Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates

Farajpour, Ali; Yazdi, Mohammad Reza Hairi; Rastgoo, Abbas; Loghmani, Masih; Mohammadi, M.

doi:10.1016/j.compstruct.2015.12.039

Cited by 147 publications

(58 citation statements)

References 54 publications

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“…For wave propagation analysis [24], three unknown fields are assumed as u; w; ψ f g¼ U; W; Ψ f g e ik xÀct ð Þ in which k is wave number, c is phase velocity, and U, W, and Ψ are amplitudes of axial and transverse displacements and electric potential. Substitution of assumed solutions into governing equations of motion by ignoring the force terms lead to:…”

Section: Wave Propagationmentioning

confidence: 99%

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicate that the effect of electric potential along the axial direction is very small rather than one along the transverse direction where initial voltage is applied. ARTICLE HISTORY

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Section: Wave Propagationmentioning

confidence: 99%

Transient analysis of a three-layer microbeam subjected to electric potential

Arefi

Zenkour

2017

International Journal of Smart and Nano Materials

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“…An oversimplifying way to deal with the issue, stated here for the sake of completeness, is to linearise equation (15), which would become…”

Section: Neglecting All Non-linear Termsmentioning

confidence: 99%

“…A way to circumvent this issue and arrive at displacement based workable models, is to neglect some non-linear non-local terms of the equilibrium equations, but the rationale for neglecting those terms and the ensuing errors are issues of concern. Using Airy's stress function -hence not following a totally displacement based approach -offers another solution to sidestep the aforementioned coupling [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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On displacement based non-local models for non-linear vibrations of thin nano plates

Chuaqui

Ribeiro

2018

MATEC Web Conf.

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Abstract. This paper addresses the formulation of displacement based, non-linear, plate models adopting Eringen's non-local elasticity, to study the modes of vibration of thin, nano plates. Plate models governed by ordinary differential equations of motion with generalized displacements as unknowns have some advantages over mixed type formulations, but difficulties arise in the development of such non-linear models when non-local effects are taken into account. To circumvent those difficulties, approximations of debatable justification can be imposed. Different approximations are discussed here and the accuracy of the best non-local, non-linear displacement based model achieved is put to test, by carrying out comparisons with a model based on Airy's stress function.

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“…Also, Ansari et al [32] studied the effect of temperature field on forced vibration of MEE nanobeams based on the nonlocal third-order beam theory. Farajpour et al [10] presented largeamplitude vibration analysis of MEE nanoplates based on nonlocal plate model.…”

Section: Introductionmentioning

confidence: 99%

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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This work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic functionally graded (METE-FG) nanoplates in thermal environments based on a refined trigonometric plate theory. Temperature field has uniform, linear, and nonlinear distributions across the thickness. Nonlinear thermal loadings are considered as heat conduction (HC) and sinusoidal temperature rise (STR). A power law function is applied to govern the gradation of material properties through the nanoplate thickness. Considering coupling impacts between magneto, electro, thermo-mechanical loadings, the equations of motion, and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived. The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier's method. Moreover, the accuracy of the present formulation is examined by comparing the obtained results with published ones. Furthermore, the effects played by the magneto-electrical field, various temperature rises, nonlocality, power law index, side-tothickness ratio, and aspect ratio on the critical buckling temperature response are all investigated and reported.ARTICLE HISTORY

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Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates

Cited by 147 publications

References 54 publications

Transient analysis of a three-layer microbeam subjected to electric potential

Transient analysis of a three-layer microbeam subjected to electric potential

On displacement based non-local models for non-linear vibrations of thin nano plates

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

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