Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments

Ebrahimi, Farzad; Salari, Erfan

doi:10.1016/j.compstruct.2015.03.023

Cited by 161 publications

(37 citation statements)

References 32 publications

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“…These results are compared with those of Esfahani et al [28], Ebrahimi and Salari [2] based on FSDT. It is observed that the present solutions are in good agreement with those of [28] for C-C beams under the Fourier-law NLTR while there is slight deviations for several values of p between the present solutions and those of [2] for H-H beams under LTR. It is noted that the superscript "a" is used to indicate that Poisson's ratio effect is not included in the constitutive equation and thermal stress resultant (Q 11 = E(z)) and this index will be used in the next examples for verification studies.…”

Section: Conditions (H-h C-h and C-c) Fg Beams Are Made Of Ceramic (Simentioning

confidence: 94%

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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Section: Conditions (H-h C-h and C-c) Fg Beams Are Made Of Ceramic (Simentioning

confidence: 94%

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

Nguyen

et al. 2017

Composite Structures

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“…The beam geometry has the following dimensions: L (length) = 10 nm and h (thickness) = varied. Due to the fact that there is no available numerical result for the buckling responses of FG piezoelectric nanobeams based on the nonlocal elasticity theory, the only available work is thermal buckling of FG nanobeams under linear temperature rise presented by Ebrahimi and Salari [35]. Therefore, Table 2 compares critical buckling temperatures of the present theory with those of nonlocal FGM Timoshenko beams.…”

Section: Resultsmentioning

confidence: 99%

“…Also, Akgöz and Civalek [34] studied thermo-mechanical size-dependent buckling of embedded FG microbeams based on sinusoidal shear deformation beam and modified couple stress theories. Ebrahimi and Salari [35] investigated the thermal effects on buckling and free vibration characteristics of FG size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading by presenting a Navier-type solution. Ansari et al [36] proposed an exact solution for the nonlinear forced vibration of FG nanobeams in thermal environment based on the surface elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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In the present work, thermo-electro-mechanical buckling behavior of functionally graded piezoelectric (FGP) nanobeams is investigated based on higher-order shear deformation beam theory. The FGP nanobeam is subjected to four types of thermal loading including uniform, linear, and sinusoidal temperature rise as well as heat conduction through the beam thickness. Thermo-electromechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To consider the influences of small-scale sizes, Eringen's nonlocal elasticity theory is adopted. Applying Hamilton's principle, the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Naviertype analytical solution. The significance of various parameters, such as thermal loadings, external electric voltage, power-law index, nonlocal parameter, and slenderness ratio on thermal buckling response of size-dependent FGP nanobeams is investigated. ARTICLE HISTORY

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“…Potential energy (V) due applied load is International Frontier Science Letters Vol. 9 13 considered to be zero, as the system executes free vibration. The kinetic energy of the system is expressed as,…”

Section: Volumementioning

confidence: 99%

“…Jia et al [8] studied the size effect on the free vibration of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force based on Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. Ebrahimi and Salari [9] represented the thermal effect on buckling and free vibrational behaviours of functionally graded (FG) size-dependent Timoshenko nanobeams loaded to an in-plane thermal loading by implementing a Navier type solution. Pradhan and Chakraverty [10] implemented classical and first order shear deformation beam theories to investigate the free vibration behavior of functionally graded material (FGM) beams which is subjected to different sets of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

Lohar¹,

Mitra

Sahoo³

2016

IFSL

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Abstract.A displacement based semi-analytical method is utilized to study non-linear free vibration and mode shapes of an exponential tapered axially functionally graded (AFG) beam resting on an elastic foundation. In the present study geometric nonlinearity induced through large displacement is taken care of by non-linear strain-displacement relations. The beam is considered to be slender to neglect the rotary inertia and shear deformation effects. In the present paper at first the static problem is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic analysis is carried out as a standard eigen value problem. Energy principles are used for the formulation of both the problems. The static problem is solved by using minimum potential energy principle whereas in case of dynamic problem Hamilton's principle is employed. The free vibrational frequencies are tabulated for exponential taper profile subject to various boundary conditions and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane and in some particular case the mode shape results are furnished.

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Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments

Cited by 161 publications

References 32 publications

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

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

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Natural Frequency and Mode Shapes of Exponential Tapered AFG Beams on Elastic Foundation

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