scholarly journals Free Vibration of Piezo-Nanowires Using Timoshenko Beam Theory with Consideration of Surface and Small Scale Effects

2014 ◽  
Vol 61 (1) ◽  
pp. 139-152 ◽  
Author(s):  
Atta Oveisi
Keyword(s):  
Timoshenko Beam ◽  
Surface Effect ◽  
Scale Effects ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Local Effect ◽  
Form Solution ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Nonlocal Timoshenko Beam Theory

Abstract This paper investigates the influence of surface effects on free transverse vibration of piezoelectric nanowires (NWs). The dynamic model of the NW is tackled using nonlocal Timoshenko beam theory. By implementing this theory with consideration of both non-local effect and surface effect under simply support boundary condition, the natural frequencies of the NW are calculated. Also, a closed form solution is obtained in order to calculate fundamental buckling voltage. Finally, the effect of small scale effect on residual surface tension and critical electric potential is explored. The results can help to design piezo-NW based instruments.

scholarly journals Variational Principles for Multiwalled Carbon Nanotubes Undergoing Vibrations Based on Nonlocal Timoshenko Beam Theory

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Ismail Kucuk ◽  
Ibrahim S. Sadek ◽  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Multiwalled Carbon Nanotubes ◽  
Timoshenko Beam ◽  
Variational Principles ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Small Scale ◽  
Multiwalled Carbon ◽  
Nonlocal Timoshenko Beam Theory

Variational principles are derived for multiwalled carbon nanotubes undergoing linear vibrations using the semi-inverse method with the governing equations based on nonlocal Timoshenko beam theory which takes small scale effects and shear deformation into account. Physical models based on the nonlocal theory approximate the nanoscale phenomenon more accurately than the local theories by taking small scale phenomenon into account. Variational formulation is used to derive the natural and geometric boundary conditions which give a set of coupled boundary conditions in the case of free boundaries which become uncoupled in the case of the local theory. Hamilton's principle applicable to this case is also given.

AN INVESTIGATION ON THE CHARACTERISTICS OF BENDING, BUCKLING AND VIBRATION OF NANOBEAMS VIA NONLOCAL BEAM THEORY

2014 ◽  
Vol 11 (06) ◽  
pp. 1350085 ◽  
Author(s):  
SOUMIA BENGUEDIAB ◽  
ABDELWAHED SEMMAH ◽  
FOUZIA LARBI CHAHT ◽  
SOUMIA MOUAZ ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Scale Effects ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Small Scale ◽  
Shear Stresses ◽  
Nonlocal Timoshenko Beam Theory ◽  
Walled Carbon Nanotubes

In the present study, a nonlocal hyperbolic shear deformation theory is developed for the static flexure, buckling and free vibration analysis of nanobeams using the nonlocal differential constitutive relations of Eringen. The theory, which does not require shear correction factor, accounts for both small scale effects and hyperbolic variation of shear strains and consequently shear stresses through the thickness of the nanobeam. The equations of motion are derived from Hamilton's principle. Analytical solutions for the deflection, buckling load and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories. Present solutions can be used for the static and dynamic analyses of single-walled carbon nanotubes.

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