An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory

European Journal of Mechanics, A/Solids

Volumn 51, Issue , 2015, Pages 29-43

  Hosseini Hashemi, Shahrokh ^a   Kermajani, Mehdi ^a   Nazemnezhad, Reza ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Analytical solution; Nonlocal elasticity; Reddy plate theory

Indexed keywords

ASPECT RATIO; BOUNDARY CONDITIONS; BUCKLING; EQUATIONS OF MOTION; NANOSTRUCTURES; NATURAL FREQUENCIES; SHEAR DEFORMATION; SHEAR FLOW;

CLOSED FORM SOLUTIONS; HAMILTON'S PRINCIPLE; NATURAL BOUNDARY CONDITION; NON-LOCAL ELASTICITIES; NUMERICAL TECHNIQUES; REDDY PLATE THEORIES; THIRD-ORDER SHEAR DEFORMATION PLATE THEORIES; TRANSVERSE VIBRATIONS;

VIBRATION ANALYSIS;

EID: 84919776386     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2014.11.005     Document Type: Article

References (32)

1. Aghababaei, R., Reddy, J., 2009. Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound Vib. 326, 277-289.
2. Aksencer, T., Aydogdu, M., 2011. Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory. Phys. E 43, 954-959.
3. Aksencer, T., Aydogdu, M., 2012. Forced transverse vibration of nanoplates using nonlocal elasticity. Phys. E 44, 1752-1759.
4. Alavinasab, A., 2009. Nonlocal Theory and Finite Element Modeling of Nano-composites. Clarkson University.
5. Ansari, R., Arash, B., Rouhi, H., 2011a. Vibration characteristics of embedded multi-layered graphene sheets with different boundary conditions via nonlocal elasticity. Compos. Struct. 93, 2419-2429.
6. Ansari, R., Gholami, R., Hosseini, K., Sahmani, S., 2011b. A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory. Math. Comput. Model. 54, 2577-2586.
7. Ansari, R., Rajabiehfard, R., Arash, B., 2010a. Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets. Comput. Mater. Sci. 49, 831-838.
8. Ansari, R., Sahmani, S., Arash, B., 2010b. Nonlocal plate model for free vibrations of single-layered graphene sheets. Phys. Lett. A 375, 53-62.
9. Bedroud, M., Hosseini-Hashemi, S., Nazemnezhad, R., 2013. Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity. Acta Mech. 1-14.
10. Chandra, Y., Chowdhury, R., Scarpa, F., Adhikaricor, S., 2011. Vibrational characteristics of bilayer graphene sheets. Thin Solid Films 519, 6026-6032.
11. Eringen, A.C., 2002. Nonlocal Continuum Field Theories. Springer Verlag.
12. Farajpour, A., Shahidi, A., Mohammadi, M., Mahzoon, M., 2012. Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics. Compos. Struct. 94, 1605-1615.
13. Hosseini-Hashemi, S., Bedroud, M., Nazemnezhad, R., 2013a. An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity. Compos. Struct. 103, 108-118.
14. Hosseini-Hashemi, S., Fadaee, M., Atashipour, S., 2011a. A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates. Int. J. Mech. Sci. 53, 11-22.
15. Hosseini-Hashemi, S., Fadaee, M., Rokni Damavandi Taher, H., 2011b. Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory. Appl. Math. Model. 35, 708-727.
16. Hosseini-Hashemi, S., Fakher, M., Nazemnezhad, R., 2013b. Surface effects on free vibration analysis of nanobeams using nonlocal elasticity: a comparison between Euler-Bernoulli and Timoshenko. J. Solid Mech. 5, 290-304.
17. Hosseini-Hashemi, S., Khorshidi, K., Amabili, M., 2008. Exact solution for linear buckling of rectangular Mindlin plates. J. Sound Vib. 315, 318-342.
18. Hosseini-Hashemi, S., Nahas, I., Fakher, M., Nazemnezhad, R., 2013c. Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity. Acta Mech. 1-10.
19. Hosseini-Hashemi, S., Nazemnezhad, R., Bedroud, M., 2014. Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity. Appl. Math. Model..
20. Hosseini-Hashemi, S., Zare, M., Nazemnezhad, R., 2013d. An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity. Compos. Struct. 100, 290-299.
21. Lu, P., Zhang, P., Lee, H., Wang, C., Reddy, J., 2007. Non-local elastic plate theories. Proc. R. Soc. A 463, 3225-3240.
22. Murmu, T., Pradhan, S., 2009a. Small-scale effect on the vibration of nonuniform nanocantilever based on nonlocal elasticity theory. Phys. E 41, 1451-1456.
23. Murmu, T., Pradhan, S., 2009b. Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity. J. Appl. Phys. 106, 104301-104309.
24. Nazemnezhad, R., Hosseini-Hashemi, S., 2014. Nonlocal nonlinear free vibration of functionally graded nanobeams. Compos. Struct. 110, 192-199.
25. Pradhan, S., 2009. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys. Lett. A 373, 4182-4188.
26. Pradhan, S., Kumar, A., 2010. Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method. Comput. Mater. Sci. 50, 239-245.
27. Pradhan, S., Kumar, A., 2011. Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method. Compos. Struct. 93, 774-779.
28. Pradhan, S., Murmu, T., 2009. Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics. Comput. Mater. Sci. 47, 268-274.
29. Pradhan, S., Phadikar, J., 2009. Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models. Phys. Lett. A 373, 1062-1069.
30. Reddy, J., 2007. Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288-307.
31. Shen, Z.-B., Tang, H.-L., Li, D.-K., Tang, G.-J., 2012. Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory. Comput. Mater. Sci. 61, 200-205.
32. Wang, C., Zhang, Y., He, X., 2007. Vibration of nonlocal Timoshenko beams. Nanotechnology 18, 105401.