Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation. (December 2015)

• Record Type: Journal Article
• Authors: El-Borgi, Sami; Fernandes, Ralston; Reddy, J.N.
• Is Part Of: International journal of non-linear mechanics. Volume 77(2015)
• Page Start: 348
• Page End: 363
• Publication Date: 2015-12
• Subjects: Graded nanobeam -- Eringen׳s non-local model -- Method of Multiple Scales (MMS) -- Variational iteration method (VIM); Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2015.09.013
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We consider in this paper the free and forced vibration response of simply-supported functionally graded (FG) nanobeams resting on a non-linear elastic foundation. The two-constituent Functionally Graded Material (FGM) is assumed to follow a power-law distribution through the beam thickness. Eringen׳s non-local elasticity model with material length scales is used in conjunction with the Euler–Bernoulli beam theory with von Kármán geometric non-linearity that accounts for moderate rotations. Non-linear natural frequencies of non-local FG nanobeams are obtained using He׳s Variational Iteration Method (VIM) and the direct and discretized Method of Multiple Scales (MMS), while the primary resonance analysis of an externally forced non-local FG nanobeam is performed only using the MMS. The effects of the non-local parameter, power-law index, and the parameters of the non-linear elastic foundation on the non-linear frequency-response are investigated. Abstract : Highlights: Nonlocal nonlinear vibration of graded nanobeams on nonlinear elastic foundations. Nonlinear nonlocal natural frequencies obtained analytically. Primary resonance analysis performed using Multiple Scales Methods.