Finite-Element Solution to Nonlocal Elasticity and Scale Effect on Frequency Behavior of Shear Deformable Nanoplate Structure
Publication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
In this article, the eigenfrequency responses of a nanoplate structure are evaluated numerically via a novel higher-order mathematical model and finite-element method including nonlocal elasticity theory. A new computer program has been prepared based on the present model to compute the frequencies of the nanoplate structure. The accuracy of the numerical solutions has been checked through proper convergence and comparison with available published data by evaluating an adequate number of examples. The conclusions related to the capability of solving nanoplate structural problem and subsequent accuracy of the current higher-order finite-element model have been demonstrated by solving several illustrations. Also, the numerical examples are solved by considering the nonlocal elasticity as well as the scale effect and other geometrical and material parameters (aspect ratio, size, and nonlocal parameter) that may directly affect the final solutions are discussed.
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References
Aghababaei, R., and J. N. Reddy. 2009. “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates.” J. Sound Vib. 326 (1–2): 277–289. https://doi.org/10.1016/j.jsv.2009.04.044.
Alibeigloo, A. 2011. “Free vibration analysis of nano-plate using three-dimensional theory of elasticity.” Acta Mech. 222 (1–2): 149–159. https://doi.org/10.1007/s00707-011-0518-7.
Ansari, R., B. Arash, and H. Rouhi. 2011. “Vibration characteristics of embedded multi- layered graphene sheets with different boundary conditions via nonlocal elasticity.” Compos. Struct. 93 (9): 2419–2429. https://doi.org/10.1016/j.compstruct.2011.04.006.
Aydogdu, M. 2009. “A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration.” Phys. E Low-Dimensional Syst. Nanostruct 41 (9): 1651–1655. https://doi.org/10.1016/j.physe.2009.05.014.
Challamel, N., Z. Zhang, and C. M. Wang. 2015. “Nonlocal equivalent continua for buckling and vibration analyses of microstructured beams.” J. Nanomech. Micromech. 5 (1): A4014004. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000062.
Cook, R. D., D. S. Malkus, M. E. Plesha, and R. J. Witt. 2009. Concepts and applications of finite element analysis. 3rd ed. Singapore: Wiley.
Daneshmehr, A., A. Rajabpoor, and A. Hadi. 2015. “Size dependent free vibration analysis of nano-plates made of functionally graded materials based on nonlocal elasticity theory with high order theories.” Int. J. Eng. Sci. 95: 23–35. https://doi.org/10.1016/j.ijengsci.2015.05.011.
Duan, W. H., C. M. Wang, and Y. Y. Zhang. 2007. “Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics.” J. Appl. Phys. 101 (2): 024305. https://doi.org/10.1063/1.2423140.
Eringen, A. C. 1983. “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves.” J. Appl. Phys. 54 (9): 4703–4710. https://doi.org/10.1063/1.332803.
Eringen, A. C. 2002. Nonlocal continuum field theories. New York: Springer.
Goodarzi, M., M. Mohammadi, A. Farajpour, and M. Khooran. 2014. “Investigation of the effect of pre-stressed on vibration frequency of rectangular nano-plate based on a visco-Pasternak foundation.” J. Solid Mech. 1 (1): 98–121.
Gurses, M., B. Akgoz, and O. Civalek. 2012. “Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation.” Appl. Math. Comput. 219 (6): 3226–3240.
Han, Y., and J. Elliott. 2007. “Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites.” Comput. Mater. Sci. 39 (2): 315–323. https://doi.org/10.1016/j.commatsci.2006.06.011.
Jomehzadeh, E., and A. R. Saidi. 2011. “A study on large amplitude vibration of multilayered graphene sheets.” Comput. Mater. Sci. 50 (3): 1043–1051. https://doi.org/10.1016/j.commatsci.2010.10.045.
Kananipour, H. 2014. “Static analysis of nano-plates based on the nonlocal Kirchhoff and Mindlin plate theories using DQM.” Lat. Am. J. Solids Struct. 11 (10): 1709–1720. https://doi.org/10.1590/S1679-78252014001000001.
Karimi, M., H. R. Mirdamadi, and A. R. Shahidi. 2017. “Shear vibration and buckling of double layer orthotropic nano-plates based on RPT resting on elastic foundations by DQM including surface effects.” Microsyst. Technol. 23 (3): 765–797. https://doi.org/10.1007/s00542-015-2744-8.
Karimi, M., M. H. Shokrani, and A. R. Shahidi. 2015. “Size-dependent free vibration analysis of rectangular nano-plates with the consideration of surface effects using finite difference method.” J. Appl. Comput. Mech. 1 (3): 122–133.
