Optimal time delay control for nonlinear vibration of single walled carbon nano-tube on elastic medium

The primary resonance of a single-walled carbon nano-tube (SWCNT) is mitigated by an optimal time-delay feedback control method. The nonlinear governing equations of motion of the SWCNT rested on elastic medium controlled by a Lorentz force excited by a longitudinal magnetic field are derived. The optimal control parameters are worked out by minimum optimal method, which takes the attenuation ratio as the objective function and the stable vibration regions of the feedback gains as constrained conditions. The optimal controllers are designed to control the dynamic behaviors of the nonlinear vibration systems. It is found that the optimal feedback gain obtained by the optimal method can enhance the control performance of SWCNT devices.

[1]  Yiming Fu,et al.  Analysis of nonlinear vibration for embedded carbon nanotubes , 2006 .

[2]  Jinhao Qiu,et al.  Nonlinear vibrations of beams with spring and damping delayed feedback control , 2013 .

[3]  Ali H. Nayfeh,et al.  Nonlinear Normal Modes of a Cantilever Beam , 1995 .

[4]  Khaled A. Alhazza,et al.  Non-linear vibrations of cantilever beams with feedback delays , 2008 .

[5]  Ali H. Nayfeh,et al.  Characterization of the mechanical behavior of an electrically actuated microbeam , 2002 .

[6]  M. Mohammadi,et al.  An investigation on primary resonance phenomena of elastic medium based single walled carbon nanotubes , 2012 .

[7]  A. Maccari.  Vibration Control for the Primary Resonance of a Cantilever Beam by a Time Delay State Feedback , 2003 .

[8]  Nong Zhang,et al.  Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber , 2010 .

[9]  Metin Aydogdu,et al.  Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity , 2012 .

[10]  Y. J. Yan,et al.  Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix , 2010 .

[11]  B. Bhushan,et al.  Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques. , 2003, Ultramicroscopy.

[12]  Reza Ansari,et al.  Nonlinear vibrations of embedded multi-walled carbon nanotubes using a variational approach , 2011, Math. Comput. Model..

[13]  Liying Jiang,et al.  NONLINEAR VIBRATION OF A DOUBLE-WALLED CARBON NANOTUBE EMBEDDED IN A POLYMER MATRIX , 2011 .

[14]  B. Rao,et al.  Large-amplitude free vibrations of simply supported uniform beams with immovable ends , 1992 .

[15]  W.A.A. El-Ganaini,et al.  Vibration suppression of a dynamical system to multi-parametric excitations via time-delay absorber , 2012 .

[16]  Michael L. Roukes,et al.  Dynamic range of nanotube- and nanowire-based electromechanical systems , 2005 .

[17]  Arvind Raman,et al.  Nonlinear and nonplanar dynamics of suspended nanotube and nanowire resonators. , 2008, Nano letters.

[18]  Hui‐Shen Shen,et al.  Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates , 2011 .

[19]  H. Wagner,et al.  Buckling and Collapse of Embedded Carbon Nanotubes , 1998 .

[20]  Jiashi Tang,et al.  A time delay control for a nonlinear dynamic beam under moving load , 2008 .

[22]  A. Mioduchowski,et al.  Vibration and instability of carbon nanotubes conveying fluid , 2005 .

[23]  E. Cigeroglu,et al.  Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions , 2012 .

[24]  M. A. McCarthy,et al.  Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach , 2012 .

[25]  S. Narendar,et al.  Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory , 2012 .

[26]  Ali H. Nayfeh,et al.  Non-linear vibrations of parametrically excited cantilever beams subjected to non-linear delayed-feedback control , 2008 .

[27]  Colin H. Hansen,et al.  The response of a Duffing-van der Pol oscillator under delayed feedback control , 2006 .

[28]  J. Rogers,et al.  Mechanics of buckled carbon nanotubes on elastomeric substrates , 2008 .