Semi-analytical motion analysis of nano-steering devices, segmented piezotube scanners

Although the scanning probe microscopes (SPMs) and especially the atomic force microscope (AFM) are unrivaled devices for nanorobotic applications, their performance is hampered by some error sources, especially the scanner nonlinearities. For nonlinearities modeling and compensation, the present paper tries to introduce a new comprehensive viewpoint on the nonlinear behavior of the piezo scanners, especially the cylindrical ones. The static and free vibration analyses of the segmented piezotube scanners, presented using a semi-analytic approach, named the generalized differential quadrature method (GDQM), and some significant conclusions are achieved. Using a unique formulation for static solution, the negligibility of the cantilever mass and some manipulation forces are also proven. At the end, the effects of segmentation parameters are introduced and completely analyzed for the design optimization.

[1]  M. Sitti,et al.  Survey of nanomanipulation systems , 2001, Proceedings of the 2001 1st IEEE Conference on Nanotechnology. IEEE-NANO 2001 (Cat. No.01EX516).

[2]  K. M. Liew,et al.  Analysis of wave propagation in piezoelectric coupled cylinder affected by transverse shear and rotary inertia , 2003 .

[3]  P. C. Dumir,et al.  Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load , 1998 .

[4]  C. Hong.  Computational approach of piezoelectric shells by the GDQ method , 2010 .

[5]  Seok Heo,et al.  Dynamic modelling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators , 2009 .

[6]  Chang Shu,et al.  A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates , 1997 .

[7]  Siak Piang Lim,et al.  AN APPROXIMATE FREQUENCY FORMULA FOR PIEZOELECTRIC CIRCULAR CYLINDRICAL SHELLS , 2001 .

[8]  Ö. Civalek.  Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns , 2004 .

[9]  Hui‐Shen Shen,et al.  Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes , 2010 .

[10]  D. D. Ebenezer,et al.  Piezoelectric thin shell theoretical model and eigenfunction analysis of radially polarized ceramic cylinders , 1998 .

[11]  Kang Yong Lee,et al.  Static and dynamic behavior of simply-supported cross-ply laminated piezoelectric cylindrical panels with imperfect bonding , 2006 .

[12]  Chang Shu,et al.  Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates , 1997 .

[13]  Sadegh Sadeghzadeh,et al.  Aspect ratio and dimension effects on nanorod manipulation by atomic force microscope , 2010 .

[14]  Robert L. Clark,et al.  Active Control of Structurally Radiated Sound from an Enclosed Finite Cylinder , 1994 .

[15]  D. Redekop.  Vibration analysis of a torus–cylinder shell assembly , 2004 .

[16]  M. Sitti,et al.  Atomic force microscope based two-dimensional assembly of micro/nanoparticles , 2005, (ISATP 2005). The 6th IEEE International Symposium on Assembly and Task Planning: From Nano to Macro Assembly and Manufacturing, 2005..

[17]  Sylvie Lefebvre,et al.  Piezoelectric Actuator Models for Active Sound and Vibration Control of Cylinders , 1993 .

[18]  D. D. Ebenezer,et al.  EIGENFUNCTION ANALYSIS OF RADIALLY POLARIZED PIEZOELECTRIC CYLINDRICAL SHELLS OF FINITE LENGTH , 1997 .

[19]  M. Meyyappan,et al.  Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic force microcantilevers , 2004 .

[20]  J. N. Reddy,et al.  A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories , 1989 .

[21]  Y. Xiang,et al.  Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions , 2006 .

[22]  Stanley B. Dong,et al.  Frequency Spectra of Laminated Piezoelectric Cylinders , 1994 .

[23]  Joseph A. Turner,et al.  Dynamic behaviour of dagger-shaped cantilevers for atomic force microscopy , 2004 .

[24]  Parviz Malekzadeh,et al.  A three-dimensional layerwise-differential quadrature free vibration analysis of laminated cylindrical shells , 2008 .

[25]  Yi-Heng Chen,et al.  On the explicit formulations of circular tube, bar and shell of cylindrically piezoelectric material under pressuring loading , 2001 .

[26]  Moharam Habibnejad Korayem,et al.  A new modeling and compensation approach for creep and hysteretic loops in nanosteering by SPM’s piezotubes , 2009 .

[27]  Ömer Civalek,et al.  Numerical analysis of free vibrations of laminated composite conical and cylindrical shells , 2007 .

[28]  Li Hua,et al.  Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method , 1998 .