Structural dynamic analysis of composite beams
TL;DR: In this paper, the structural dynamic characteristics of a composite beam are analyzed and the results of the analysis are compared with those available in the literature, based on the comparison, the influence of the warping function in defining the coupling terms in the modulus approach and also on the natural frequencies of the beam has been identified.
About: This article is published in Journal of Sound and Vibration.The article was published on 1990-12-22. It has received 34 citations till now. The article focuses on the topics: Beam (structure) & Elastic modulus.
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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 paper, the authors developed an exact dynamic stiffness matrix of a composite beam with the effects of axial force, shear deformation and rotatory inertia taken into account, for an axially loaded composite Timoshenko beam.
122 citations
TL;DR: An exact dynamic stiffness matrix method has been developed to predict the free vibration characteristics of composite beams (or simple structures assembled from them) for which the bending and torsional displacements are (materially) coupled as discussed by the authors.
Abstract: An exact dynamic stiffness matrix method has been developed to predict the free vibration characteristics of composite beams (or simple structures assembled from them) for which the bending and torsional displacements are (materially) coupled. To achieve this, an explicit expression is presented for each of the elements of the dynamic stiffness matrix of a bending-torsion coupled composite beam. This was made possible by performing symbolic computing with the help of the package Reduce. Programming the stiffness expressions in Fortran on a SUN SPARC station indicates about 75% savings in computer time when compared with the matrix inversion method normally adopted in the absence of such expressions. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick-Williams algorithm to compute the natural frequencies and mode shapes of composite beams with substantial coupling between bending and torsional displacements. The results obtained from the present theory are compared with those available in the literature and discussed.
113 citations
TL;DR: In this paper, a generalized modal approach is presented to solve the equations of motion of a laminated composite beam obtained with a third-order shear deformation theory, where the biorthonormal eigenfunctions of the differential equations expressed in the state form are used to decouple the equations.
Abstract: A generalized modal approach is presented to solve the equations of motion of a laminated composite beam obtained with a third-order shear deformation theory. The biorthonormal eigenfunctions of the differential equations expressed in the state form are used to decouple the equations. To obtain these eigenfunctions for beams with any arbitrary beam boundary conditions, a method is presented. The solution obtained by this approach is used to calculate the beam response for spatially and temporally correlated random loads. Several sets of numerical results are presented to demonstrate the importance of shear deformations in the dynamic analysis of composite beams.
56 citations
TL;DR: In this article, a novel explicit analytical solution is proposed for obtaining twisting deformation and optimal shape control of smart laminated cantilever composite plates/beams using inclined piezoelectric actuators.
44 citations
Cites background from "Structural dynamic analysis of comp..."
...The effect of warping torsion on natural frequency of a composite beam, when considering the transverse shear deformation for various beam aspect ratios, was investigated in multiple studies[41][42][43]....
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TL;DR: In this article, experimental results were obtained for the natural frequencies and the mode shapes of graphite-epoxy and boron epoxy composite materials having fiber orientations of 0°, 15°, 30° and 90° with respect to cantilever beam axes.
Abstract: Experimental results were obtained for the natural frequencies and the mode shapes of graphite-epoxy and boron-epoxy composite materials having fiber orientations of 0°, 15° , 30° and 90° with respect to cantilever beam axes. Certain elastic constants were experimentally determined and used in a programmed numerical solution in which rotary inertia, trans verse shear, and coupled bending-torsion effects were included. The experi mental results for the 15° and 30° beams gave a clear indication of the interaction between bending and twisting and good agreement was obtained with the numerical results.
118 citations
TL;DR: In this article, a formulation, an efficient solution procedure, a microcomputer program, and a graphics routine for an anisotropic symmetrically laminated beam finite element in cluding the effect of shear deformation is introduced.
Abstract: A formulation, an efficient solution procedure, a microcomputer program, and a graphics routine for an anisotropic symmetrically laminated beam finite element in cluding the effect of shear deformation is introduced. The emphasis of the formulation and solution procedure is for simplicity, efficiency, and easy implementation on microcomputers. The element possesses six d.o.f.'s at each of the two nodes: trans verse deflection and slope due to bending and shear, respectively, and a twisting angle and its derivative with respect to the beam axis. The formulation, solution procedure, and the program have been evaluated by performing a systematic choice of examples; whenever possible, the present solutions are compared with alternative existing solu tions.
92 citations
TL;DR: In this paper, the free-vibration characteristics of directionally stiffened, laminated composite beam-like structures such as high-aspect-ratio lifting surfaces are discussed.
Abstract: This paper discusses the free-vibration characteristics of directionally stiffened, laminated composite beamlike structures such as high-aspect-ratio lifting surfaces. A bounded nondimensional parameter, , is defined to describe the degree of elastic coupling between bending curvature and twist rate for a laminated beam. In addition, three different stiffness models commonly used to model laminated beam/tube deformation are described and compared. Using one of these models, the ability of the laminate design to control mode shape or node line characteristics is illustrated for a cross-coupled laminated cantilever beam. Finally, the effect of the nondimensional cross-coupling parameter, i/s on cantilever beam free-vibration node line positions and frequencies is illustrated, independent of a specific laminate design.
92 citations
TL;DR: In this paper, a theoretical analysis of the vibrations of fiber reinforced composite beams is presented, where a continuous model is used and both shear and rotatory inertia are included, and an illustrative example is worked out to show the effect of shear deformation and fibre orientation.
89 citations