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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 국제구조공학회 Structural Engineering and Mechanics, An Int'l Journal Structural Engineering and Mechanics, An Int'l Journal Vol.61 No.2
- 발행연도
- 2017.1
- 수록면
- 209 - 220 (12page)
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The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton’s principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy’s power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.
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참고문헌 (30)
참고문헌 신청
Ansari, R. / 2016 / Coupled longitudinal-transverserotational free vibration of post-buckled functionally graded first-order shear deformable micro-and nano-beams based on the Mindlin’s strain gradient Theory / Appl. Math. Model 40(23):9872~9891
Asghari, M. / 2011 / The modified couple stress functionally graded Timoshenko beam formulation / Mater. Des 32(3):1435~1443
Süleyman M. Bağdatlı / 2015 / Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory / Structural Engineering and Mechanics, An Int＇l Journal 55(2):281~298
M. Bayat / 2013 / Vibration of electrostatically actuated microbeam by means of homotopy perturbation method / Structural Engineering and Mechanics, An Int＇l Journal 48(6):823~831
Farzad Ebrahimi / 2016 / Application of Eringen\'s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams / Smart Structures and Systems, An International Journal 17(5):837~857
Asghari, M. / 2011 / The modified couple stress functionally graded Timoshenko beam formulation / Mater. Des 32(3):1435~1443
Süleyman M. Bağdatlı / 2015 / Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory / Structural Engineering and Mechanics, An Int＇l Journal 55(2):281~298
M. Bayat / 2013 / Vibration of electrostatically actuated microbeam by means of homotopy perturbation method / Structural Engineering and Mechanics, An Int＇l Journal 48(6):823~831
Farzad Ebrahimi / 2016 / Application of Eringen\'s nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams / Smart Structures and Systems, An International Journal 17(5):837~857
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