Linear free vibration of micro-/nano-plates with cut-out in thermal environment via modified couple stress theory and Ritz method

Ziaee, Sima

doi:10.1016/j.asej.2017.05.003

Cited by 7 publications

(8 citation statements)

References 32 publications

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“…and the plate is supposed to be made from isotropic material with the properties (27). The presented results contain the first three vibration modes calculated for μ = 1 nm 2 and size of cutouts associated with the following ratio: c 1 /a = 0.7, c 2 /a = 0.3.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Isogeometric analysis was applied to the study of large amplitude free vibration of porous skew and elliptical nanoplates based on nonlocal elasticity by Tao and Dai [26] . The studies devoted to the micro/nanoplates of complex geometry also include works [27][28][29] (plates with a hole, and L-shaped plate, and skew plate, respectively), where the authors use the modified couple stress theory accounting for the small-scale effects.…”

Section: Introductionmentioning

confidence: 99%

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Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

et al. 2022

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Free vibrations of the orthotropic micro/nanoplate with nonclassical shape are investigated. The considered model is based on the nonlocal elasticity theory. The developed method uses the Ritz method as well as R-function theory for the construction of the system of coordinate functions. The linear frequencies are obtained for a rectangular plate with two cutouts on opposite sides, while the boundary conditions are considered of several types, including simply supported and clamped edges. The small-scale effects for various sizes of cutouts are discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

et al. 2022

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“…Early scholars analyzed the linear vibration of plates. Ziaee [3] used the Ritz method to study linear vibration of nanoplates. The effects of different parameters on polysilicon microplate were discussed.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model

Jin

Xie

et al. 2022

Fractal Fract

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In this study, an efficacious method for solving viscoelastic dynamic plates in the time domain is proposed for the first time. The differential operator matrices of different orders of Bernstein polynomials algorithm are adopted to approximate the ternary displacement function. The approximate results are simulated by code. In addition, it is proved that the proposed method is feasible and effective through error analysis and mathematical examples. Finally, the effects of external load, side length of plate, thickness of plate and boundary condition on the dynamic response of square plate are studied. The numerical results illustrate that displacement and stress of the plate change with the change of various parameters. It is further verified that the Bernstein polynomials algorithm can be used as a powerful tool for numerical solution and dynamic analysis of viscoelastic plates.

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“…Varying the location and size of the cutouts can change their characteristics that may be used designing micro/nanoplates. Among papers aimed at micro/nanoplates with complex shape there is the investigation of the linear vibrations of a rectangular plate with an internal square hole in a thermal environment by Ziaee [50], where the Ritz method is used. Tsiatas and Yiotis [51] used the modified couple stress theory for the investigation of bending, buckling and vibrations of an orthotropic skew plate.…”

Section: Introductionmentioning

confidence: 99%

Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

2020

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Free vibrations of microplates with non‐classical shape are considered in the paper. Governing equations are based on the modified couple stress theory and Kirchhoff–Love plate theory. It is assumed that the plate is isotropic or orthotropic and satisfy various boundary conditions. An analysis is performed by the variational‐structural method which is based on R‐functions theory and Ritz method. The testing of the proposed method is carried out by comparison with known in literature results and analytical solutions. The developed method is applied to the study of the influence of the material length scale parameter, boundary conditions, shape parameters, material characteristics on vibration frequencies. Also, size‐dependent analysis for buckling of the isotropic and orthotropic microplate subjected to uniaxial load is performed by the proposed approach. Critical loads for a plate with complex shape, different types of boundary conditions and material are calculated in order to study their effect on buckling.

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Linear free vibration of micro-/nano-plates with cut-out in thermal environment via modified couple stress theory and Ritz method

Cited by 7 publications

References 32 publications

Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model

Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

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