Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation

被引：55
作者：
El-Borgi, Sami [1 ,2 ]
Fernandes, Ralston [1 ]
Reddy, J. N. [3 ]
机构：
[1] Texas A&M Univ, Mech Engn Program, Educ City, Doha 77843, Qatar
[2] Univ Carthage, Tunisia Polytech Sch, Appl Mech & Syst Res Lab, La Marsa 2078, Tunisia
[3] Texas A&M Univ, Dept Mech Engn, College Stn, TX 77843 USA
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2015年 / 77卷
关键词：
Graded nanobeam; Eringen's non-local model; Method of Multiple Scales (MMS); Variational iteration method (VIM); LARGE-AMPLITUDE FREE; MODERATE ROTATION THEORY; COUPLE STRESS THEORY; SMALL STRAIN; MODEL; FORMULATION; STABILITY; ENERGY;
D O I：
10.1016/j.ijnonlinmec.2015.09.013
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
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 Karman 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. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：348 / 363
页数：16
相关论文
共 69 条
[31]   A NONCLASSICAL REDDY-LEVINSON BEAM MODEL BASED ON A MODIFIED COUPLE STRESS THEORY [J].
Ma, H. M. ;
Gao, X. -L. ;
Reddy, J. N. .
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 2010, 8 (02) :167-180
[32]   A microstructure-dependent Timoshenko beam model based on a modified couple stress theory [J].
Ma, H. M. ;
Gao, X-L ;
Reddy, J. N. .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2008, 56 (12) :3379-3391
[33]  
Mindlin R., 1963, Experimental Mechanics, V3, P1, DOI 10.1007/BF02327219
[34]   Miniaturized flexible temperature sensor [J].
Moser, Yves ;
Gijs, Maitin A. M. .
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, 2007, 16 (06) :1349-1354
[35]   Dynamics and Global Stability of Beam-based Electrostatic Microactuators [J].
Najar, F. ;
Nayfeh, A. H. ;
Abdel-Rahman, E. M. ;
Choura, S. ;
El-Borgi, S. .
JOURNAL OF VIBRATION AND CONTROL, 2010, 16 (05) :721-748
[36]  
Nayfeh AH, 1998, JSME INT J C-MECH SY, V41, P510
[37]  
Nayfeh AH, 2008, LINEAR NONLINEAR STR, DOI DOI 10.1002/9783527617562
[38]  
Nayfeh AH., 1979, Nonlinear Oscillations
[39]   Nonlocal nonlinear free vibration of functionally graded nanobeams [J].
Nazemnezhad, Reza ;
Hosseini-Hashemi, Shahrokh .
COMPOSITE STRUCTURES, 2014, 110 :192-199
[40]   A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation [J].
Niknam, H. ;
Aghdam, M. M. .
COMPOSITE STRUCTURES, 2015, 119 :452-462
1234567