Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments

Barati, Mohammad Reza; Zenkour, Ashraf M.

doi:10.1080/15376494.2017.1308603

Cited by 39 publications

(11 citation statements)

References 34 publications

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“…But, when the nonlocal procedures are concerned, inclusion of the shift of neutral surface is much less common; for the isothermal strain gradient formulation see [35][36][37][38] and for the integral based [39]. For the gradient based thermoelastic beams including hygro effects, see [15]. In the case of stress-driven nonlocal thermoelasticity, these are practically non-existent.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Barretta

Čanađija

Sciarra

2019

Composite Structures

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An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

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Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Barretta

Čanađija

Sciarra

2019

Composite Structures

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“…Therefore, in Kerr foundation, the concentrated reactions do not occur due to existence of upper layer of springs. Barati and Zenkour 48 investigated the size-dependent forced vibration behavior of FG nanobeams resting on Kerr foundation subjected to an in-plane hygrothermal loading and lateral concentrated and uniform dynamic loads via a higher-order refined beam theory. Moreover, Barati 49 explored dynamic response of porous inhomogeneous nanobeams subjected to concentrated and distributed loads resting on Kerr foundation.…”

Section: Introductionmentioning

confidence: 99%

Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment

Shahraki

Riahi

Izadinia

et al. 2019

Journal of Thermoplastic Composite Materials

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This article examines the application of simplified Mindlin’s strain gradient theory to free vibration analysis of functionally graded carbon nanotube–reinforced composite (FG-CNTRC) thick rectangular nanoplates resting on Kerr elastic foundation in thermal environment. The theory contains only one length scale parameter corresponding to strain gradient effects. Also, a quasi-3D hyperbolic theory considering transverse shear deformation and thickness stretching effects is employed to present the formulation. In this study, properties of the carbon nanotubes (CNTs) and the polymeric matrix are assumed to be temperature dependent. Distribution of CNTs across the thickness of the nanoplate is considered to be uniform (UD) or functionally graded (FG-X, FG-V, and FG-O). According to Hamilton’s principle and the generalized differential quadrature method, the governing equations and associated boundary conditions are obtained and discretized, respectively. The natural frequencies of FG-CNTRC nanoplates are determined by solving eigenvalue problem. The numerical results of the present formulation are compared with those available in the literature to explain the accuracy of the suggested theories. Then, parametric studies are presented to examine the effects of elastic foundation coefficients, size parameter, temperature change, volume fraction and dispersion profile of CNTs, aspect ratio, length-to-thickness ratio, and different boundary conditions on vibration behavior of FG-CNTRC nanoplates. The results confirmed that size parameter and changes in temperature play an important role in determining natural frequencies. In addition, the shear layer parameter of Kerr foundation has more influence with respect to the coefficients of the upper and lower layers.

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“…47 The specific applications of size-dependent beams resting on an elastic foundation are FG thin films 48,49 deposited on a substrate in MEMS and NEMS, slider-level micro-actuator, 50 etc. In recent years, research works on vibration analysis of size-dependent FG beams resting on elastic foundation 47,51,52 became available and these were based on nonlocal elasticity theory. Based on higher order refined beam theory, Barati and Zenkour 47 investigated the geometrically linear forced vibration behavior of FG nano-beams resting on Kerr foundation.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, research works on vibration analysis of sizedependent FG beams resting on elastic foundation 47,51,52 became available and these were based on nonlocal elasticity theory. Based on higher order refined beam theory, Barati and Zenkour 47 investigated the geometrically linear forced vibration behavior of FG nano-beams resting on Kerr foundation. For FG nano-beams resting on a nonlinear elastic foundation, Niknam and Aghdam 51 and El-Borgi et al 52 carried out nonlinear free and forced vibration analysis, respectively, using EBT.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

Das

2018

Proceedings of the Institution of Mechanical Engineers, Part L:

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Geometrically nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam is presented, where the beam is supported on a three-parameter Winkler–Pasternak-type nonlinear elastic foundation and subjected to a harmonically varying distributed load. The modified couple stress theory of elasticity is employed in the formulation to address the size-dependent effect. Hamilton’s principle is used to derive the displacement-based governing equations considering Reddy’s third-order shear deformation theory. Ritz method is followed to convert the governing equations to nonlinear algebraic form in the frequency domain by approximating the displacement fields. A mixed algorithm for nonlinear equations based on the iterative substitution method with successive relaxation and Broyden’s method is successfully employed to solve the stable regions of the frequency-response curves. The results are presented for hinged and clamped beams, and the effects of different parameters such as size-dependent thickness, load amplitude, foundation parameters, and gradation-profile parameter are studied. The effect of thermal loading due to uniform temperature rise is also studied considering temperature-dependent material properties.

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Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments

Cited by 39 publications

References 34 publications

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment

Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified couple stress theory

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