Surface effects on flutter instability of nanorod under generalized follower force

Qiu-Xiang Xiao, Jiaqi Zou, Kang Yong Lee and Xian-Fang Li

Abstract

This paper studies on dynamic and stability behavior of a clamped-elastically restrained nanobeam under the action of a nonconservative force with an emphasis on the influence of surface properties on divergence and flutter instability. Using the Euler-Bernoulli beam theory incorporating surface effects, a governing equation for a clamped-elastically restrained nanobeam is derived according to Hamilton‟s principle. The characteristic equation is obtained explicitly and the forcefrequency interaction curves are displayed to show the influence of the surface effects, spring stiffness of the elastic restraint end on critical loads including divergence and flutter loads. Divergence and flutter instability transition is analyzed. Euler buckling and stability of Beck‟s column are some special cases of the present at macroscale.

Key Words

surface elasticity; flutter instability; divergence instability; nanocantilever; elastically restrained end

Address

Qiu-Xiang Xiao : School of Civil Engineering, Central South University, Changsha 410075, PR China Jiaqi Zou : School of Civil Engineering, Central South University, Changsha 410075, PR China Kang Yong Lee : State Key Laboratory of Structural Analysis for Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China Xian-Fang Li : School of Civil Engineering, Central South University, Changsha 410075, PR China; State Key Laboratory of Structural Analysis for Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China

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