Vibration Analysis of Twisted Cantilevered Conical Composite Shells

Lee, Joseph; Yeom, Chan-Hong; Lee, In

doi:10.1006/jsvi.2001.4207

Cited by 23 publications

(9 citation statements)

References 17 publications

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“…Rebière and Gamby [2004] employed a variational approach to model the behavior of composite cross-ply laminates damaged by transverse and longitudinal cracking and delamination, while Aydogdu and Timarci [2003] and Tripathi et al [2007] studied the free-vibration behavior of a delaminated composite employing the finite element method. Lee et al [2002] carried out the vibration analysis of a twisted cantilevered conical composite shell using a finite element method based on the Hellinger-Reissner principle, again for single and multiple delaminations. Parhi et al [2001] and Aymerich et al [2009] have demonstrated the effects of multiple delamination on laminated composites using FEM.…”

Section: Resultsmentioning

confidence: 99%

Untitled

2012

J. Mech. Mater. Struct.

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A generalized plane strain micromechanical model is developed to predict the stress and strain fields and overall elastic properties of a unidirectional fiber-reinforced composite subjected to various axial and transverse normal loading conditions using a least-squares-based differential quadrature element method (DQEM). The representative volume element (RVE) of the composite consists of a quarter of the fiber surrounded by matrix to represent the real composite with a repeating square array of fibers. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain and the new versions of the governing equations and boundary conditions are also derived. The fully bonded fiber-matrix interface condition is considered and the displacement continuity and traction reciprocity are imposed on the fiber-matrix interface. Application of DQEM to the problem leads to an overdetermined system of linear equations mainly due to the particular periodic boundary conditions of the RVE. A least-squares differential quadrature element method is used to obtain solutions for the governing partial differential equations of the problem. The numerical results are in excellent agreement with the available analytical and finite element studies. Moreover, the results of this study reveal that the presented model can provide highly accurate results with a very small number of elements and grid points within each element. In addition, the model shows advantages over conventional analytical models for fewer simplifying assumptions related to the geometry of the RVE.

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Section: Resultsmentioning

confidence: 99%

Untitled

2012

J. Mech. Mater. Struct.

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“…4 studied the vibration characteristics of pretwisted conical shell, while Lee et al. 5 worked on the vibration analysis of twisted cantilever conical composite shell based on the Hellinger–Reissner principle. McGee and Chu 6 reported the three-dimensional continuum vibration analysis including full geometric nonlinearities and centrifugal accelerations in composite blades, while the free vibration characteristics of rotating laminated composite pretwisted cantilever plates were investigated by Karmakar and Sinha.…”

Section: Introductionmentioning

confidence: 99%

Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

Maji

Rout²,

Karmakar

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Finite element procedure is employed to analyze the free vibration characteristics of rotating functionally graded carbon nanotubes reinforced composite conical shell with pretwist under the thermal environment. In this paper, four types of carbon nanotube grading are considered, wherein the distribution of carbon nanotubes are made through the thickness direction of the conical shell. An eight-noded isoparametric shell element is used in the present formulation to model the panel based on the first-order shear deformation theory. For moderate rotational speeds, the generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, neglecting the Coriolis effect. The finite element code is developed to investigate the effect of twist angle, temperature, aspect ratio, and rotational speed on natural frequencies. The mode shapes of a carbon nanotube reinforced functionally graded conical shell at different twist angles and rotational speeds are also presented.

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“…On the contrary, free vibration of laminated composite employing finite element method analyzed by both Aydogdu and Timarci [12] as well as Tripathi et al [26]. Further, Lee et al [7] exhibited the vibration analysis of twisted cantilevered conical composite shell by using finite element method based on the Hellinger-Reissner principle. Of late, Karmakar and kishimoto [1] investigated on free vibration of delaminated rotating cylindrical shells.…”

Section: Introductionmentioning

confidence: 99%

Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

Dey

Karmakar

2012

Shock and Vibration

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Abstract. Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

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Vibration Analysis of Twisted Cantilevered Conical Composite Shells

Cited by 23 publications

References 17 publications

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Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

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