Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

Abstract The vibration characteristics of a simply supported viscoelastic nanoplate are studied using the nonlocal plate theory by including the effect of viscoelastic foundation. The material properties of nanoplate are assumed to be orthotropic and viscoelastic and the viscoelastic medium is modeled as Kelvin–Voigt foundation. The complex frequency which is associated with the nonlocal parameter, structural damping of the nanoplate and foundation effects is obtained in a closed-form expression. The predicted results are validated by carrying out the comparison studies for the isotropic elastic nanoplates against existing results in the literature. Moreover, the effects of different parameters such as the nonlocal parameter, structural damping, the stiffness and damping coefficient of the foundation and the aspect ratio on the frequency are elucidated. The results show that the frequency significantly decreases with increasing the structural damping coefficient as well as the damping coefficient of foundation.

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

[2]  S. C. Pradhan,et al.  Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models , 2009 .

[3]  Junhong Chen,et al.  Reduced graphene oxide for room-temperature gas sensors , 2009, Nanotechnology.

[4]  M. Aydogdu,et al.  Forced transverse vibration of nanoplates using nonlocal elasticity , 2012 .

[5]  Reza Ansari,et al.  Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets , 2010 .

[6]  Scott S. Verbridge,et al.  Electromechanical Resonators from Graphene Sheets , 2007, Science.

[7]  L. Catherine Brinson,et al.  Polymer Engineering Science and Viscoelasticity , 2008 .

[8]  S. C. Pradhan,et al.  Nonlocal elasticity theory for vibration of nanoplates , 2009 .

[9]  N. Koratkar,et al.  Viscoelastic Properties of Graphene-Polymer Composites , 2012 .

[10]  Freund.  Thin Film Materials , 2004 .

[11]  Tony Murmu,et al.  Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity , 2009 .

[12]  L. Sekaric,et al.  Nanofabrication and electrostatic operation of single-crystal silicon paddle oscillators , 1999 .

[13]  Zhi Yang,et al.  Exceptional negative thermal expansion and viscoelastic properties of graphene oxide paper , 2012 .

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

[15]  J. Lagnese.  Boundary Stabilization of Thin Plates , 1987 .

[16]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

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

[18]  J. S. Rao.  Dynamics of Plates , 1998 .

[19]  Behrooz Farshi,et al.  Vibration characteristics of circular nanoplates , 2010 .

[20]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[21]  S. C. Pradhan,et al.  Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory , 2009 .

[22]  E. Jomehzadeh,et al.  Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates , 2011 .

[23]  S. C. Pradhan,et al.  SMALL-SCALE EFFECT ON THE FREE IN-PLANE VIBRATION OF NANOPLATES BY NONLOCAL CONTINUUM MODEL , 2009 .

[24]  Quan Wang,et al.  Detection of gas atoms via vibration of graphenes , 2011 .

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

[26]  P. Malekzadeh,et al.  Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates , 2011 .

[27]  Aleksey D. Drozdov,et al.  Viscoelastic structures : mechanics of growth and aging , 1998 .