Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory

Ys, Li; Ma, Peifeng; Wang, W

doi:10.1177/1045389x15585899

Cited by 69 publications

(26 citation statements)

References 36 publications

(38 reference statements)

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“…The cross section of the nanobeam is set as rectangular and Visco-Pasternak foundation is considered for the nanobeam model. Li et al [7] studied the bending, buckling, and free vibration characteristics of the magneto-electro-elastic nanobeam, the nonlocal theory and Timoshenko beam theory are adopted in this article. Arefi and Soltan [8] proposed the functionally graded (FG) nanobeams which are subjected to magneto-electro-elastic loading.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

Shi

Wang

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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In this article, wave based method (WBM) is proposed as a new semi-analytical method to analyze the wave propagation characteristics of the magneto-electro-thermo-elastic nanobeams with arbitrary boundary conditions. According to the Timoshenko beam theory and Hamilton principle, the governing equations of the nanobeam which are related to Eringen's nonlocal theory are obtained. The displacement and external potential variables are expanded as wave function forms. In the light of the introduction of several type boundary conditions, the total matrix of the nanobeam is constituted. Searching the zero locations of the total matrix determinant by the bisection method, the natural frequencies of the nanobeam under arbitrary boundary conditions are received. To further illustrate the calculation correctness of the presented method, the results are compared with the solutions in reported references. Furthermore, a series of numerical examples are proposed to investigate the effect of each parameter on the free vibration characteristics of the nanobeam with several boundary conditions, such as beam length and thickness, external temperature rise, magnetic and electric potential. Some new numerical solutions and conclusions are presented in this paper to provide the basic foundation for subsequent research.

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Section: Introductionmentioning

confidence: 99%

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

Shi

Wang

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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“…In the past two decades, much attention has been paid to the bending analysis of the MEE plates [2][3][4][5] , and some achievements on the bending problems of MEE nanoplates have been made [6][7] . Considering the size effects of nanostructures, the nonlocal theory initiated by Eringen [8][9] has been successfully used to analyze magnetoelectric nanostructures in recent years [10][11][12][13] . Among them, Li et al [10] and Guo et al [12] investigated the buckling problems of the MEE nanoplates and the multilayered MEE nanoplates under the nonlocal theory, respectively.…”

Section: Introductionmentioning

confidence: 99%

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Feng

Yan

Lin

et al. 2020

Appl. Math. Mech.-Engl. Ed.

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Based on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. Finally, the effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures.

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“…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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Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory

Cited by 69 publications

References 36 publications

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on 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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