A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams

Hashemi, Seyed M.; Richard, Marc J.

doi:10.1016/s1270-9638(00)00114-0

Cited by 48 publications

(59 citation statements)

References 14 publications

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“…So the research and development of composite materials in the design of aerospace, mechanical and civil structures has grown tremendously in the past few decades. A variety of structural components made of composite materials such as turbine blades, vehicle axles, aircraft wing, and helicopter blade can be approximated as laminated composite beams, which requires a deeper understanding of the vibration characteristics of the composite beams as mentioned by Reddy [6] has written a higher order theory for laminated composite plates and concluded the possible in some cases to disregard the effects of shear deformation and rotary inertia. Dancila and Armanios [14] have used an analytical model, considering the bending torsion and tensile torsion couplings in a closed section, and validated the results with a finite element model.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Rand [4][5] has worked on laminated composite beam and calculated its shear stresses using a complete out-of-plane shear deformation model. Hashemi and Richard [6] have investigated a dynamic finite element model for free vibration of bending-torsion coupled beams. Chandra et al [7] calculated static displacements of a carbon/epoxy beam with a box section, comparing experimental results with those found by a finite element model and an analytical model.…”

Section: Literature Reviewmentioning

confidence: 99%

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Effect of Fiber Orientation and Position of Circular Hole on Torsional Natural Frequency of Laminated Composite Beam

Padhi¹

2018

IJRASET

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The composite materials are well known by their excellent combination of high structural stiffness and low weight. The main feature of these anisotropic materials is their ability to be tailored for specific applications by optimizing design parameters such as stacking sequence, ply orientation and performance targets. Finding free torsional vibrations characteristics of laminated composite beams is one of the bases for designing and modeling of industrial products. With these requirements, this work considers the free torsional vibrations for laminated composite beams of doubly symmetrical cross sections. The torsional vibrations of the laminated beams are analyzed analytically based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes due to fiber orientation of the laminated beams are neglected. Also, the torsional vibrations of the laminated beams analyzed by shear deformation theory in which the shear deformation effects are considered. Numerical analysis has been carried out using finite element method (FEM). The finite element software package ANSYS 13.0 is used to perform the numerical analyses using an eight-node layered shell element to describe the torsional vibration of the laminated beams. The rotary inertia and shear deformation effects of the element are taken. The influence of fiber directions and stacking sequences of laminates on torsional natural frequencies were investigated. Also, the effects of boundary conditions are demonstrated. Numerical results, obtained by the ANSYS 13.0, classical lamination theory, and shear deformation theory are presented to highlight the effects of fibers orientation and layers stacking sequence on torsional frequencies of the beams. The results obtained by ANSYS are compared against the classical lamination theory, as well as shear deformation theory.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Effect of Fiber Orientation and Position of Circular Hole on Torsional Natural Frequency of Laminated Composite Beam

Padhi¹

2018

IJRASET

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“…The determinant function also produces undefined regions, known as poles [41], where the determinant value approaches infinity. These regions represent the denominator of the determinant function [12].…”

Section: Shock and Vibrationmentioning

confidence: 99%

“…The matrix thus developed is not case specific and can be assembled. The boundary and loading conditions are applied in a manner similar to FEM [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

Elahi

Hashemi

2017

Shock and Vibration

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Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MATLAB5 software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

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“…Since its inception, the DFE method has been used in beam, beam-like, and blade vibration modelling and analysis. Hashemi and his coworkers (see, e.g., [18][19][20]) have extensively studied the free vibration of various beam configurations, such as isotropic, sandwich, composite, and thin-walled beams subjected to diverse loading configurations, using the Dynamic Finite Element (DFE) method. The results have consistently shown the DFE method to have a higher accuracy and rate of convergence compared to conventional FEM owing to the increased efficiency of the frequency-dependent, trigonometric shape functions based on the exact solutions to the governing equation which the DFE method employs.…”

Section: Introductionmentioning

confidence: 99%

New Frequency‐Dependent Trigonometric Interpolation Functions for the Dynamic Finite Element Analysis of Thin Rectangular Plates

Jayasinghe

Hashemi

2018

Shock and Vibration

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The Dynamic Finite Element (DFE) formulation is a superconvergent, semianalytical method used to perform vibration analysis of structural components during the early stages of design. It was presented as an alternative to analytical and numerical methods that exhibit various drawbacks, which limit their applicability during the preliminary design stages. The DFE method, originally developed by the second author, has been exploited heavily to study the modal behaviour of beams in the past. Results from these studies have shown that the DFE method is capable of arriving at highly accurate results with a coarse mesh, thus, making it an ideal choice for preliminary stage modal analysis and design of structural components. However, the DFE method has not yet been extended to study the vibration behaviour of plates. Thus, the aim of this study is to develop a set of frequencydependent, trigonometric shape functions for a 4-noded, 4-DOF per node element as a basis for developing a DFE method for thin rectangular plates. To this end, the authors exploit a distinct quasi-exact solution to the plate governing equation and this solution is then used to derive the new, trigonometric basis and shape functions, based on which the DFE method would be developed.

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A Dynamic Finite Element (DFE) method for free vibrations of bending-torsion coupled beams

Cited by 48 publications

References 14 publications

Effect of Fiber Orientation and Position of Circular Hole on Torsional Natural Frequency of Laminated Composite Beam

Effect of Fiber Orientation and Position of Circular Hole on Torsional Natural Frequency of Laminated Composite Beam

A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

New Frequency‐Dependent Trigonometric Interpolation Functions for the Dynamic Finite Element Analysis of Thin Rectangular Plates

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