Large amplitude free vibration analysis of functionally graded nano/micro beams on nonlinear elastic foundation

Setoodeh, A.R.; Rezaei, Mohammad Parsa

doi:10.12989/sem.2017.61.2.209

Cited by 5 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, in another work, Shenas et al [24] presented vibrational behaviors of rotating pre-twisted functionally graded micro beams in thermal environment. Setoodeh and Rezaei [25] employed modi ed couple stress theory to analyze large amplitude free vibration of FG nano/micro beams on nonlinear elastic foundation. Ke and Wang [26] investigated size e ects on the dynamic stability of functionally graded micro beams based on modi ed coupe stress theory.…”

Section: Introductionmentioning

confidence: 99%

An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

Setoodeh

Rezaei

2017

Scientia Iranica

View full text Add to dashboard Cite

Abstract. In this article, an analytical solution to the moderately large amplitude transverse vibration of thin Functionally Graded Micro-Plates (FGMPs) is presented based on a practical approach. The size-dependent nonlinear governing equation is obtained in conjunction with the Kirchho 's plate and modi ed couple stress theories. The material properties of Functionally Graded (FG) micro-plates vary according to the Reddy's model. The employed non-classical theory contains one material length-scale parameter to capture the size e ects. The highly nonlinear governing equation is solved by means of homotopy analysis method so as to obtain accurate analytic approximations. Both of simply supported and clamped micro-plates with immovable edges are considered. The comparison made between the present results and those of earlier studies con rms the reliability and e ectiveness of the present formulation for the design purpose. Furthermore, the e ects of di erent parameters, such as material gradient index, length-scale parameter, and aspect ratio, on the nonlinear frequency ratio are investigated.

show abstract

Section: Introductionmentioning

confidence: 99%