Katariya, P. V. 2014. “Free vibration and buckling behaviour of laminated composite panel under thermal and mechanical loading.” M.Tech. thesis, Dept. of Mechanical Engineering, NIT Rourkela. http://ethesis.nitrkl.ac.in/6692/.
Lim, C. W., Q. Yang, and J. B. Zhang. 2012. “Thermal buckling of nanorod based on nonlocal elasticity theory.” Int. J. Non Linear Mech. 47 (5): 496–505. https://doi.org/10.1016/j.ijnonlinmec.2011.09.023.
Liu, C., L. Ke, and Y. Wang. 2015. “Nonlinear vibration of nonlocal piezoelectric nano-plates.” Int. J. Str. Stab. Dyn. 15 (8): 1540013. https://doi.org/10.1142/S0219455415400131.
Mantari, J. L., A. S. Oktem, and C. Guedes Soares. 2011. “Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory.” Compos. Struct. 94 (1): 37–49. https://doi.org/10.1016/j.compstruct.2011.07.020.
Mechab, I., N. E. Meiche, and F. Bernard. 2016. “Free vibration analysis of higher-order shear elasticity nanocomposite beams with consideration of nonlocal elasticity and Poisson effect.” J. Nanomech. Micromech. 6 (3): 04016006. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000110.
Mehar, K., and S. K. Panda. 2017. “Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings.” Int. J. Comput. Methods 14 (2): 1750019. https://doi.org/10.1142/S0219876217500190.
Mouloodi, S., J. Khojasteh, M. Salehi, and S. Mohebbi. 2014. “Size dependent free vibration analysis of multi crystalline nano-plates by considering surface effects as well as interface region.” Int. J. Mech. Sci. 85: 160–167. https://doi.org/10.1016/j.ijmecsci.2014.05.023.
Murmu, T., and S. C. Pradhan. 2009. “Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM.” Physica E 41 (7): 1232–1239. https://doi.org/10.1016/j.physe.2009.02.004.
Naderi, A., and A. R. Saidi. 2014. “Modified nonlocal mindline plate theory for buckling analysis of nano-plates.” J. Nanomech. Micromech. 4 (4): A4013015. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000068.
Nami, M. R., and M. Janghorban. 2013. “Static analysis of rectangular nano-plates using trigonometric shear information theory based on nonlocal elasticity theory.” Bailstein J. Nanotechnol. 4: 968–973. https://doi.org/10.3762/bjnano.4.109.
Phadikar, J. K., and S. C. Pradhan. 2010. “Variational formulation and finite element analysis for nonlocal elastic nano-beams and nano-plates.” Comput. Mater. Sci. 49 (3): 492–499. https://doi.org/10.1016/j.commatsci.2010.05.040.
Reddy, J. N. 2004. Mechanics of laminated composite plates and shells: Theory and analysis. Boca Raton, FL: CRC Press.
Salehipour, H., A. R. Shahidi, and H. Nahvi. 2015. “Modified nonlocal elasticity theory for functionally graded materials.” Int. J. Eng. Sci. 90: 44–57. https://doi.org/10.1016/j.ijengsci.2015.01.005.
Shen, L., H. S. Shen, and C. L. Zhang. 2010. “Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments.” Comput. Mater. Sci. 48 (3): 680–685. https://doi.org/10.1016/j.commatsci.2010.03.006.
Thai, H. T., and S. E. Kim. 2010. “Free vibration of laminated composite plates using two variable refined plate theories.” Int. J. Mech. Sci. 52 (4): 626–633. https://doi.org/10.1016/j.ijmecsci.2010.01.002.
Tounsi, A., A. Semmah, and A. A. Bousahla. 2013. “Thermal buckling behavior of nanobeams using an efficient higher-order nonlocal beam theory.” J. Nanomech. Micromech. 3 (3): 37–42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057.
Wang, Y. Z., and F. M. Li. 2014. “Nonlinear primary resonance of nano beam with axial initial load by nonlocal continuum theory.” Int. J. Non Linear Mech. 61: 74–79. https://doi.org/10.1016/j.ijnonlinmec.2014.01.008.
Zhen, Y. 2016. “Vibration and instability analysis of double-carbon nanotubes system conveying fluid.” J. Nanomech. Micromech. 6 (4): 04016008. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000112.
Zhu, H. X., and B. L. Karihaloo. 2008. “Size-dependent bending of thin metallic films.” Int. J. Plast. 24 (6): 991–1007. https://doi.org/10.1016/j.ijplas.2007.08.002.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 9 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Nov 3, 2017
Accepted: Apr 30, 2018
Published online: Jul 16, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 16, 2018
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