Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity

Salehipour, Hamzeh; Nahvi, Hassan; Shahidi, Alireza

doi:10.1016/j.physe.2014.10.001

Cited by 38 publications

(12 citation statements)

References 26 publications

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“…Kiani et al proposed a mathematical model for functionally graded nano beam moving with constant velocity. They have investigated the effect of power-law parameter, small-scale parameter and length of the functionally graded nanobeam, on the frequencies and stability of the moving nanobeam [16] . Uymaz studied the forced vibration of FG nanobeams based on the nonlocal elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

Hosseini

Rahmani

2018

TSE

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The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam. The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

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Section: Introductionmentioning

confidence: 99%

Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

Hosseini

Rahmani

2018

TSE

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“…Salehipour et al [31] established the exact analytical solution of free vibration of FG micro/nanoplates by using three-dimensional theory of elasticity accounting small-scale effect. Salehipour et al [32] developed the modified nonlocal elasticity for examination of the natural frequency of FG micro/nanoplates.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Panyatong

Chinnaboon

Chucheepsakul

2016

Composite Structures

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“…Ansari et al [43] studied the free vibration analysis of functionally graded circular/ annular microplates based on the generalized differential quadrature method and the modified strain gradient elasticity theory. Salehipour et al [44] considered Navier approach for the free vibration of functionally graded micro/nano-plate with simply supported boundary conditions using nonlocal elasticity.…”

Section: Introductionmentioning

confidence: 99%

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

2015

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In this paper, the natural frequencies of a functionally graded nanoplate are analyzed for different combinations of boundary conditions. Application of new materials and specially the functionally graded materials in the micro-and nano-scale devices and systems is increasingly spread. Therefore, the study of the natural frequencies of functionally graded materials for different boundary conditions seems to be necessary in the micro/nano-structures. The article presented here covers broad types of common boundary conditions for the free vibration of functionally graded rectangular nanoplates for the first time. The analytical solution method used here is new for this subject and solves the governing equations with no approximation. The size dependency is considered according to Eringen's differential form of nonlocal elasticity theory. The elasticity modulus and mass density of the plate are varied along the thickness of the plate according to a power-law distribution of the constituents' volume fractions. As the in-plane and out-of-plane displacement variables are coupled in the equations of motion, a new exact solution method is introduced to solve the displacement fields analytically. The method is capable of dealing with new combinations of boundary conditions which have not been studied before in the literature. The validity and accuracy of the present method is investigated by comparing some of the present results to their counterparts reported in the literature. The results presented here are new and discussed for the first time in this subject. As a novelty a detailed study is carried out to examine the effects of power-law distribution, the characteristic internal length, the plate aspect ratio and the mode number on the natural frequencies of functionally graded rectangular plates for different boundary conditions. It's shown that the type of boundary condition affects considerably on the values of natural frequency but the behavior of the frequency variations is in the same manner for different combinations of boundary conditions. These results can be used as benchmark for future studies.

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Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity

Cited by 38 publications

References 26 publications

Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

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