Elasticity-based free vibration of anisotropic thin-walled beams

Heyliger, Paul R.

doi:10.1016/j.tws.2015.06.014

Cited by 12 publications

(4 citation statements)

References 42 publications

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“…Since the early work of Bauld and Tzeng [1], many studies have been done to develop appropriate models for vibration [2][3][4][5][6][7][8][9][10][11][12] and lateral buckling problems [13][14][15][16][17][18][19][20] of thin-walled composite beams and only a few of them are cited here. More details of these works can be found in some books written by Kollar and Springer [21], Librescu and Song [22], and Hodges [23].…”

Section: Introductionmentioning

confidence: 99%

Vibration and lateral buckling optimisation of thin-walled laminated composite channel-section beams

Nguyễn

Lee

et al. 2016

Composite Structures

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Citation: Nguyen, Hoang, Lee, Jaehong, Vo, Thuc and Lanc, Domagoj (2016) 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.) AbstractThis study presents vibration and lateral buckling optimisation of thin-walled laminated composite beams with channel sections. While flanges' width, web's height, and fibre orientation are simultaneously treated as design variables, the objective function involves maximising the fundamental frequency and critical buckling moment. Based on the classical beam theory, the beam element with seven degrees of freedom at each node is developed to solve the problem. Micro Genetic Algorithm (micro-GA) is then employed as an optimisation tool to obtain optimal results. A number of composite channel-section beams with different types of boundary conditions, span-to-height ratios, and lay-up schemes are investigated for the optimum design. The outcomes reveal that geometric parameters severely govern the optimal solution rather than the fibre orientation and it is considerably effective to use micro-GA compared with regular GA in term of optimal solution and convergence rate.

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Section: Introductionmentioning

confidence: 99%

Vibration and lateral buckling optimisation of thin-walled laminated composite channel-section beams

Nguyễn

Lee

et al. 2016

Composite Structures

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“…Computers and Structures. 80 (7)(8), 691-695. The subject of the considerations was the vibrations of a prismatic beam with any cross section.…”

Section: Introductionmentioning

confidence: 99%

“…Thin-Walled Structures. 43 10 (7)(8), 671-683., a nonlinear finite element with two joints and seven degrees of freedom was formulated and used to analyse the post-buckling behaviour of a thinwalled beam. The nonlinear equations stemming from this problem were solved using the iterative-incremental Newton-Raphson method.…”

Section: Introductionmentioning

confidence: 99%

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Szybiński

Ruta

2019

Studia Geotechnica Et Mechanica

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This article deals with the vibrations of a nonprismatic thin-walled beam with an open cross section and any geometrical parameters. The thin-walled beam model presented in this article was described using the membrane shell theory, whilst the equations were derived based on the Vlasov theory assumptions. The model is a generalisation of the model presented by Wilde (1968) in ‘The torsion of thin-walled bars with variable cross-section’, Archives of Mechanics, 4, 20, pp. 431–443. The Hamilton principle was used to derive equations describing the vibrations of the beam. The equations were derived relative to an arbitrary rectilinear reference axis, taking into account the curving of the beam axis and the axis formed by the shear centres of the beam cross sections. In most works known to the present authors, the equations describing the nonprismatic thin-walled beam vibration problem do not take into account the effects stemming from the curving (the inclination of the walls of the thin-walledcross section towards to the beam axis) of the analysed systems. The recurrence algorithm described in Lewanowicz’s work (1976) ‘Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series’, Applicationes Mathematicae, XV(3), pp. 345–396, was used to solve the derived equations with variable coefficients. The obtained solutions of the equations have the form of series relative to Legendre polynomials. A numerical example dealing with the free vibrations of the beam was solved to verify the model and the effectiveness of the presented solution method. The results were compared with the results yielded by finite elements method (FEM).

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“…Detailed investigations of uncracked thin-walled straight and curved beams for different configurations have also been reported in previous studies. 27–39 It is important to mention that these available literatures did not discuss the mechanics of cracked thin-walled beams. Ricci and Viola 40 and Viola et al 41 studied the modal characteristics of cracked T-section beams by excluding warping effects.…”

Section: Introductionmentioning

confidence: 99%

A statistics and optimization-based approach for crack parameter identification in curved beams

Dey

Talukdar

2017

Structural Health Monitoring

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This article presents a study for detecting crack parameters (crack location and crack-depth ratio) in horizontally curved thin-walled channel section beams utilizing only dynamic information from a post-damage event based on combined statistical and optimization tools. A combined response surface methodology and genetic algorithm have been utilized in the present research work. Finite element computations based on design of experiment have been used in order to obtain the coefficients of a second-order polynomial model for the response surface function. Genetic algorithm is then used as a searching tool to determine the optimum parameters by minimizing an objective function which is formed as the root mean square of the errors between the computed responses from response surface functions and measured responses. Two cases of different subtended central angles are considered to illustrate the approach. Each case required 18 laboratory experiments to provide measured input to the proposed integrated approach. It was found that large variation can occur in the calculation of natural frequencies of thin-walled beams, when the effect of warping stiffness is neglected in mathematical model. This study reveals that the precision of the localization and quantification of cracks are dependent on subtended angle. The present method has great potential in crack detection as it does not require the response of an uncracked beam as baseline criteria.

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Elasticity-based free vibration of anisotropic thin-walled beams

Cited by 12 publications

References 42 publications

Vibration and lateral buckling optimisation of thin-walled laminated composite channel-section beams

Vibration and lateral buckling optimisation of thin-walled laminated composite channel-section beams

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

A statistics and optimization-based approach for crack parameter identification in curved beams

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