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Journal ArticleDOI

A generalized element for the free vibration analysis of composite beams

03 Jun 1994-Computers & Structures (Pergamon)-Vol. 51, Iss: 5, pp 607-610
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.
Citations
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Dissertation
01 Mar 2013
TL;DR: In this paper, the free and the forced vibration response of symmetric linear-thickness-and-width-tapered composite beams are considered considering a variety of tapered configurations according to different types of plies drop-off configurations.
Abstract: Variable-width variable-thickness laminated composite beams provide stiffness-tailoring and mass-tailoring design capabilities. They are increasingly and widely being used in engineering applications including robotic manipulators, aircraft wings, space structures, helicopter blades and yokes, turbine blades, and civil infrastructure. These structures are subjected to time-varying loadings. In the present work, the free and the forced vibration response of symmetric linear-thickness-and-width-tapered laminated composite beams are considered. Considering a variety of tapered configurations according to different types of plies drop-off configurations, both conventional and advanced finite element formulations are developed based on the Kirchhoff and cylindrical laminated beam bending theories. Natural frequencies, mode shapes and forced vibration response of different types of internally-tapered composite beams are determined. Rigid and elastic supports are considered for the free vibration response of the beams. Rigid supports are considered for the forced vibration response of the beams. Comparison of the finite element solution with the Rayleigh-Ritz solution is performed. A parametric study is conducted to investigate the effects of taper configurations, thickness-tapering angle, width-ratios, damping and boundary conditions on the free and forced vibration response of the variable-thickness variable-width laminated composite beams.

3 citations


Cites background from "A generalized element for the free ..."

  • ...Nabi and Ganesan [43] developed a general finite element formulation based on a first-order shear deformation theory with 16 degrees of freedom per element to study the free vibration characteristics of laminated composite beams....

    [...]

  • ...Uniform-width thickness-tapered laminated composite beams have been studied for their dynamic response in the works of Ganesan and Zabihollah [41] and [42] using an advanced finite element formulation and parametric study....

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  • ...Rao and Ganesan [21] investigated the harmonic response of uniform-width thickness-tapered composite beams with general boundary conditions using finite element method....

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  • ...Then, I offer my sincerest gratitude to my supervisor, Dr. Rajamohan Ganesan, who has supported me, throughout my thesis research with his enthusiasm, inspiration, patience and immense knowledge....

    [...]

  • ...Signed by the final Examining Committee: ___________________________________ Chair Dr. O. Kuzgunkaya ___________________________________ Examiner Dr. M. Hojjati ___________________________________ Examiner Dr. A. Amer (external) ___________________________________ Supervisor Dr. R. Ganesan Approved by: ___________________________________________________ Dr. S. Narayanswamy, MASc Program Director Department of Mechanical and Industrial Engineering ___________________________________ Dean Dr. Robin Drew Faculty of Engineering & Computer Science Date: _____________ iii ABSTRACT Vibrations of Thickness-and-width Tapered Laminated Composite Beams with Rigid and Elastic Supports Pooya Salajegheh Variable-width variable-thickness laminated composite beams provide stiffness- tailoring and mass-tailoring design capabilities....

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Journal ArticleDOI
TL;DR: In this article, a parametric study on the free vibration frequencies of symmetric cross-ply laminated arches with constant curvature is performed based on the first order shear deformation theory.
Abstract: A parametric study on the free vibration frequencies of symmetric cross-ply laminated arches with constant curvature is performed based on the first order shear deformation theory. Governing equations of symmetric laminated circular arches made of a linear, homogeneous, and orthotropic material are obtained in a straightforward manner based on the classical beam theory. The transfer matrix method is used for the free vibration analysis of the continuous parameter system. The rotary inertia effects are also incorporated in the formulation. The effects all of the slenderness ratios (20 and 100), the number of plies (4 and 100), the opening angles (0°-360°), the boundary conditions (fixed-free, fixed-hinged, and fixed-fixed), the width/thickness ratios of rectangular sections (10 and 0.1) and the material types (Graphite-epoxy and Kevlar-epoxy) on the natural frequencies are presented in both graphical and tabular forms and discussed briefly.

2 citations

Dissertation
27 Sep 2013
TL;DR: In this paper, the free and the forced vibration response of symmetric linear-thickness-and width-tapered composite beams are considered considering a variety of tapered configurations according to different types of plies drop-off configurations.
Abstract: Tapered laminated composite beams provide stiffness-tailoring and mass-tailoring design capabilities. They are increasingly and widely being used in engineering applications including robotic manipulators, aircraft wings, space structures, helicopter blades and yokes, turbine blades, and civil infrastructure. In the present work, the free and the forced vibration response of symmetric linear-thickness-and-width-tapered laminated composite beams are considered. Considering a variety of tapered configurations according to different types of plies drop-off configurations both conventional and hierarchical finite element formulations are developed based on cylindrical laminated beam bending theory. Natural frequencies, mode shapes and forced vibration response of different types of internally-tapered composite beams are determined. Comparison of the hierarchical finite element solution with the Rayleigh-Ritz and a higher-order finite element solution is performed. A parametric study is conducted to investigate the effects of boundary conditions, width-ratio, taper configurations, thickness-tapering angle, laminate configuration, compressive axial force and damping on the free and forced vibration response of thickness- and width-tapered laminated composite beams.

