Dynamic response of functionally graded beams in a thermal environment under a moving load

Malekzadeh, P.; Monajjemzadeh, S.M.

doi:10.1080/15376494.2014.949930

Cited by 41 publications

(17 citation statements)

References 34 publications

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“…The applied temperature is similar to the case of LNR; however, the temperature distribution is set to follow the heat conduction rule and obtained by solving the steady state equation [27] as: …”

Section: Non-linear Temperature Rise (Nlnr)mentioning

confidence: 99%

“…Sankar and Tzeng [26] used CBT to study the thermal stresses of simply supported FG beams. The FOBT was employed to investigate various behaviours of FG beams such as dynamic responses under a moving load [27], thermal stability with non-linear hardening elastic foundations [28], thermal dynamic buckling [29], and thermal buckling and post-buckling with non-linear elastic foundation [30]. Wattanasakulpong et al [31] used Ritz method based on the HOBT to study the buckling and vibration of FG beams, however, it was limit on uniform temperature distribution only.…”

Section: Introductionmentioning

confidence: 99%

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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: Non-linear Temperature Rise (Nlnr)mentioning

confidence: 99%

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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“…Moreover, the thermo-elastic material properties of FG beams are also expressed in terms of temperature T (K) ( [31]):…”

Section: Materials Propertiesmentioning

confidence: 99%

“…Ma and Lee [30] proposed exact solutions for nonlinear bending behaviour of FG beams under an in-plane thermal loading. Malekzadeh and Monajjemzadeh [31] investigated the dynamic thermal response of FG beams under a moving load. Sankar [32] studied the thermal stresses of simply supported FG beams.…”

Section: Introductionmentioning

confidence: 99%

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded 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.)Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams AbstractThe hygro-thermal effects on vibration and buckling analysis of functionally graded beams are presented in this paper. The present work is based on a higher-order shear deformation theory which accounts for a hyperbolic distribution of transverse shear stress and higher-order variation of in-plane and out-of-plane displacements. Equations of motion are obtained from Lagrange's equations. Ritz solution method is used to solve problems with different boundary conditions. Numerical results for natural frequencies and critical buckling temperatures of functionally graded beams are compared with those obtained from previous works. Effects of power-law index, span-to-depth ratio, transverse normal strain, temperature and moisture changes on the results are discussed.

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“…Praveen and Reddy [26] investigated the static and transient behaviors of FGM plates by the finite element method and analyzed the influences of material properties and the variation in temperature on the dynamic behaviors of FGM plates. Malekzadeh [27] used Newmark's time integration technique and the finite element method to analyze the dynamic response of FGM plates under moving and thermal load. Numerical methods such as the Galerkin method and finite element method have been proven to be efficient and precise techniques.…”

Section: Introductionmentioning

confidence: 99%

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

et al. 2019

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The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.

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Dynamic response of functionally graded beams in a thermal environment under a moving load

Cited by 41 publications

References 34 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

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

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