An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity

Composite Structures

Volumn 100, Issue , 2013, Pages 290-299

  Hosseini Hashemi, Shahrokh ^a   Zare, Mojtaba ^a   Nazemnezhad, Reza ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Exact analytical solution; Free vibration; Mindlin plate theory; Nano plate; Nonlocal elasticity theory

Indexed keywords

ANALYTICAL APPROACH; ANALYTICAL PROCEDURE; DIFFERENT BOUNDARY CONDITION; EXACT ANALYTICAL SOLUTIONS; FREE VIBRATION; NANO-PLATE; NON-LOCAL ELASTICITIES; NON-LOCAL ELASTICITY THEORIES;

ASPECT RATIO; BOUNDARY CONDITIONS; ELASTICITY; MINDLIN PLATES; NATURAL FREQUENCIES;

NANOSTRUCTURES;

EID: 84875282255     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.11.035     Document Type: Article

References (28)

1. Freund L.B., Suresh S. Thin film materials 2003, Cambridge University Press, Cambridge, UK.
2. Zalalutdinov M.K., Baldwin J.W., Marcus M.H., Reichenbach R.B., Parpia J.M., Houston B.H. Two-dimensional array of coupled nanomechanical resonators. Appl Phys Lett 2006, 88:14350.
3. Tighe T.S., Worlock J.M., Roukes M.L. Direct thermal conductance measurements on suspended monocrystalline nanostructures. Appl Phys Lett 1997, 70:2687-2689.
4. Evoy S., Carr D.W., Sekaric L., Olkhovets A., Parpia J.M., Craighead H.G. Nanofabrication and electrostatic operation of single-crystal silicon paddle oscillations. J Appl Phys 1999, 86:6072-6077.
5. Bunch J.S., van der Zande A.M., Verbridge S.S., Frank I.W., Tanenbsum D.M., Parpi J.M., et al. Electromechanical resonators from graphene sheets. Science 2007, 315:490-493.
6. Liang Y.C., Dou J.H., Bai Q.S. Molecular dynamic simulation study of AFM single-wall carbon nanotube tip-surface interactions. Mater Sci Eng 2007, 339:206-210.
7. Eringen A.C. Nonlocal continuum field theories 2002, Springer, New York (NY).
8. ShenShen H., Zhang C.L. Torsional buckling and post buckling of double-walled carbon nanotubes by nonlocal shear deformable shell model. Compos Struct 2010, 92:1073-1084.
9. Wang Q., Liew K.M. Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Phys Lett A 2007, 363:236-242.
10. Reddy J.N. Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 2007, 45:288-307.
11. Kitipornchai S., He X.Q., Liew K.M. Continuum model for the vibration of multilayered graphene sheets. Phys Rev B 2005, 72(7):75443-75446.
12. Aghababaei R., Reddy J.N. Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J Sound Vib 2009, 326:277-289.
13. Lu P., Zhang P.Q., Lee H.P., Wang C.M., Reddy J.N. Non-local elastic plate theories. Proc Roy Soc A 2007, 463(2088):3225-3240.
14. Pradhan S.C., Phadikar J.K. Nonlocal elasticity theory for vibration of nanoplates. J Sound Vib 2009, 325:206-223.
15. Ansari R., Sahmani S., Arash B. Nonlocal plate model for free vibrations of single-layered graphene sheets. Phys Lett A 2010, 375:53-62.
16. Pradhan S.C. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys Lett A 2009, 373:4182-4188.
17. Samaei A.T., Abbasion S., Mirsayar M.M. Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory. Mech Res Commun 2011, 38:481-485.
18. Aksencer T., Aydogdu M. Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory. Physica E 2011, 43:954-959.
19. Jomehzadeh E., Saidi A.R. Decoupling the nonlocal elasticity equations for three dimensional vibration analysis of nano-plates. Compos Struct 2011, 93:1015-1020.
20. Ansari R., Rajabiehfard R., Arash B. Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Computat Mater Sci 2010, 49:831-838.
21. Ansari R., Gholami R., Hosseini K., Sahmani S. A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory. Math Comput Modell 2011, 54:2577-2586.
22. Pradhan S.C., Kumar A. Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method. Compos Struct 2011, 93:774-779.
23. Hosseini-Hashemi Sh., Fadaee M., Rokni-Damavandi-Taher H. Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory. Appl Math Modell 2011, 35:708-727.
24. Hosseini-Hashemi S., Fadaee M., Atashipour S.R. A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates. Int J Mech Sci 2011, 53:11-22.
25. Hosseini-Hashemi Sh., Arsanjani M. Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates. Int J Solids Struct 2005, 42:819-853.
26. Reddy J.N. Mechanics of laminated composite plates and shells 1997, Boca Raton, London, New York, Washington, DC.
27. Alvinasab A. Nonlocal theory and finite element modeling of nano-composites. Ph.D. Thesis. vol. 103. CLARKSON UNIVERSITY; 2009. p. 3376480.
28. Lu P., He L.H., Lee H.P., Lu C. Thin plate theory including surface effects. Int J Solids Struct 2006, 43:4631-4647.