RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM

Mohsen Bastami; Bashir Behjat

RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM

Abstract

In this paper, free vibration and buckling of single-layered isotropic rectangular nanoplate is investigated based on classic plate theory (CPT). Nonlocal elasticity theory accounts for the small-nonlocal effects. Both Winkler-type and Pasternak-type foundation models are employed to simulate the surrounding elastic matrix. Governing differential weak form equations of the plate based on nonlocal elasticity theory are derived. The Ritz method is used to solve the problem of buckling and free vibration nanoplate for various boundary conditions. In order to confirm the accuracy of the results, data are compared with the other results published in literature. The effects of different parameters on the plate behavior, such as nonlocal parameter, aspect ratio, boundary conditions, Winkler and shear modulus are investigated.

Keywords

References

[1] Gurtin, M.E. and Murdoch, A.I. "Surface stress in solids", International Journal of Solids and Structures, 14, pp.431-440 (1978).
[2] Fleck, N. and Hutchinson, J. "Strain gradient plasticity" Advances in applied mechanics, 33, pp.295-361 (1997).
[3] Tsiatas, G.C. "A new Kirchhoff plate model based on a modified couple stress theory", International Journal of Solids and Structures, 46, pp.2757-2764 (2009).
[4] Eringen, A.C. Edelen, D. " On nonlocal elasticity", International Journal of Engineering Science, 10, pp.233-248 (1972).
[5] Pradhan, S. and Phadikar, J. "Nonlocal elasticity theory for vibration of nanoplates", Journal of Sound and Vibration, 325, pp.206-223 ( 2009).
[6] Ansari, R., Sahmani, S. and Arash, B. "Nonlocal plate model for free vibrations of single-layered graphene sheets", Physics Letters A, 375, pp.53-62 (2010).
[7] Murmu, T. and Adhikari, S. "Nonlocal vibration of bonded double-nanoplate-systems", Composites Part B: Engineering, 42, pp.1901-1911 (2011).
[8] Pradhan, S. and Phadikar, J." Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Physics Letters A, 373, pp.1062-1069 (2009).

[9] Malekzadeh, P., Setoodeh, A. and Beni, A.A. "Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates", Composite Structures, 93, pp.1631-1639 (2011).
[10] Pouresmaeeli, S., Fazelzadeh, S. and Ghavanloo, E. "Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium", Composites Part B: Engineering, 43 pp.3384-3390 (2012).
[11] Chakraverty, S.and Behera, L. "Free vibration of rectangular nanoplates using Rayleigh–Ritz method", Physica E: Low-dimensional Systems and Nanostructures, 56, pp.357-363 (2014).
[12] Mohammadi, M., Ghayour, M., and Farajpour, A. "Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model", Composites Part B: Engineering, 45, pp.32-42 (2013).
[13] Mohammadi, M. Farajpour, A. and Goodarzi, M. "Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium". Computational Materials Science, 82, pp.510-520 (2014).
[14] Aksencer, T. and Aydogdu, M. "Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory", Physica E: Low-dimensional Systems and Nanostructures, 43, pp.954-959 (2011).
[15] Pradhan, S. and Murmu, T. "Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics", Computational Materials Science, 47, pp.268-274 (2009).
[16] Hashemi, S.H. and Samaei, A.T. "Buckling analysis of micro/nanoscale plates via nonlocal elasticity theory", Physica E: Low-dimensional Systems and Nanostructures, 43, pp.1400-1404 (2011).
[17] Murmu, T. and Pradhan, S. "Buckling of biaxially compressed orthotropic plates at small scales", Mechanics Research Communications, 36, pp.933-938 (2009).
[18] Farajpour, A. Shahidi, A.R., Mohammadi, M. and Mahzoon, M. "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Composite Structures, 94, pp.1605-1615 (2012).
[19] Babaei, H. and Shahidi, A. "Small-scale effects on the buckling of quadrilateral nanoplates based on nonlocal elasticity theory using the Galerkin method", Archive of Applied Mechanics, 81, pp.1051-1062 (2011).
[20] Farajpour, A., Mohammadi, M., Shahidi, A.R. and Mahzoon, M. "Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model", Physica E: Low-dimensional Systems and Nanostructures, 43, pp.1820-1825 (2011).
[21] Pradhan, S. and Murmu, T. "Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory", Physica E: Low-dimensional Systems and Nanostructures, 42, pp.1293-1301 (2010).
[22] Murmu, T. and Pradhan, S. "Nonlocal buckling of double-nanoplate-systems under biaxial compression". Composites Part B: Engineering, 44, pp.84-94 (2013).
[23] Behfar, K. and Naghdabadi, R. "Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium". Composites Science and Technology, 65, pp.1159-1164 (2005).
[24] Eringen, A.C. "Nonlocal polar elastic continua". International journal of engineering science, 10, pp.1-16 (1972).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mohsen Bastami This is me
Iran

Bashir Behjat This is me
Iran

Publication Date

June 1, 2017

Submission Date

August 3, 2016

Acceptance Date

February 25, 2017

Published in Issue

Year 2017 Volume: 35 Number: 2

IZ

https://izlik.org/JA26UG34RY

Cite

RIS / Bibtex

APA

Bastami, M., & Behjat, B. (2017). RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM. Sigma Journal of Engineering and Natural Sciences, 35(2), 285-302. https://izlik.org/JA26UG34RY

AMA

1.Bastami M, Behjat B. RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM. SIGMA. 2017;35(2):285-302. https://izlik.org/JA26UG34RY

Chicago

Bastami, Mohsen, and Bashir Behjat. 2017. “RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM”. Sigma Journal of Engineering and Natural Sciences 35 (2): 285-302. https://izlik.org/JA26UG34RY.

EndNote

Bastami M, Behjat B (June 1, 2017) RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM. Sigma Journal of Engineering and Natural Sciences 35 2 285–302.

IEEE

[1]M. Bastami and B. Behjat, “RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM”, SIGMA, vol. 35, no. 2, pp. 285–302, June 2017, [Online]. Available: https://izlik.org/JA26UG34RY

ISNAD

Bastami, Mohsen - Behjat, Bashir. “RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM”. Sigma Journal of Engineering and Natural Sciences 35/2 (June 1, 2017): 285-302. https://izlik.org/JA26UG34RY.

JAMA

1.Bastami M, Behjat B. RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM. SIGMA. 2017;35:285–302.

MLA

Bastami, Mohsen, and Bashir Behjat. “RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM”. Sigma Journal of Engineering and Natural Sciences, vol. 35, no. 2, June 2017, pp. 285-02, https://izlik.org/JA26UG34RY.

Vancouver

1.Mohsen Bastami, Bashir Behjat. RITZ SOLUTION OF BUCKLING AND VIBRATION PROBLEM OF NANOPLATES EMBEDDED IN AN ELASTIC MEDIUM. SIGMA [Internet]. 2017 Jun. 1;35(2):285-302. Available from: https://izlik.org/JA26UG34RY