Small Scale Effect on the Vibration of Orthotropic Plates Embedded in an Elastic Medium and Under Biaxial In-plane Pre-load Via Nonlocal Elasticity Theory

Subject Areas : Engineering

M Mohammadi ¹ (Department of Engineering, Ahvaz branch, Islamic Azad university)
M Goodarzi ² (Department of Engineering, Ahvaz branch, Islamic Azad university)
M Ghayour ³ (Department of Mechanical Engineering, Isfahan University of Technology)
S Alivand ⁴ (Department of Engineering, Ahvaz branch, Islamic Azad university)

Received: 2012-02-06 Accepted : 2012-04-08 Published : 2012-06-30

Keywords:

References:

[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56–58.

[2] Wang J., 2005, Carbon-Nanotube based electrochemical biosensors: A Review, Electro Analysis 17: 7–14.

[3] Kinaret J.M., Nord T., Viefers S., 2003, A carbon-nanotube-based nanorelay, Physics Letters A 82: 1287–1289.

[4] Reddy C.D., Rajendran S., Liew K.M., 2006, Equilibrium configuration and continuum elastic properties of finite sized grapheme, Nanotechnology 17: 864–870.

[5] Sakhaeepour A., Ahmadian M., Vafai A., 2007, Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications 145: 168-172.

[6] Zhang Y.Q., Liu G.R., Han X., 2006, Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure, Physics Letters A 349: 370–376.

[7] Aydogdu M., 2009, Axial vibration of the nanorods with the nonlocal continuum rod model, Physica E 41: 861–864.

[8] Filiz S., Aydogdu M., 2010, Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity, Computational Materials Science 49: 619-627.

[9] Murmu T., Adhikari S., 2011, Nonlocal vibration of carbon nanotubes with attached buckyballs at tip, Mechanics Research Communications 38: 62–67.

[10] Malekzadeh P., Setoodeh A.R, Alibeygibeni A., 2011,Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium, Composite Structures 93: 2083-2089.

[11] Khademolhosseini F., Rajapakse R.K.N.D., Nojeh A., 2010, Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models, Computational Materials Science 48: 736–742.

[12] Eringen A.C., 1983, On differential of non-local elasticity and solutions of screw dislocation and surface waves, Journal Applied Physic 54: 4703–4710.

[13] Pradhan S.C., Murmu T., 2009, Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science 47: 268–274.

[14] Pradhan S.C., 2009, Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics Letters A 373: 4182–4188.

[15] Murmu, T. Pradhan, S.C., 2009, Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, Journal Applied Physic 105: 064319.

[16] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multi layered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 1062–1069.

[17] Aghababaei R., Reddy J.N., 2009, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration 326: 277-289.

[18] Pradhan S.C., Murmu T., 2009, Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science 47: 268–274.

[19] Murmu T., Pradhan S.C., 2009, Buckling of biaxially compressed orthotropic plates at small scales, Mechanics Research Communications 36: 933–938.

[20] Murmu T., Pradhan S.C., 2009, Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, Journal Applied Physic 106: 104301.

[21] Chen Y., Lee J.D., Eskandarian A., 2004, Atomistic viewpoint of the applicability of microcontinuum theories, International Journal Solids Structure 41: 2085-2097.

[22] Bert CW., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanic Review 49: 1–27.

[23] Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., 2012, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures 94: 1605–1615.

[24] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39: 23– 27.

[25] Shu C, Richards Be.,1992, Application of generalized differential quadrature to solve two-dimensional incompressible Navier Stokes equations, International Journal for Numerical Methods in Fluids 15: 791–798.

[26] Shu C., 2000, Differential Quadrature and its Application in Engineering, Springer, Great Britain.

[27] Wang Q., Wang C.M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18: 075702.

[28] Duan W.H., Wang C.M., 2007, Exact solutions for axisymmetric bending of micro/ nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704.

[29] Liew K., He M., X Q., Kitipornchai S., 2006, Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix, Acta Material 54: 4229-4236.