NDLI: Nonlinear free vibration analysis of Timoshenko nanobeams with surface energy

Content Provider	Springer Nature Link
Author	Nazemnezhad, Reza Hosseini Hashemi, Shahrokh
Copyright Year	2014
Abstract	In this study, influences of balance condition and surface density in addition to the surface elasticity and stress on the nonlinear free vibration of Timoshenko and Euler–Bernoulli nanobeams are investigated. In order to consider the balance condition between the nanobeam bulk and its surfaces, it is assumed that the normal stress varies linearly along the nanobeam thickness. Accordingly, the surface density in addition to the surface stress and elasticity is introduced into the governing equations. Moreover, besides using the bulk density, the surface density is also employed to obtain the kinetic energy of the nanobeams. The multiple scale method is used to obtain an analytical solution for the nonlinear governing equations. This results in the modal response frequencies (the amplitude dependence of the response frequencies due to the nonlinearity) of nanobeams. It is observed that considering the surface density effect and satisfying the balance condition cause a reduction in the frequency ratios, and this reduction is a little more for Timoshenko nanobeams than Euler–Bernoulli ones for all types of boundary conditions used. It is believed that this work is a comprehensive study for investigating effects of all components of the surface energy on the linear and nonlinear free vibrations of Timoshenko and Euler–Bernoulli nanobeams with different boundary conditions while the balance condition is also satisfied.
Starting Page	1027
Ending Page	1044
Page Count	18
File Format	PDF
ISSN	00256455
Journal	Meccanica
Volume Number	50
Issue Number	4
e-ISSN	15729648
Language	English
Publisher	Springer Netherlands
Publisher Date	2014-08-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear free vibration Timoshenko nanobeam Surface density Analytical solution Balance condition Mechanics Civil Engineering Automotive Engineering Mechanical Engineering
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Mechanical Engineering

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