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.
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TL;DR: In this paper, the effects of shear deformation, axial force and end condition on the natural frequencies, buckling loads and/or mode shapes of the laminated composite beams are thoroughly analyzed.
34 citations
TL;DR: In this article, the stiffness method is used for the solution of the purely in-plane free vibration problem of symmetric cross-ply laminated beams, and the rotary inertia, axial and transverse shear deformation effects are considered in the mathematical model by the first-order shear deformability theory.
30 citations
TL;DR: In this article, a modeling method for the modal analysis of a rotating composite cantilever beam is presented, where linear differential equations of motion are derived using the assumed mode method.
Abstract: A modeling method for the modal analysis of a rotating composite cantilever beam is presented in this paper. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. Symmetrical laminated composite beams are considered to obtain the numerical results. The effects of the dimensionless angular velocity, the hub radius and the fiber orientation angle on the variations of modal characteristics are investigated.
29 citations
TL;DR: In this article, the spectral finite element method is adopted with particular reference to the Wittrick-Williams algorithm when investigating the free vibration of axially loaded composite beams, and the exact spectral element matrix is established by directly solving the governing differential equations of the laminated beams in free vibration.
23 citations
TL;DR: In this paper, the free vibration response of laminated composite and sandwich beams has been studied by using a recently developed C0 finite element beam model, which is based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core.
Abstract: Free vibration response of laminated sandwich beams having a soft core is studied by using a recently developed C0 finite element beam model. The model has been developed based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. Numerical examples on free vibration covering different features of laminated composite and sandwich beams are presented. Many new results are also presented which should be useful for future research.
22 citations
Cites background from "A generalized element for the free ..."
...For the static and buckling analysis of sandwich plates with soft compressible core, Pandit et al. (2008a,b) proposed a HOZT. Recently Pandit et.al (2010) have presented an improved HOZT for vibration of soft core sandwich plates with randommaterial properties....
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...Nabi and Ganesan (1994) have developed a two node finite element (FE) beam model based on FSDT considering bi-axial bending, extensional and torsional effects as well as including shear deformation for the free vibration analysis of composite beam with arbitrary boundary conditions....
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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