Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory

Ansari, R.; Gholami, R.; Rouhi, H.

doi:10.1016/j.compstruct.2015.02.068

Cited by 139 publications

(40 citation statements)

References 43 publications

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“…(Chang, 2013) presented the free vibration, deterministic vibration and random vibration characteristics of transversely isotropic magneto-electro-elastic rectangular plates in contact with the fluid. Ansari et al, (2015) developed a nonlocal geometrically nonlinear beam model for magneto-electro-thermo-elastic nanobeams subjected to external electric voltage, external magnetic potential and uniform temperature rise. Ke et al, (2014b) studied the free vibration of embedded magneto-electro-elastic cylindrical nanoshells based on Love's shell theory.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Ragb¹,

Mohamed²,

Matbuly³

2019

MAS

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Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

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Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Ragb¹,

Mohamed²,

Matbuly³

2019

MAS

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“…Hence, it is of great signicance to consider the size effect in mechanical characteristics of piezoelectric-piezomagnetic nanostructures. Since the molecular dynamics simulations for large-scale nanostructures are restricted by computational capacities and conducting controlled experiments and operating precision at the nanoscale are difcult, the size-dependent continuum theories including the nonlocal elasticity theory [23], strain gradient elasticity theory [24], modified couple stress theory [25], modified strain gradient theory [26] and surface stress elasticity theory [27,28] have been proposed and have been widely utilized to develop the size-dependent beam, plate and shell models for the analysis of size-dependent mechanical characteristics of these small-scale structures [29][30][31][32][33][34][35][36][37]. Among these theories, the Eringen's nonlocal elasticity theory is commonly utilized to develop the nonlocal continuum models in which the effect of small scale parameter is incorporated.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Geometrically Nonlinear Free Vibration of First-Order Shear Deformable Piezoelectric-Piezomagnetic Nanobeams Using the Nonlocal Theory

Ansari¹

2018

AAMM

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This article investigates the geometrically nonlinear free vibration of piezoelectric-piezomagnetic nanobeams subjected to magneto-electro-thermal loading taking into account size effect using the nonlocal elasticity theory. To this end, the sizedependent nonlinear governing equations of motion and corresponding boundary conditions are derived according to the nonlocal elasticity theory and the first-order shear deformation theory with von Kármán-type of kinematic nonlinearity. The effects of size-dependence, shear deformations, rotary inertia, piezoelectric-piezomagnetic coupling, thermal environment and geometrical nonlinearity are taken into account. The generalized differential quadrature (GDQ) method in conjunction with the numerical Galerkin method, periodic time differential operators and pseudo arclength continuation method is utilized to compute the nonlinear frequency response of piezoelectric-piezomagnetic nanobeams. The influences of various parameters such as non-dimensional nonlocal parameter, temperature change, initial applied electric voltage, initial applied magnetic potential, length-to-thickness ratio and different boundary conditions on the geometrically nonlinear free vibration characteristics of piezoelectric-piezomagnetic nanobeams are demonstrated by numerical examples. It is illustrated that the hardening spring effect increases with increasing the non-dimensional nonlocal parameter, positive initial applied voltage, negative initial applied magnetic potential, temperature rise and decreases with increasing the negative initial applied voltage, positive initial applied magnetic potential and length-tothickness ratio.

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“…According to the main idea of this nonlocal theory, the basic relations for FG-MEE substance without considering body force can be written as follows (Ansari et al 2015b;Farajpour et al 2016)…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

“…1 The geometry of FG-MEE nanoplate with multiple attached nanoparticle resting on Pasternak medium (color figure online) Vaezi et al (2016) for investigating natural frequencies and buckling loads of MEE microbeam. Moreover, there are a number of literatures regarding the influences of small scale on the MEE nanostructures such as MEE nanobeams Ansari et al 2015b;Li et al 2016;Ma et al 2017) and MEE nanoplates Wu et al 2015;Kiani et al 2017) by taking into account the nonlocal parameter. Functionally graded materials (FGMs) are a special subgroup of novel composite materials which contain the heterogeneous property and have a continuous variation of material properties from one surface to another.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

et al. 2017

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In the current paper, the sensitivity performance of functionally graded magneto-electro-elastic (FG-MEE) nanoplate with attached nanoparticles as a nanosensor is analyzed based on nonlocal Mindlin plate assumption. Power law distribution model is employed to display how the material properties of FG-MEE nanoplate vary across the thickness direction. It is supposed that FG-MEE nanoplate is under initial external electric and magnetic potentials. Boundary condition of each edge of FG-MEE nanoplate is assumed to be simply supported. Furthermore, a Pasternak substrate is applied for modelling the total reaction pressure between nanoplate and foundation. Partial differential equations and corresponding boundary conditions are first achieved using Hamilton's variational principle and then analytically solved to determine the frequency shift utilizing Navier's approach. Numerical examples are performed to elucidate the dependency of the sensitivity performance of FG-MEE nanosensor on the volume fraction exponent, nonlocal parameter, total attached mass and location of the nanoparticle, aspect ratio, mode number, initial external electric voltage, initial external magnetic potential, and Pasternak medium coefficients. It is clearly indicated that these factors have highly significant impacts on the variations of frequency shift.

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Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory

Cited by 139 publications

References 43 publications

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

Size-Dependent Geometrically Nonlinear Free Vibration of First-Order Shear Deformable Piezoelectric-Piezomagnetic Nanobeams Using the Nonlocal Theory

Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

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