Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory

Subject Areas : Engineering

M Ghadiri ¹ , N Shafiei ² , S Hossein Alavi ³

1 - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
2 - Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
3 - School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Received: 2017-02-23 Accepted : 2017-04-19 Published : 2017-06-30

Keywords:

References:

[1] Van Delden R. A., Ter Wiel M. K. J., Pollard M. M., Vicario J., Koumura N., Feringa B. L., 2005, Unidirectional molecular motor on a gold surface, Nature 437(7063): 1337-1340.
[2] Li J., Wang X., Zhao L., Gao X., Zhao Y., Zhou R., 2014, Rotation motion of designed nano-turbine, Scientific Reports 4: 5846.
[3] Fleck N., Muller G.M., Ashby M.F., Hutchinson J.W. ,1994, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia 42(2): 475-487.
[4] Chong A. C. M., Yang F., Lam D. C. C., Tong P., 2001, Torsion and bending of micron-scaled structures, Journal of Materials Research 16(04): 1052-1058.
[5] 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.
[6] Eringen A.C., 1972, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science 10(5): 425-435.
[7] Chen M., 2013, Large deflection of a cantilever nanobeam under a vertical end load, Applied Mechanics and Materials 353: 3387-3390.
[8] Murmu T., Adhikari S., 2010, Scale-dependent vibration analysis of prestressed carbon nanotubes undergoing rotation, Journal of Applied Physics 108(12): 123507-123514.
[9] Narendar S., Gopalakrishnan S., 2011, Nonlocal wave propagation in rotating nanotube,Results in Physics 1(1): 17-25.
[10] Narendar, S., Mathematical modelling of rotating single-walled carbon nanotubes used in nanoscale rotational actuators, Defence Science Journal 61(4): 317-324.
[11] Akgoz B.,CIvalek O., 2012, Analysis of micro-sixed beams for various boundary conditions based on the strain gradient elasticity theory, Archive of Applied Mechanics 82(3): 423-443.
[12] Challamel N., Wang C.M., 2008, The small length scale effect for a non-local cantilever beam: a paradox solved, Nanotechnology 19(34): 345703.
[13] Lim C., Li C., Yu J., 2009, The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams, Interaction and Multiscale Mechanics: an International Journal 1(3): 223-233.
[14] Narendar S., 2012, Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia, Applied Mathematics and Computation 219(3): 1232-1243.
[15] Pradhan S.C., Murmu T., 2010, Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever, Physica E: Low-dimensional Systems and Nanostructures 42(7): 1944-1949.
[16] Aranda-Ruiz J., Loya J., Fernández-Sáez J., 2012, Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory, Composite Structures 94(9): 2990-3001.
[17] Ghadiri M., Hosseini S., Shafiei N., 2016, A power series for vibration of a rotating nanobeam with considering thermal effect, Mechanics of Advanced Materials and Structures 23(12): 1414-1420.
[18] Ghadiri M., Shafiei N., 2016, Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method, Microsystem Technologies 22(12): 2853-2867.
[19] 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 Nanostructures 44(1): 229-248.
[20] 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(1): 249-269.
[21] 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.
[22] Kiani K., 2013,Vibrations of biaxially tensioned-embedded nanoplates for nanoparticle delivery, Indian Journal of Science and Technology 6(7): 4894-4902.
[23] Salehipour H., Nahvi H., Shahidi A., 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.
[24] Ansari R., Shahabodini A., Shojaei M.F., 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.
[25] Wang C., Reddy J.N., Lee K., 2000, Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier.
[26] Reddy J.N., El-Borgi S., 2014, Eringen’s nonlocal theories of beams accounting for moderate rotations, International Journal of Engineering Science 82(0):159-177.
[27] Wang J.S., Shaw D., Mahrenholtz O., 1987, Vibration of rotating rectangular plates, Journal of Sound and Vibration 112(3): 455-468.
[28] Shu C., Richards B.E.,1992, Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids 15(7): 791-798.
[29] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325(1-2): 206-223.
[30] Mohammadi M., Moradi A., Ghayour M., Farajpour A., 2014, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures 11: 437-458.
[31] Shen Z. B., Tang H.L., Daokui L., Tang G.J., 2012, Vibration of single-layered graphene sheet-based nanomechanical sensor via nonlocal Kirchhoff plate theory, Computational Materials Science 61(0):200-205.
[32] 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.