Resonant frequency analysis of Timoshenko nanowires with surface stress for different boundary conditions

2012 ◽  
Vol 112 (7) ◽  
pp. 074322 ◽  
Author(s):  
Qilu He ◽  
Carmen M. Lilley
Keyword(s):  
Boundary Conditions ◽  
Resonant Frequency ◽  
Frequency Analysis ◽  
Surface Stress ◽  
Different Boundary Conditions

Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions Between Inner and Outer Tubes

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Kai-Yu Xu ◽  
Elias C. Aifantis ◽  
Yong-Hua Yan
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Resonant Frequency ◽  
Free Vibrations ◽  
Original Method ◽  
Reduced Form ◽  
Vibrational Modes ◽  
Resonant Frequencies ◽  
Different Boundary Conditions ◽  
Double Walled Carbon Nanotubes

Free vibrations of a double-walled carbon nanotube (DWNT) are studied. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting each other by van der Waals forces. An original method is proposed to calculate the first seven order resonant frequencies and relative vibrational modes. Detailed results are demonstrated for DWNTs according to the different boundary conditions between inner and outer tubes, such as fixed-free, cantilever-free, fixed-simple and fixed-fixed (reduced form) supported ends. Our results indicate that there is a special invariable frequency for a DWNT that is not affected by different combinations of boundary conditions. All vibrational modes of the DWNT must be coaxial when the resonant frequency is smaller than this frequency. Some noncoaxial vibrations will occur when their resonant frequencies exceed the frequency. Especially, the first noncoaxial resonant frequency is still invariable for all different boundary conditions. A change of resonant frequency for various lengths of DWNTs is discussed in detail. In addition, our model predicts a new coaxial-noncoaxial vibrational mode in fixed-simple supports for inner and outer tubes of a DWNT.

Natural frequency analysis of fluid conveying pipeline with different boundary conditions

2010 ◽  
Vol 240 (3) ◽  
pp. 461-467 ◽  
Author(s):  
Huang Yi-min ◽  
Liu Yong-shou ◽  
Li Bao-hui ◽  
Li Yan-jiang ◽  
Yue Zhu-feng
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Frequency Analysis ◽  
Different Boundary Conditions ◽  
Natural Frequency Analysis
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