A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation

Bounouara, Fatima; Benrahou, Kouider Halim; Belkorissat, Ismahene; Tounsi, Abdelouahed

doi:10.12989/scs.2016.20.2.227

Cited by 192 publications

(49 citation statements)

References 66 publications

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“…The explicit relation of the nonlocal normal force can be derived by substituting for the second derivative of N from Equation (23) into Equation (27) as follows:…”

Section: Nonlocal Higher-order Fg Piezoelectric Nanobeam Modelmentioning

confidence: 99%

“…Zemri et al [26] presented mechanical response of functionally graded nanoscale beam based on a refined nonlocal shear deformation beam theory. Bounouara et al [27] presented a nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation. Ebrahimi and Barati [28] presented dynamic modeling of a thermo-piezoelectrically actuated nanosize beam subjected to a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The explicit relation of the nonlocal normal force can be derived by substituting for the second derivative of N from Equation (23) into Equation (27) as follows:…”

Section: Nonlocal Higher-order Fg Piezoelectric Nanobeam Modelmentioning

confidence: 99%

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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“…(49) and (50) are employed to obtain the nonlinear frequency of the system as a function of the vibration amplitude. The dimensionless nonlinear frequency of the RVE versus amplitude of oscillation for different BCs is shown in Fig.…”

Section: 3mentioning

confidence: 99%

“…After calculating the elastic modulus of the considered sample in different directions or calculating the average modulus, the system behavior in terms of bending, buckling, natural frequencies and free and forced vibrations are investigated [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Also in some studies the elastic foundation theory is used in modeling [47][48][49][50]. In addition, different theoretical approaches are used to extract mathematical equations in order to investigate the mechanical and vibration behavior of nanocomposites, particularly the functionally graded CNT-reinforced composite.…”

Section: Introductionmentioning

confidence: 99%

A study on nonlinear vibration behavior of CNT-based representative volume element

Jamal‐Omidi

ShayanMehr

Shokrollahi

et al. 2016

Aerospace Science and Technology

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“…From elasticity points of view, the main feature of this theory is that the stress of each point does not only depend on the state of stress of that point but also on the state of stresses at its neighboring points. To date, there exist a large body of researches on nonlocal dynamics of nanoscale structures (i.e., rod-like, beam-like, plate-like, and shell-like nanostructures) including free vibration [18][19][20][21][22][23][24], forced vibrations [25][26][27], and nonlinear vibrations [28][29][30][31]. Further, vibrations of fluids-conveying SWCNTs has been widely researched by the NCT of Eringen from various aspects including free transverse vibration and dynamic instability [32][33][34][35][36] as well as longitudinal and transverse forced vibrations [37,38].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors

Kiani

2017

Acta Phys. Pol. A

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This work displays both longitudinal and transverse vibrations of magnetically affected inclined single-walled carbon nanotubes for conveying fluid flow. By employing an equivalent continuum structure on the basis of the nonlocal Timoshenko beam model as well as plug-like model for the nanofluidic flow inside the pore, the nonlocal governing equations are obtained accounting for nonlocality, frictionless nature of the inside wall, the Knudsen number, and full longitudinal and transverse interactions of the fluid flow with the single-walled carbon nanotubes. By implementing Galerkin-based assumed mode method, the equations of motion are discretized appropriately and then solved for the unknown dynamical deformation fields. The roles of nanofluidic flow velocity, small-scale parameter, inclination angle of single-walled carbon nanotube, and magnetic field strength on maximum values of longitudinal and transverse displacements are explained and discussed. The results show that the maximum dynamic deflection of the inclined nanotube would lessen by increase of the magnetic field strength. This fact is also more apparent for higher levels of fluid flow velocity. Additionally, variation of the longitudinal magnetic field has a trivial influence on the variation of longitudinal displacement. The predicted results reveal that application of the longitudinal magnetic field could be used as an efficient methodology to reduce the lateral vibrations of single-walled carbon nanotubes as nanofluidic conveyors.

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A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation

Cited by 192 publications

References 66 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

A study on nonlinear vibration behavior of CNT-based representative volume element

Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors

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