2 citations


Cites background from "A generalized element for the free ..."

  • ...Then, I offer my sincerest gratitude to my supervisor, Dr. Rajamohan Ganesan, who has supported me, throughout my thesis research with his kind attention, inspiring guidance, patience and immense knowledge....

    [...]

  • ...Thickness-tapered laminated composite beams have been studied for their response in the works of Ganesan and Zabihollah [20, 21] using an advanced finite element formulation and parametric study....

    [...]

  • ...Roy and Ganesan [18] have studied the response of a tapered composite beam with general boundary conditions....

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  • ...Nabi and Ganesan [26] developed a general finite element formulation based on FSDT with 16 degrees of freedom per element to study the free vibration characteristics of laminated composite beams....

    [...]

  • ...Signed by the final Examining Committee: ___________________________________ Chair Dr. Z.C. Chen ___________________________________ Examiner Dr. S.V. Hoa ___________________________________ Examiner Dr. Y. Shayan (external) ___________________________________ Supervisor Dr. R. Ganesan Approved by: ___________________________________________________ Chair of Department or Graduate Program Director ___________________________________________________ Dean of Faculty Date: September 30, 2013 iii ABSTRACT Vibration Analysis of Thickness- and Width-Tapered Laminated Composite Beams using Hierarchical Finite Element Method Mohammad Amin Fazili Tapered laminated composite beams provide stiffness-tailoring and mass-tailoring design capabilities....

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Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of thin-walled composite beam with channel sections is performed based on series solutions, and the dynamic stiffness matrix is presented using the homogeneous form of the simultaneous ordinary differential equations.
Abstract: Based on series solutions, the free vibration analysis of thin-walled composite beam with channel sections is performed. For this, the dynamic stiffness matrix is presented using the homogeneous form of the simultaneous ordinary differential equations. The general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing Vlasov's assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Then the exact dynamic stiffness matrix is determined using force-displacement relationships. In addition, the finite element model based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of this study, numerical solutions are presented and compared with the analytical solutions from other researchers and ...

2 citations


Cites methods from "A generalized element for the free ..."

  • ...Nabi and Ganesan (1994) studied bi-axial bending, axial, and torsional vibrations using the finite element method and the first-order shear deformation theory....

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Dissertation
26 Jul 2016
TL;DR: In this paper, free vibration and dynamic instability analyses of doubly-tapered rotating cantilever composite beams are conducted considering three different types of vibrations (out-ofplane bending, in-plane bending and axial). Rayleigh-Ritz approximate method based on classical lamination theory has been employed to formulate the free vibration problem and solve it.
Abstract: Due to the outstanding engineering properties, such as high strength/stiffness to weight ratios, capability to be stiff at one location and flexible at another location and favorable fatigue characteristics, doubly-tapered composite beam is used in the rotating structures such as helicopter rotor blades and wind turbine blades. Due to its distinct characteristics from static beam and wide range of applications, rotating beam requires a comprehensive research to understand its dynamic response. Design of mechanical components using doubly-tapered composite beams requires a better understanding of their behavior in free vibration and their dynamic instability. In the present thesis, free vibration and dynamic instability analyses of doubly-tapered rotating cantilever composite beams are conducted considering three different types of vibrations (out-of-plane bending, in-plane bending and axial). Rayleigh-Ritz approximate method based on classical lamination theory has been employed to formulate the free vibration problem and solve it. Bolotin’s method is applied to determine the instability regions. Numerical and symbolic computations have been performed using the software MATLAB. The results for natural frequencies have been validated using Finite Element Analysis (FEA) tool ANSYS. A comprehensive parametric study is conducted in order to understand the effects of various design parameters. Moreover, critical speed of doubly-tapered rotating composite beam is determined and change of critical speed due to double-tapering is investigated. Also, change in maximum deflection due to rotational velocity and double-tapering is observed in this thesis. The material chosen in this thesis for numerical calculations is NCT-301 graphite-epoxy prepreg.

2 citations


Cites background from "A generalized element for the free ..."

  • ...Nabi and Ganesan [53] developed a general finite element formulation based on a first-order shear deformation theory with 16 degrees of freedom per element to study the free vibration characteristics of laminated composite beams....

    [...]

  • ...Ganesan and Zabihollah [11] analyzed the free vibration and buckling of uniform-width thickness-tapered composite beams using both conventional and advanced finite element formulations....

    [...]

  • ...Then I wish to express my most sincere gratitude to my supervisor Dr. Rajamohan Ganesan for his time, patience, tolerance and keen guidance especially for the thesis writing corrections....

    [...]

References
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Book
28 Feb 1986
TL;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

Journal ArticleDOI
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

Journal ArticleDOI
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

Book
01 Jan 1969

144 citations

Journal ArticleDOI
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