Vibration Analysis of Orthotropic Triangular Nanoplates Using Nonlocal Elasticity Theory and Galerkin Method
Subject Areas : EngineeringA.R Shahidi 1 , S.H Shahidi 2 , A Anjomshoae 3 , E Raeisi Estabragh 4
1 - Department of Mechanical Engineering, Isfahan University of Technology
2 - Department of Mechanical Engineering, Isfahan University of Technology
3 - Department of Mechanical Engineering, Isfahan University of Technology
4 - Department of Mechanical Engineering, University of Jiroft
Keywords:
Abstract :
[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56-58.
[2] Stankovich S., Dikin D.A., Dommett G. H. B., Kohlhaas K., Zimney E., Stach E., Piner R., Nguyen S., Ruoff R., 2006, Graphene-based composite materials, Nature 442: 282-286.
[3] Mylvaganam K., Zhang L., 2004, Important issues in a molecular dynamics simulation for characterizing the mechanical properties of carbon nanotubes, Carbon 42(10): 2025-2032.
[4] Sears A., Batra R. C., 2004, Macroscopic properties of carbon nanotubes from molecular-mechanics simulations, Physical Review B 69(23): 235406.
[5] Sohi N., Naghdabadi R., 2007, Torsional buckling of carbon nanopeapods, Carbon 45: 952-957.
[6] Popov V. N., Doren V. E. V., Balkanski M., 2000, Elastic properties of single-walled carbon nanotubes, Physical Review B 61: 3078-3084.
[7] Sun C., Liu K., 2008, Dynamic torsional buckling of a double-walled carbon nanotube embedded in an elastic medium, European Journal of Mechanics - A/Solids 27: 40-49.
[8] Behfar K., Seifi P., Naghdabadi R., Ghanbari J., 2006, An analytical approach to determination of bending modulus of a multi-layered Graphene sheet, Thin Solid Films 496(2): 475-480.
[9] Wong E. W., Sheehan P. E., Lieber C. M., 1997, Nanobeam mechanics: elasticity, strength, and toughness of nano rods and nano tubes, Science 277: 1971-1975.
[10] Liew K. M., He X. Q., Kitipornchai S., 2006, Predicting nanovibration of multi-layered Graphene sheets embedded in an elastic matrix, Acta Materialia 54: 4229-4236.
[11] Eringen C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.
[12] Eringen C., 2002, Nonlocal Continuum Field Theories, Springer, New York.
[13] Wang Q., Wang C. M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modeling carbon nanotubes, Nanotechnology 18(7): 075702.
[14] Civalek Ö., Akgöz B., 2010, Free vibration analysis of microtubules as cytoskeleton components: nonlocal euler-bernoulli beam modeling, Journal of Scientia Iranica 17(5): 367-375.
[15] Civalek Ö., Çigdem D., 2011, Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory, Applied Mathematical Modeling 35: 2053-2067.
[16] Murmu T., Adhikari S., 2010, Nonlocal transverse vibration of double-nanobeam-systems, Journal of Applied Physics 108: 083514.
[17] Khademolhosseini F., Rajapakse R. K. N. D., Nojeh A., 2010, Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models, Computational Materials Science 48: 736-742.
[18] Wang Q., Varadan V. K., 2006, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Materials and Structures 15: 659-666.
[19] Reddy J. N., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45: 288-307.
[20] Luo X., Chung D. D. L., 2000, Vibration damping using flexible graphite, Carbon 38: 1510-1512.
[21] Zhang L., Huang H., 2006, Young’s moduli of ZnO nanoplates: Ab initio determinations, Applied Physics Letters 89: 183111.
[22] Freund L. B., Suresh S., 2003, Thin Film Materials, Cambridge University Press, Cambridge.
[23] Scarpa F., Adhikari S., Srikantha Phani A., 2009, Effective elastic mechanical properties of single layer Graphene sheets, Nanotechnology 20: 065709.
