TY - JOUR
T1 - Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation
AU - Ouakad, Hassen M.
AU - Younis, Mohammad I.
N1 - Funding Information:
The authors would like to thank the National Science Foundation , which supported this work through Grant no. 0928494 , and Prof. Paul L. McEuen and Mr. Arend van der Zande of Cornell University for their useful discussions.
PY - 2011/6/20
Y1 - 2011/6/20
N2 - Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been an active research subject over the past few years. Despite the importance of the topic, robust knowledge is still missing in the understanding of the role of various physical parameters affecting the natural frequencies, such as the stretching of doubly clamped CNTs, the DC electrostatic force, and the initial curvature of slack CNTs. In this investigation, we use a 2D nonlinear curved beam model in the form of an arch to simulate the coupled in-plane and out-of-plane motions of a CNT with curvature. We calculate the variation of its natural frequencies and mode shapes with the level of slackness and the DC electrostatic load. Towards this end, we derive a reduced-order model using a multimode Galerkin procedure. We show various scenarios of mode crossing and mode veering as the levels of slackness and DC load are varied. Finally, we tackle the forced vibration problem of a curved CNT when actuated by small DC and AC loads. The results show the transfer of energy among the vibration modes involved in the veering phenomenon.
AB - Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been an active research subject over the past few years. Despite the importance of the topic, robust knowledge is still missing in the understanding of the role of various physical parameters affecting the natural frequencies, such as the stretching of doubly clamped CNTs, the DC electrostatic force, and the initial curvature of slack CNTs. In this investigation, we use a 2D nonlinear curved beam model in the form of an arch to simulate the coupled in-plane and out-of-plane motions of a CNT with curvature. We calculate the variation of its natural frequencies and mode shapes with the level of slackness and the DC electrostatic load. Towards this end, we derive a reduced-order model using a multimode Galerkin procedure. We show various scenarios of mode crossing and mode veering as the levels of slackness and DC load are varied. Finally, we tackle the forced vibration problem of a curved CNT when actuated by small DC and AC loads. The results show the transfer of energy among the vibration modes involved in the veering phenomenon.
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U2 - 10.1016/j.jsv.2010.12.029
DO - 10.1016/j.jsv.2010.12.029
M3 - Article
AN - SCOPUS:79953679241
SN - 0022-460X
VL - 330
SP - 3182
EP - 3195
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 13
ER -