Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

Ansari, R.; Gholami, R.; Sahmani, S.

doi:10.1016/j.compstruct.2011.06.024

Cited by 285 publications

(77 citation statements)

References 35 publications

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“…Asghari et al [62] investigated the size-dependent static and vibration behavior of microbeams made of FG materials on the basis of the modified couple stress theory in the elastic range. Ansari et al [63] studied the free vibration characteristics of microbeams made of FG materials based on the strain gradient Timoshenko beam theory. Moreover, a comparison between the various beam models on the basis of the classical theory, modified couple stress theory, and strain gradient theory was presented for different values of material property gradient index.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closedform solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

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Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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“…Meany researchers employed different gradient elasticity theories mentioned above in conjunction with different classical continuum mechanic theories to study the mechanical behavior of size-dependent micro/nanostructures so far (Ansari et al, 2011(Ansari et al, , 2013 A new size-dependent sinusoidal plate model to predict mechanical behavior of thin, moderately thick and thick microplate was suggested by Akgöz and Civalek (2015) as well. They employed a modified strain gradient elasticity hypothesis to incorporate the size effect into the classical continuum plate theory.…”

Section: Introductionmentioning

confidence: 99%

Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

Ziaee

2017

jtam

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This article aims to study the natural frequency of defective graphene sheets since the existence of cut-outs in plates may be essential on the basis of their desired functionality. A combination of the Aifantis theory and Kirchhoff thin plate hypothesis is used to derive governing equations of motion. The Ritz method is employed to derive discrete equations of motion. The molecular structural mechanics method is also employed to specify the effective length scale parameter. In the 'numerical results' Section, the effects of different parameters such as boundary conditions and diameter of the hole-to-side length ratio on the fundamental frequency of graphene sheets are studied.

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“…Thus, to have a proper design of these systems, the knowledge of the mechanical behavior of FG microstructures is necessary. Recently, some research works have been conducted on the microscale structure made of functionally grade materials (Sahmani and Ansari (2013); Asghari et al (2011);Ansari et al (2011)). …”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

Ansari

Hasrati

Shojaei

et al. 2016

Lat. Am. j. solids struct.

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In this paper, a size-dependent microscale plate model is developed to describe the bending, buckling and free vibration behaviors of microplates made of functionally graded materials (FGMs). The size effects are captured based on the modified strain gradient theory (MSGT), and the formulation of the paper is on the basis of Mindlin plate theory. The presented model accommodates the models based upon the classical theory (CT) and the modified couple stress theory (MCST) if all or two scale parameters are set to zero, respectively. By using Hamilton's principle, the governing equations and related boundary conditions are derived. The bending, buckling and free vibration problems are considered and are solved through the generalized differential quadrature (GDQ) method. A detailed parametric and comparative study is conducted to evaluate the effects of length scale parameter, material gradient index and aspect ratio predicted by the CT, MCST and MSGT on the deflection, critical buckling load and first natural frequency of the microplate. The numerical results indicate that the model developed herein is significantly sizedependent when the thickness of the microplate is on the order of the material scale parameters.

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Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

Cited by 285 publications

References 35 publications

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Linear free vibration of graphene sheets with nanopore via Aifantis theory and Ritz method

Size-Dependent Bending, Buckling and Free Vibration Analyses of Microscale Functionally Graded Mindlin Plates Based on the Strain Gradient Elasticity Theory

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