Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties

Shegokar, Niranjan L.; Lal, Achchhe

doi:10.1007/s11012-013-9852-2

Cited by 46 publications

(17 citation statements)

References 41 publications

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“…Lezgy-Nazargah et al [45] suggested an efficient three-nodded beam element model for static, free vibration, and dynamic response of FG piezoelectric material beams. Large amplitude free flexural vibration of shear deformable FG beams with surface-bonded piezoelectric layers subjected to thermo-piezoelectric loadings with random material properties was presented by Shegokar and Lal [46]. The major disadvantage of this study is that they fail to consider small size influence.…”

Section: Introductionmentioning

confidence: 87%

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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Section: Introductionmentioning

confidence: 87%

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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“…Lezgy-Nazargah et al [26] suggested an efficient three-nodded beam element model for static, free vibration and dynamic response of FGP material beams. Large amplitude free flexural vibration of shear deformable FG beams with surface-bonded piezoelectric layers subjected to thermo-piezoelectric loadings with random material properties presented by Shegokar and Lal [27]. Therefore it could be noted that the most important imperfection of above researches is that the small size effects is not considered in these studies.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

Ebrahimi

Barati

2016

J Braz. Soc. Mech. Sci. Eng.

119

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to suit the functionality of structures. The gradually composition variations of the material constituents from one surface to another provide a proper solution to the problem of induced transverse shear stresses due to the two bonded dissimilar materials with high difference in material properties. Also, due to containing outstanding mechanical properties, FGMs are appropriate for design of engineering structures [1][2][3][4][5][6][7].In recent years, FGMs have been extensively utilized in micro-electromechanical and nano-electromechanical systems and devices [8]. On the other hand, size-dependent structures such as micro and nano scale beams are key components in many systems. Therefore, mechanical analysis of micro/nano beams has received striking attention from research communities. The classical continuum theory which is extensively used in mechanical analysis of macroscopic structures should be extended to consider the size effect on mechanical behaviors of micro/nano structures. Therefore, this can be attained by the nonlocal elasticity theory proposed by Eringen in which a stress state at a reference point is suggested as a function of the strain of all neighbor points. It is noted that some studies are published on mechanical behavior of size-dependent FG beams. Among them, Simsek and Yurtcu [9] investigated bending and buckling behavior of size-dependent FG nanobeam using analytical method and Timoshenko and EulerBernoulli beam models. Also, the static and stability behavior of FG nanobeams based on nonlocal continuum theory studied by Eltaher et al. [10]. Nonlinear free vibration of functionally graded nanobeams within the framework of Euler-Bernoulli beam model including the von Kármán geometric nonlinearity studied by Sharabiani and Yazdi [11]. Also, forced vibration analysis of FG nanobeams based on the nonlocal elasticity theory and using Navier method for various shear deformation theories studied by Abstract This paper investigates buckling response of higher-order shear deformable nanobeams made of functionally graded piezoelectric (FGP) materials embedded in an elastic foundation. Material properties of FGP nanobeam change continuously in thickness direction based on power-law model. To capture small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of FGP nanobeams embedded in elastic foundation are obtained. To predict buckling behavior of embedded FGP nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of sizedependent FGP nanobeams.

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“…The effect of the prestress on the overall mechanical properties of the random elastic composite with residual stresses is considered by Dal Corso and Deseri [54]. First order perturbation technique is applied to find the solution of random eigenvalue problem by Shegokar and Lal [55], where large amplitude free vibrations of shear deformable functionally graded material beams with thermopiezoelectric loadings, and with random material properties are presented. An efficient uncertainty quantification scheme for frequency responses of laminated composite plates is examined by Dey et al [56].…”

Section: Introductionmentioning

confidence: 99%

The effect of uncertain material properties on free vibrations of thin periodic plates

Jędrysiak

Ostrowski

2017

Meccanica

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Thin periodic plates with uncertain properties in a periodicity cell are investigated. To describe dynamics of these plates the non-asymptotic tolerance modelling method, cf. Woźniak and Wierzbicki (Averaging techniques in thermomechanics of composite solids. Wydawnictwo Politechniki Często-chowskiej, Częstochowa, 15), Woźniak et al. (eds.) (Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach. Wydawnictwo Politechniki Łódzkiej, Łódź, 16), for those plates is applied. The governing equations of tolerance models based on this method take into account the effect of period lengths on the overall behaviour of the plate. Hence, the additional effects of the periodicity can be analysed, as higher order vibrations. Moreover, properties of the plate in the periodicity cell are determined uncertainly. To analyse an influence of random variables of the properties with a fixed probability distribution on vibrations of the plate the Monte Carlo analysis is applied.

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Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties

Cited by 46 publications

References 41 publications

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

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

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

The effect of uncertain material properties on free vibrations of thin periodic plates

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