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Journal ArticleDOI

Free vibration of cross-ply laminated beams with arbitrary boundary conditions

TL;DR: In this paper, the authors developed analytical solutions of refined beam theories to study the free vibration behavior of cross-ply rectangular beams with arbitrary boundary conditions in conjunction with the state space approach.
About: This article is published in International Journal of Engineering Science.The article was published on 1994-12-01. It has received 150 citations till now. The article focuses on the topics: Boundary value problem.
Citations
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Journal ArticleDOI
Metin Aydogdu1
TL;DR: In this paper, a new higher-order deformable laminated composite plate theory is proposed, which is constructed from 3-D elasticity bending solutions by using an inverse method, and exactly satisfies stress boundary conditions on the top and the bottom of the plate.

450 citations

Journal ArticleDOI
TL;DR: A critical review of literature on bending, buckling and free vibration analysis of shear deformable isotropic, laminated composite and sandwich beams based on equivalent single layer theories, layerwise theories, zig-zag theories and exact elasticity solution is presented in this paper.

327 citations

Journal ArticleDOI
TL;DR: In this paper, the state-space concept in conjunction with the Jordan canonical form is presented to solve the governing equations for the bending of cross-ply laminated composite beams, and the classical, first-order, second-order and third-order theories have been used in the analysis.

160 citations

Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this paper, a set of fundamental dynamic equations of a one-dimensional higher order theory for laminated composite beams subjected to axial stress is derived through Hamilton's principle, which can predict the natural frequencies, buckling stresses and interlaminar stresses of multilayered composite beams as accurately as three-dimensional elasticity solutions.

143 citations

References
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Journal ArticleDOI
TL;DR: In this article, the correction for shear of the differential equation for transverse vibrations of prismatic bars is discussed, where the correction is based on the correction of the transverse vibration of a prismatic bar.
Abstract: (1921). LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 41, No. 245, pp. 744-746.

2,255 citations

Journal ArticleDOI
TL;DR: In this article, the transverse vibrations of bars of uniform cross-section were studied and the authors proposed a method to measure the transversal vibrations of a bar of uniform shape.
Abstract: (1922). X. On the transverse vibrations of bars of uniform cross-section. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 43, No. 253, pp. 125-131.

917 citations

Journal ArticleDOI
M. Levinson1
TL;DR: In this paper, a new theory for beams of rectangular cross-section which includes warping of the cross-sections is presented, and results for two typical static examples are given for both the new theory and Timoshenko beam theory.

471 citations

Journal ArticleDOI
TL;DR: In this paper, the finite element equations for a variationally consistent higher-order beam theory are presented for the static and dynamic behavior of rectangular beams, which correctly accounts for the stress-free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution.

364 citations

Journal ArticleDOI
TL;DR: In this paper, the buckling and free-vibration behavior of cross-ply rectangular composite laminates under various boundary conditions was studied. But the bucklings and free vibration properties were not investigated.
Abstract: Analytical and finite-element solutions of the classical, first-order, and third-order laminate theories are developed to study the buckling and free-vibration behavior of cross-ply rectangular composite laminates under various boundary conditions

252 citations