Influences of Small-Scale Effect and Boundary Conditions on the Free Vibration of Nano-Plates: A Molecular Dynamics Simulation
محورهای موضوعی : Engineering
S.F Asbaghian Namin
1
(University of Mohaghegh Ardabili, Ardabil, Iran)
R Pilafkan
2
(University of Mohaghegh Ardabili, Ardabil, Iran)
کلید واژه: Nonlocal elasticity theory, Nonlocal parameter, Molecular dynamics simulations, Nano-plates, Fundamental frequencies,
چکیده مقاله :
This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the most common nano-plates. On the other hand, governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different side lengths, boundary conditions, and nonlocal parameter are inspected for the aforementioned methods. The results obtained from the MD simulations are compared with those of nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. As a result, for the first time, the nonlocal parameter values are suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.
[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.
