Dynamic stiffness formulation and free vibration analysis of functionally graded beams

Su, Huijuan; Banerjee, J.R.; Cheung, C. W.

doi:10.1016/j.compstruct.2013.06.029

Cited by 97 publications

(61 citation statements)

References 18 publications

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“…Due to the excellent properties in mechanical and thermal behaviours, a wide range of application for functionally graded (FG) structures can be found in different fields, leading to the intensive study in many types of FG structures in the last three decades. Chebyshev collocation method, finite element method and differential quadrature method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For analytical approaches, a Navier solution has been widely used to study various mechanical behaviours of simply supported beams [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

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An analytical method for vibration and buckling behaviours of Functionally Graded (FG) beams with various boundary conditions under mechanical and thermal loads is presented. Based on linear straindisplacement relations, equations of motion and essential boundary conditions are derived from Hamilton's principle. In order to account for thermal effects, three cases of the temperature rise through the thickness, which are uniform, linear and nonlinear, are considered. The exact solutions are derived using the state space approach. Numerical results are presented to investigate the effects of boundary conditions, temperature distributions, material parameters and slenderness ratios on the critical temperatures, critical buckling loads, and natural frequencies as well as load-frequencies curves, temperature-frequencies curves of FG beams under thermal/mechanical loads. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

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Section: Introductionmentioning

confidence: 99%

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Trinh

Vo²,

Thai

et al. 2016

Composites Part B: Engineering

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“…Su and Banerjee [5,6] developed dynamic stiffness method for FG beams' free vibration analysis using CBT and FOBT.…”

Section: Various Shear Deformation Theories and Analysis Techniques Hmentioning

confidence: 99%

Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach

Trinh

Osofero

et al. 2016

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.) AbstractThe state space approach is used to provide analytical solution for fundamental frequency analysis of functionally graded sandwich beams. The classical beam theory, first-order and higher-order shear deformation theories are employed to consider beams of various classical and non-classical boundaryconditions. Governing equations of motions are derived from Hamilton's principle. The research investigates the effect of boundary conditions on the fundamental frequency with nine combinations of classical boundary conditions created from clamped, hinged, pinned and free conditions in accordance with three combinations of non-classical boundary conditions created from the assumption of an elastic support. In addition, the influence of material parameter and arrangement of layers as well as the slenderness ratio in vibration of functionally graded sandwich beams is examined.

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“…The dynamic stiffness method and the W-W algorithm have been used in free vibration analysis of skeletal structures such as nonuniform Timoshenko beams [23], three-layered sandwich beams [24] and functionally graded beams [25]. However, limited attention is paid to the plates and shells from the computational community.…”

Section: Introductionmentioning

confidence: 99%

An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

Chen

2018

Mathematical Problems in Engineering

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An exact dynamic stiffness formulation is proposed for calculating the natural frequencies of shells of revolution based on the firstorder Reissner-Mindlin theory. Equations of motion are reduced to be one-dimensional, should the circumferential wave number is specified, and then are rewritten in Hamilton form. Therefore, a shell of revolution with a moderate thickness is analysed as a special skeletal structure with five degrees of freedom at element ends. Dynamic stiffnesses are constructed directly from the one-dimensional governing vibration equations using classic skeletal theory. Number of natural frequencies below a specific value is counted by applying the Wittrick-Williams (W-W) algorithm, and exact eigenvalues can be simply obtained using bisection method. A solution to the number of clamped-end frequencies J 0 in the W-W algorithm is also proposed and proven to be reliable. Numerical examples on a variety of shells with different boundary conditions are investigated, and results are well compared and validated. Influences of a variety of shell parameters on natural frequencies of both cylindrical and spherical shells are discussed in detail, demonstrating that the proposed dynamic stiffness formulation is applicable to analyse natural frequencies of moderately thick shells of revolution with high accuracy.

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Dynamic stiffness formulation and free vibration analysis of functionally graded beams

Cited by 97 publications

References 18 publications

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach

An Exact Dynamic Stiffness Formulation for Predicting Natural Frequencies of Moderately Thick Shells of Revolution

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