Vibration and Stability Analysis of a Pasternak Bonded Double-GNR-System Based on Different Nonlocal Theories
محورهای موضوعی : EngineeringA Ghorbanpour Arani 1 , R Kolahchi 2 , H Vossough 3 , M Abdollahian 4
1 - Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
2 - Faculty of Mechanical Engineering, University of Kashan
3 - Faculty of Mechanical Engineering, University of Kashan
4 - Faculty of Mechanical Engineering, University of Kashan
کلید واژه: Modified couple stress theory, GNR, Strain gradient theory, Rayleigh beam theory, Coupled system,
چکیده مقاله :
This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the coupled system. The three vibrational states including out-of-phase vibration, in-phase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient theory is higher than the Eringen's and modified couple stress theories. Moreover, the small scale effect in the case of in-phase vibration is higher than that in the other cases. This study might be useful for the design of nano-devices in which GNRs act as basic elements.
[1] Yang M., Javadi A., Li H., Gong S., Shaoqin G., 2010,Ultrasensitive immunosensor for the detection of cancer biomarker based on graphene sheet, Biosensors and Bioelectronics 26: 560-565.
[2] Arash B., Wang Q., Liew K.M., 2012, Wave propagation in graphene sheets with nonlocal elastic theory via finite element formulation, Computer Methods in Applied Mechanics and Engineering 223: 1-9.
[3] Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., 2004, Quenching of the Hall effect in localised high magnetic field regions, Science 306: 666-669.
[4] Zeng H., Zho J., Wei J., Xu D., Leburton J.P., 2012, Controllable tuning of the electronic transport in pre-designed graphene nanoribbon, Current Appllied Physics 12: 1611-1614.
[5] Cao H.Y., Guo Z.X., Xiang H., Gong X.G., 2012, Layer and size dependence of thermal conductivity in multilayer graphene nanoribbons, Physics Letters A 376: 525-528.
[6] Shi J.X., Ni Q.Q., Lei X.W., Natsuki T., 2011, Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model, Computational Material Science 50: 3085-3090.
[7] Eringen A.C., 1972, Nonlocal polar elastic continua, International Journal of Engineering Science 10: 1–16.
[8] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.
[9] Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer-Verlag, New York.
[10] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25: 2385-2391.
[11] Mindlin R.D., 1965, Second gradient of strain and surface tension in linear elasticity, International Journal of Solids and Structures 1: 417-438.
[12] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of Mechanics and Physics of Solid 51: 1477-1508.
[13] Kong S.L., Zhou S.J., Nie Z.F., Wang K., 2009, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science 47: 487-498.
[14] Yin L., Qian Q., Wang, L., 2011, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modeling 35: 2864-2873.
[15] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 2731-2743.
[16] Şimşek S., 2010, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science 48: 1721-1732.
[17] Shi J.X., Ni Q.Q., Lei X.W., Natsuki T., 2012, Nonlocal vibration of embedded double-layer graphene nanoribbonsin-phase and anti-phase modes, Physica E 44:1136–1141.
[18] Shi J.X., Ni Q.Q., Lei X.W., Natsuki T., 2011, Nonlocal elasticity theory for the buckling of double-layer graphene nanoribbons based on a continuum model, Computational Material Science 50: 3085-3090.
[19] Murmu T., Adhikari S., 2011, Axial instability of double-nanobeam-system, Physics Letters A 375: 601–608.
[20] Murmu T., Adhikari S., 2012, Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems, European Journal of Mechanics A/Solid 34: 52-62.
[21] Murmu T., Adhikari, S., 2011, Nonlocal vibration of bonded double-nanoplate-systems, Composite Part B 42: 1901–1911.
[22] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407: 4458-4465.
[23] Wu J.X., Li X.F., Tang G.J. 2012, Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix, Physica B 407: 684–688.
[24] Stonjanovic V., Kozic, P., 2012, Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load, International Journal of Mechanical Science 60: 59-71.
[25] Pradhan S.C., Murmu, T., 2009, Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Material Science 47: 268-274.
[26] Kiani K., 2012, Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model, Applied Mathematical Modeling 37: 1836-1850.
[27] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory, Physica B 407: 4281-4286.
[28] Akgoz B., Civalek O., 2011, Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science 49: 1268-1280.
