TY - JOUR
T1 - Free torsional vibration of nanotubes based on nonlocal stress theory
AU - Lim, C. W.
AU - Li, C.
AU - Yu, J. L.
PY - 2012/6/4
Y1 - 2012/6/4
N2 - A new elastic nonlocal stress model and analytical solutions are developed for torsional dynamic behaviors of circular nanorods/nanotubes. Unlike the previous approaches which directly substitute the nonlocal stress into the equations of motion, this new model begins with the derivation of strain energy using the nonlocal stress and by considering the nonlinear history of straining. The variational principle is applied to derive an infinite-order differential nonlocal equation of motion and the corresponding higher-order boundary conditions which contain a nonlocal nanoscale parameter. Subsequently, free torsional vibration of nanorods/nanotubes and axially moving nanorods/nanotubes are investigated in detail. Unlike the previous conclusions of reduced vibration frequency, the solutions indicate that natural frequency for free torsional vibration increases with increasing nonlocal nanoscale. Furthermore, the critical speed for torsional vibration of axially moving nanorods/nanotubes is derived and it is concluded that this critical speed is significantly influenced by the nonlocal nanoscale. © 2012 Elsevier Ltd. All rights reserved.
AB - A new elastic nonlocal stress model and analytical solutions are developed for torsional dynamic behaviors of circular nanorods/nanotubes. Unlike the previous approaches which directly substitute the nonlocal stress into the equations of motion, this new model begins with the derivation of strain energy using the nonlocal stress and by considering the nonlinear history of straining. The variational principle is applied to derive an infinite-order differential nonlocal equation of motion and the corresponding higher-order boundary conditions which contain a nonlocal nanoscale parameter. Subsequently, free torsional vibration of nanorods/nanotubes and axially moving nanorods/nanotubes are investigated in detail. Unlike the previous conclusions of reduced vibration frequency, the solutions indicate that natural frequency for free torsional vibration increases with increasing nonlocal nanoscale. Furthermore, the critical speed for torsional vibration of axially moving nanorods/nanotubes is derived and it is concluded that this critical speed is significantly influenced by the nonlocal nanoscale. © 2012 Elsevier Ltd. All rights reserved.
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U2 - 10.1016/j.jsv.2012.01.016
DO - 10.1016/j.jsv.2012.01.016
M3 - RGC 21 - Publication in refereed journal
SN - 0022-460X
VL - 331
SP - 2798
EP - 2808
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 12
ER -