "Analytical solutions to vibration o..."
...It is observed that the present results are in good agreement with previous studies ([16], [23], [24], [25]) for all fiber angles....
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References
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Book•
01 Sep 1982
TL;DR: In this article, the Statique Reference Record was created on 2004-09-07, modified on 2016-08-08, and was used for Elasticite and Plasticite.
Abstract: Keywords: Elasticite ; Plasticite ; Statique Reference Record created on 2004-09-07, modified on 2016-08-08
2,023 citations
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: In this paper, a two-dimensional linear theory of motions of heterogeneous plates is deduced from the three-dimensional theory of elasticity, which is specialized to cases of symmetrically laminated aeolotropic, orthotropic and isotropic plates.
710 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