Influences of Small-Scale Effect and Boundary Conditions on the Free Vibration of Nano-Plates: A Molecular Dynamics Simulation

Subject Areas : Engineering

S.F Asbaghian Namin ¹ , R Pilafkan ²

1 - University of Mohaghegh Ardabili, Ardabil, Iran
2 - University of Mohaghegh Ardabili, Ardabil, Iran

Received: 2018-05-28 Accepted : 2018-07-02 Published : 2018-09-30

Keywords:

References:

[1] Ramsden J., 2011, Nanotechnology: An Introduction, Elsevier.
[2] Murmu T., Pradhan S.C., 2009, Small-scale effect on the free in-plane vibration of nano plates by nonlocal continuum model, Physica E: Low-Dimensional Systems and Nanostructures 41(8): 1628-1633.
[3] Baughman R.H., Zakhidov A.A., De Heer W.A., 2002, Carbon nanotubes-the route toward applications, Science 297(5582): 787-792.
[4] Liew K.M., Zhang Y., Zhang L.W., 2017, Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges, Journal of Modeling in Mechanics and Materials 1(1): 0159.
[5] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nano plates, Journal of Sound and Vibration 325(1): 206-223.
[6] Hosseini-Hashemi S., Zare M., Nazemnezhad R., 2013, An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity, Composite Structures 100: 290-299.
[7] Zhang Y., Lei Z.X., Zhang L.W., Liew K.M., Yu J.L., 2015, Nonlocal continuum model for vibration of single-layered graphene sheets based on the element-free kp-Ritz method, Engineering Analysis with Boundary Elements 56: 90-97.
[8] Zhang Y., Zhang L.W., Liew K.M., Yu J.L., 2016, Free vibration analysis of bilayer graphene sheets subjected to in-plane magnetic fields, Composite Structures 144: 86-95.
[9] Ansari R., Rajabiehfard R., Arash B., 2010, Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets, Computational Materials Science 49(4): 831-838.
[10] Ansari R., Sahmani S., Arash B., 2010, Nonlocal plate model for free vibrations of single-layered graphene sheets, Physics Letters A 375(1): 53-62.
[11] Pradhan S.C., Kumar A., 2011, Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Composite Structures 93(2): 774-779.
[12] Xing Y.F., Liu B., 2009, New exact solutions for free vibrations of thin orthotropic rectangular plates, Composite Structures 89(4): 567-574.
[13] Setoodeh A.R., Malekzadeh P., Vosoughi A.R., 2011, Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
[14] Shahidi A.R., Shahidi S.H., Anjomshoae A., Estabragh E.R., 2016, Vibration analysis of orthotropic triangular nano plates using nonlocal elasticity theory and Galerkin method, Journal of Solid Mechanics 8(3): 679-692.
[15] Zhang L.W., Zhang Y., Liew K.M., 2017, Modeling of nonlinear vibration of graphene sheets using a mesh free method based on nonlocal elasticity theory, Applied Mathematical Modelling 49: 691-704.
[16] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703-4710.
[17] Reddy J.N., Phan N.D., 1985, Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory, Journal of Sound and Vibration 98(2): 157-170.
[18] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
[19] Bert C.W., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews 49: 1-28.
[20] Plimpton S., 1995, Fast parallel algorithms for short-range molecular dynamics, Journal of Computational Physics 117(1): 1-19.
[21] Haile J.M., Johnston I., Mallinckrodt A.J., McKay S., 1993, Molecular dynamics simulation: elementary methods, Computers in Physics 7(6): 625-625.
[22] http://lammps.sandia.gov/doc/Manual.html/, Sandia National Laboratories, 2015.
[23] Seifoori S., Hajabdollahi H., 2015, Impact behavior of single-layered graphene sheets based on analytical model and molecular dynamics simulation, Applied Surface Science 351: 565-572.
[24] Chu E., 2008, Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms, CRC Press.
[25] Sakhaee-Pour A., 2009, Elastic properties of single-layered graphene sheet, Solid State Communications 149(1): 91-95.