Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method

Li, Jun; Li, Xiaobin; Hu, Hua

doi:10.1007/s00419-008-0276-8

Cited by 35 publications

(5 citation statements)

References 25 publications

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“…Chen et al [27] also proposed an analytical solution based on state-space differential quadrature for vibration of composite beams. By using the dynamic stiffness matrix method, Jun et al [28,29] calculated the natural frequencies of composite beams based on third-order beam theory. A literature review shows that although Ritz procedure is efficient to deal with static, buckling and vibration problems of composite beams with various boundary conditions, the research on this interesting topic is still limited.…”

Section: Introductionmentioning

confidence: 99%

Trigonometric-series solution for analysis of laminated composite beams

Nguyen

et al. 2017

Composite Structures

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.) Trigonometric-series solution for analysis of laminated composite beams

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Section: Introductionmentioning

confidence: 99%

Trigonometric-series solution for analysis of laminated composite beams

Nguyen

et al. 2017

Composite Structures

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“…It should be noted that for the laminated beam, the membrane forces N y and N xy , the bending moment M y , the higher-order bending and twisting moments P y and P xy are all zero. 21 In other words, one can say: Equation (1) for the remaining resultant force and moments can be rewritten as:…”

Section: Derivation Of Kinetic and Potential Energies For Each Sub-beammentioning

confidence: 99%

Dynamic analysis of generally laminated composite beam with a delamination based on a higher-order shear deformable theory

Jafari-Talookolaei

Abedi

Kargarnovin

et al. 2013

Journal of Composite Materials

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In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson’s effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure–tensile, flexure–twist and tensile–twist couplings) are considered in the formulation. Results are extracted based on two methods namely the Eigen-value techniques for frequencies and the Newmark method to calculate the transient response. Then, the obtained results have been verified with the other results available in the literature and very good agreements have been observed. Furthermore, the new results have been obtained for the case where the excitation was due to a moving/non-moving force.

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“…The authors compared the results of the three theories with the first order shear theory and with their results to determine the most effective method. Jun et al (2009) introduced TSDT using the dynamic stiffness method. They also examined the influences of Poisson’s ratio, material anisotropy, slenderness, and boundary condition on the natural frequencies of the beams.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of cracked beam based on Reddy beam theory by finite element method

Taima

El-Sayed

Shehab

et al. 2022

Journal of Vibration and Control

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The lateral vibration of cracked isotropic thick beams is investigated. Generally, the analysis of thick beam based on line elements can be undertaken using either Timoshenko beam theory or a third order beam theory (TSDT) such as Reddy beam theory. TSDT is superior to Timoshenko beam theory, as it eliminates the need for a shear correction coefficient. However, there is no available solution for a cracked beam based on Reddy beam theory which is the main focus of this paper. The investigated beam is divided into several elements where their stiffness and mass matrices are derived using Reddy beam theory. Each element has two nodes with 3 degrees of freedom (1 lateral and 2 rotational) at each node. The crack was modeled using two rotating springs with stiffnesses that varied with crack depth. These elements are used to connect the adjacent beam elements. The impact of boundary conditions, slenderness ratio, crack location, and crack depth are investigated. In addition, experimental and finite element analyses of cracked steel beams is undertaken to validate the results of the present model. The results show that the maximum deviation between the analytical and the experimental results is less than 3% up to the third mode shape.

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Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method

Cited by 35 publications

References 25 publications

Trigonometric-series solution for analysis of laminated composite beams

Trigonometric-series solution for analysis of laminated composite beams

Dynamic analysis of generally laminated composite beam with a delamination based on a higher-order shear deformable theory

Vibration analysis of cracked beam based on Reddy beam theory by finite element method

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