[24] Sakhaee-Pour A., 2009, Elastic buckling of single-layered Graphene sheet, Computational Materials Science 45: 266-270.
[25] Pradhan S. C., Phadikar J. K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325: 206-223.
[26] Pradhan S. C., Phadikar J. K.,2009, Small scale effect on vibration of embedded multilayered Graphene sheets based on nonlocal continuum models, Physics Letters A 37: 1062-1069.
[27] Phadikar J. K., Pradhan S. C., 2010, Variational formulation and finite element analysis for nonlocal elastic nanobeams and nanoplates, Computational Materials Science 49: 492-499.
[28] Pradhan S. C., Kumar A., 2010, Vibration analysis of orthotropic Graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science 50: 239-245.
[29] Aydogdu M., Tolga A., 2011, Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory, Physica E 43: 954-959.
[30] Jomehzadeh E., Saidi A. R., 2011, A study on large amplitude vibration of multilayered Graphene sheets, Computational Materials Science 50: 1043-1051.
[31] Jomehzadeh E., Saidi A. R., 2011, Decoupling the nonlocal elasticity equations for three dimension a vibration analysis of nano-plates, Journal of Composite Structures 93: 1015-1020.
[32] Salehipour H. , Nahvi H., Shahidi A.R., 2015, Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity, Physica E: Low-dimensional Systems and Nanostructures 66: 350-358.
[33] Ansari R. , Shahabodini A. , Faghih Shojaei M., 2016, Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations, Physica E: Low-dimensional Systems and Nanostructures 76: 70-81.
[34] Kiani K., 2011, Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory, Journal of Sound and Vibration 330(20): 4896-4914.
[35] Kiani K., 2011, Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle, Part I: theoretical formulations, Physica E: Low-dimensional Systems and Nanostructure,s 44: 229-248.
[36] Kiani K., 2011, Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle, Part II: parametric studies, Physica E: Low-dimensional Systems and Nanostructures 44: 249-269.
[37] Kiani K., 2013, Vibrations of biaxially tensioned-embedded nanoplates for nanoparticle delivery, Indian Journal of Science and Technology 6(7): 4894-4902.
[38] Duan W. H., Wang C. M., 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704.
[39] Farajpour A., Mohammadi M., Shahidi A. R., Mahzoon M., 2011, Axisymmetric buckling of the circular Graphene sheets with the nonlocal continuum plate model, Physica E 43: 1820-1825.
[40] Babaie H., Shahidi A.R., 2011, Vibration of quadrilateral embedded multilayered Graphene sheets based on nonlocal continuum models using the Galerkin method, Acta Mechanica Sinica 27(6): 967-976.
[41] Malekzadeh P., Setoodeh A. R., Alibeygi Beni A., 2011, Small scale effect on the vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates, Journal of Composite Structures 93: 1631-1639.
[42] Anjomshoa A.,2013, Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory, Meccanica 48: 1337-1353.
[43] Shahidi R., Mahzoon M., Saadatpour M. M., Azhari M., 2005, Very large deformation analysis of plates and folded plates by finite strip method, Advances in Structural Engineering 8(6): 547-560.
[44] Liew K. M., Wang C. M., 1993, Pb-2 Rayleigh-Ritz method for general plate analysis, Engineering Structures 15(1): 55-60.
[45] Adali S., 2009, Variational principle for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler-Bernoulli beam model, Nano letters 9: 1737-1741.
[46] Reddy J. N., 1997, Mechanics of Laminated Composite Plates, Theory and Analysis, Chemical Rubber Company, Boca Raton, FL.
[47] Kim S., Dickinso S. M., 1990, The free flexural vibration of right triangular isotropic and orthotropic plates, Journal of Sound and Vibration 141(2): 291-311.
[48] Gorman J., 1985, Free vibration analysis of right triangular plates with combinations of clamped – simply supported conditions, Journal of Sound and Vibration 106(3): 419-431.
[49] Aghababaei R., Reddy J.N., 2009, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration 326: 277-289.