Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory

Abstract The potential of circular graphene sheet (GS) as a mass sensor is explored. A circular GS carrying a nanoparticle at an arbitrary position is modeled as a circular nanoplate with a concentrated micro-mass for clamped and simply supported boundary conditions. Based on the nonlocal Kirchhoff plate theory which incorporates size effects into the classical theory, the natural frequencies of the mass sensor are derived using the Galerkin method. The effects of mass and position of the nanoparticle on the frequencies and frequency shifts are discussed. The frequencies reduce to the results of the classical model for the absence of the small scale effect, which maintain in accordance with those available in literatures. Numerical results show that when the mass of the attached nanoparticle increases or its location is closer to the plate center, the natural frequency decreases, but frequency shift increases. Small scale effect diminishes the frequencies strongly, but has less effect on the frequency shifts. When the radius of the nanoplate decreases, the frequency shift increases. The results are helpful to design circular GS-based resonators as nanomechanical mass sensor.

[1]  Reza Ansari,et al.  Nonlocal plate model for free vibrations of single-layered graphene sheets , 2010 .

[2]  M. Aydogdu,et al.  Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory , 2011 .

[3]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[4]  H. Dai,et al.  Nanotubes as nanoprobes in scanning probe microscopy , 1996, Nature.

[5]  S. C. Pradhan,et al.  Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method , 2010 .

[6]  S. Adhikari,et al.  Vibrating carbon nanotube based bio-sensors , 2009 .

[7]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .

[8]  Charles M. Lieber,et al.  Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes , 1997 .

[9]  Le Shen,et al.  Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments , 2010 .

[10]  Diana V. Bambill,et al.  Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications , 2004 .

[11]  Xian‐Fang Li,et al.  Transverse vibration of nanotube-based micro-mass sensor via nonlocal Timoshenko beam theory , 2012 .

[12]  V. Sorkin,et al.  Graphene-based pressure nano-sensors , 2011, Journal of molecular modeling.

[13]  Xian‐Fang Li,et al.  Vibration of double-walled carbon nanotube based nanomechanical sensor with initial axial stress , 2012 .

[14]  W. D. Heer,et al.  Electrostatic deflections and electromechanical resonances of carbon nanotubes , 1999, Science.

[15]  A. Farajpour,et al.  Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model , 2011 .

[16]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[17]  P.A.A. Laura,et al.  A note on vibrating circular plates carrying concentrated masses , 1984 .

[18]  Small amplitude, transverse vibrations of circular plates with an eccentric rectangular perforation elastically restrained against rotation and translation on both edges , 2008 .

[19]  K. M. Liew,et al.  Continuum model for the vibration of multilayered graphene sheets , 2005 .

[20]  A. Eringen,et al.  Nonlocal Continuum Field Theories , 2002 .

[21]  Transverse vibration of thin solid and annular circular plate with attached discrete masses , 2006 .

[22]  Pisidhi Karasudhi.  Foundations of solid mechanics , 1991 .

[23]  S. C. Pradhan.  Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory , 2009 .

[24]  Jin-Xing Shi,et al.  Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model , 2011 .

[25]  R. Ansari,et al.  Prediction of the biaxial buckling and vibration behavior of graphene via a nonlocal atomistic-based plate theory , 2013 .

[26]  K. Liew,et al.  Resonance analysis of multi-layered graphene sheets used as nanoscale resonators , 2005, Nanotechnology.

[27]  C. Wang,et al.  Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory , 2007 .

[29]  Chunyu Li,et al.  Mass detection using carbon nanotube-based nanomechanical resonators , 2004 .

[30]  R. Ansari,et al.  Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity , 2011 .

[31]  R. Naghdabadi,et al.  Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium , 2005 .

[32]  R. Ansari,et al.  Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity , 2012 .

[33]  A. Vafai,et al.  Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors , 2008 .

[34]  K. Jensen,et al.  An atomic-resolution nanomechanical mass sensor. , 2008, Nature Nanotechnology.

[35]  Reza Ansari,et al.  Vibration analysis of circular and square single-layered graphene sheets: An accurate spring mass model , 2013 .

[36]  S. C. Pradhan,et al.  Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory , 2010 .

[37]  Anand Y. Joshi,et al.  Zeptogram scale mass sensing using single walled carbon nanotube based biosensors , 2011 .

[38]  S. C. Pradhan,et al.  Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method , 2011 .

[39]  Alessandra Bonanni,et al.  Graphene for electrochemical sensing and biosensing , 2010 .

[40]  J. Hsu,et al.  Frequency Shift of Carbon-Nanotube-Based Mass Sensor Using Nonlocal Elasticity Theory , 2010, Nanoscale research letters.

[41]  P Kim,et al.  ナノチューブナノピンセット | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 1999 .

[42]  Yuyan Shao,et al.  Graphene Based Electrochemical Sensors and Biosensors: A Review , 2010 .

[43]  Jin-Xing Shi,et al.  An atomic-resolution nanomechanical mass sensor based on circular monolayer graphene sheet: Theoretical analysis of vibrational properties , 2013 .