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.
Abstract: A general finite element based on a first-order deformation theory is developed to study the free vibration characteristics of laminated composite beams The formulation accounts for bi-axial bending as well as torsion The required elastic constants are derived from a two-dimensional elasticity matrix As many results are not available for bi-axial bending vibration of beams, the obtained numerical results are compared with those existing in the literature for the case of uni-axial bending The predominating modes for the first eight frequencies for different fibre orientations are presented The numerical results given explain the effects of shear deformation on various vibrational frequencies of angle ply laminates The parametric study conducted brings out the influence of beam geometry and boundary conditions on natural frequencies
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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.
Abstract: Laminated composite and sandwich structures are lightweight structures that can be found in many diverse applications especially civil, mechanical and aerospace engineering. The rapid increase in the industrial use of these structures has necessitated the development of new theories that suitable for the bending, buckling and vibration analysis of composite structures. Many review articles are reported in the literature on laminated composite plates and shells in the last few decades. But, in the whole variety of literature very few review articles are available exclusively on laminated composite and sandwich beams. In this article, 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 addition to this, literature on finite element modeling of laminated and sandwich beams based on classical and refined theories is also reviewed. Finally, displacement fields of various equivalent single layer and layerwise theories are summarized in the present study for the reference of researchers in this area. This article cites 515 references and highlights, the possible scope for the future research on laminated composite and sandwich beams.
240 citations
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.
Abstract: Laminated composite straight and curved beams are frequently used in various engineering applications. This work attempts to review most of the research done in recent years (1989–2012) on the vibration analysis of composite beams. This review is conducted 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 (viscoelastic, rotating, tip mass and others) and other areas that have been considered in research. A simple classic and shear deformation model would be explained that can be used for beams with any laminate.
134 citations
TL;DR: In this paper, a dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory, where the influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformations and rotary inertia are incorporated in the formulation.
Abstract: A dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory. The influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformation and rotary inertia are incorporated in the formulation. The dynamic stiffness matrix is formulated based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The effects of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are studied in detail by particular carefully selected examples. The numerical results of natural frequencies and mode shapes are presented and, whenever possible, compared to those previously published solutions in order to demonstrate the correctness and accuracy of the present method.
70 citations
TL;DR: In this paper, the exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is derived, and a refined laminated beam constitutive equation is derived that takes into account the breadth direction strains.
Abstract: The exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is developed in this paper. A refined laminated beam constitutive equation is derived that takes into account the breadth direction strains. The dynamic stiffness matrix is formulated directly in an exact sense by solving the governing differential equations of motion that describe the deformations of laminated beams according to the trigonometric shear deformation theory, which includes the sinusoidal variation of the axial displacement over the cross-section. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick–Williams algorithm to compute the natural frequencies and mode shapes of the composite beams. The results obtained from the present theory are compared with those available in the literature wherever possible.
58 citations
TL;DR: In this paper, the effects of shear deformation, rotary inertia, non-uniformity of the cross-section, and angle of fibre orientation on dynamic behavior are investigated.
Abstract: This study is intended to analyze free and forced vibrations of non-uniform composite beams in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The Timoshenko beam theory is adopted in the derivation of the governing equation. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. The effects of shear deformation, rotary inertia, non-uniformity of the cross-section are considered in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem accurately. The effects of non-uniformity parameters and angle of fibre orientation on dynamic behaviour are investigated.
48 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.
1,127 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.
280 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.
Abstract: Exact solutions are presented for the free vibration of symmetrically laminated composite beams. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Results have been presented to demonstrate the effect of shear deformation, material anisotropy and boundary conditions on the natural frequencies of advanced composite beams.
208 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.
Abstract: A finite element model based on a higher-order shear deformation theory is developed to study the free vibration characteristics of laminated composite beams. The Poisson effect, which is often neglected in one-dimensional laminated beam analysis, is incorporated in the formulation of the beam constitutive equation. Also, the effects of in-plane inertia and rotary inertia are considered in the formulation of the mass matrix. Numerical results for symmetrically laminated composite beams are obtained as special cases and are compared with other exact solutions available in the literature. A variety of parametric studies are conducted to demonstrate the influence of beam geometry, Poisson effect, ply orientation, number of layers and boundary conditions on the frequencies and mode shapes of generally layered composite beams.
125 citations