Surface Energy and Elastic Medium Effects on Torsional Vibrational Behavior of Embedded Nanorods

Author

School of Engineering, Damghan University, Damghan, Iran

Abstract

In this paper surface energy and elastic medium effects on torsional vibrational behavior of nanorods are studied. The surface elasticity theory is used to consider the surface energy effects and the elastic medium is modeled as torsional springs attached to the nanorod. At the next step, Hamilton’s principle is utilized to derive governing equations and boundary conditions. Then, with the aid of an analytical method, natural frequencies are obtained and effects of various parameters on torsional frequencies are studied in details. It is concluded from the present study that the surface energy can make nanorods unstable depending on the nanorod dimension and frequency number. Results of the present study can be useful in design of nanoelectromechanical systems like drive shafts.

Keywords


1.     Rashvand, K., Rezazadeh, G. and Madinei, H., "Effect of length-scale parameter on pull-in voltage and natural frequency of a micro-plate", International Journal of Engineering,  Vol. 27, No. 3, (2014), 375-384.
2.     Khanchehgardan, A., Shah-Mohammadi-Azar, A., Rezazadeh, G. and Shabani, R., "Thermo-elastic damping in nano-beam resonators based on nonlocal theory", International Journal of Engineering-Transactions C: Aspects,  Vol. 26, No. 12, (2013), 1505-1513.
3.     JafarSadeghi-Pournaki, I., Zamanzadeh, M., Madinei, H. and Rezazadeh, G., "Static pull-in analysis of capacitive fgm nanocantilevers subjected to thermal moment using eringen’s nonlocal elasticity", International Journal of Engineering-Transactions A: Basics,  Vol. 27, No. 4, (2013), 633-640.
4.     Fei, P., Yeh, P.-H., Zhou, J., Xu, S., Gao, Y., Song, J., Gu, Y., Huang, Y. and Wang, Z.L., "Piezoelectric potential gated field-effect transistor based on a free-standing zno wire", Nano letters,  Vol. 9, No. 10, (2009), 3435-3439.
5.     He, J.H., Hsin, C.L., Liu, J., Chen, L.J. and Wang, Z.L., "Piezoelectric gated diode of a single zno nanowire", Advanced Materials,  Vol. 19, No. 6, (2007), 781-784.
6.     Wang, Z.L. and Song, J., "Piezoelectric nanogenerators based on zinc oxide nanowire arrays", Science,  Vol. 312, No. 5771, (2006), 242-246.
7.     Zhong, Z., Wang, D., Cui, Y., Bockrath, M.W. and Lieber, C.M., "Nanowire crossbar arrays as address decoders for integrated nanosystems", Science,  Vol. 302, No. 5649, (2003), 1377-1379.
8.     Bai, X., Gao, P., Wang, Z.L. and Wang, E., "Dual-mode mechanical resonance of individual zno nanobelts", Applied Physics Letters,  Vol. 82, No. 26, (2003), 4806-4808.
9.     Eringen, A.C. and Edelen, D., "On nonlocal elasticity", International Journal of Engineering Science,  Vol. 10, No. 3, (1972), 233-248.
10.   Ansari, R., Gholami, R. and Ajori, S., "Torsional vibration analysis of carbon nanotubes based on the strain gradient theory and molecular dynamic simulations", Journal of Vibration and Acoustics,  Vol. 135, No. 5, (2013), 051016.
11.   Asghari, M., Kahrobaiyan, M., Rahaeifard, M. and Ahmadian, M., "Investigation of the size effects in timoshenko beams based on the couple stress theory", Archive of Applied Mechanics,  Vol. 81, No. 7, (2011), 863-874.
12.   Ghayesh, M.H., Farokhi, H. and Amabili, M., "Nonlinear dynamics of a microscale beam based on the modified couple stress theory", Composites Part B: Engineering,  Vol. 50, No., (2013), 318-324.
13.   Gurtin, M.E. and Murdoch, A.I., "A continuum theory of elastic material surfaces", Archive for Rational Mechanics and Analysis,  Vol. 57, No. 4, (1975), 291-323.
14.   Fennimore, A., Yuzvinsky, T., Han, W.-Q., Fuhrer, M., Cumings, J. and Zettl, A., "Rotational actuators based on carbon nanotubes", Nature,  Vol. 424, No. 6947, (2003), 408-410.
15.   Witkamp, B., Poot, M., Pathangi, H., Hüttel, A. and Van der Zant, H., "Self-detecting gate-tunable nanotube paddle resonators", Applied Physics Letters,  Vol. 93, No. 11, (2008), 111909.
16.   Meyer, J.C., Paillet, M. and Roth, S., "Single-molecule torsional pendulum", Science,  Vol. 309, No. 5740, (2005), 1539-1541.
17.   Dong, L., Nelson, B.J., Fukuda, T. and Arai, F., "Towards nanotube linear servomotors", Automation Science and Engineering, IEEE Transactions on,  Vol. 3, No. 3, (2006), 228-235.
18.   Williams, P., Papadakis, S., Patel, A., Falvo, M., Washburn, S. and Superfine, R., "Torsional response and stiffening of individual multiwalled carbon nanotubes", Physical Review Letters,  Vol. 89, No. 25, (2002), 255502.
19.   Murmu, T., Adhikari, S. and Wang, C., "Torsional vibration of carbon nanotube–buckyball systems based on nonlocal elasticity theory", Physica E: Low-dimensional Systems and Nanostructures,  Vol. 43, No. 6, (2011), 1276-1280.
20.   Loya, J., Aranda-Ruiz, J. and Fernández-Sáez, J., "Torsion of cracked nanorods using a nonlocal elasticity model", Journal of Physics D: Applied Physics,  Vol. 47, No. 11, (2014), 115304.
21.   Arda, M. and Aydogdu, M., "Torsional statics and dynamics of nanotubes embedded in an elastic medium", Composite Structures,  Vol. 114, No., (2014), 80-91.
 
 
 
 
 
 
 
22.   Khademolhosseini, F., Phani, A.S., Nojeh, A. and Rajapakse, N., "Nonlocal continuum modeling and molecular dynamics simulation of torsional vibration of carbon nanotubes", IEEE Transactions on Nanotechnology,  Vol. 11, No. 1, (2012), 34-43.
23.   Mohammadimehr, M., Saidi, A., Arani, A.G., Arefmanesh, A. and Han, Q., "Torsional buckling of a dwcnt embedded on winkler and pasternak foundations using nonlocal theory", Journal of Mechanical Science and Technology,  Vol. 24, No. 6, (2010), 1289-1299.
24.   Beni, Y.T. and Abadyan, M., "Size-dependent pull-in instability of torsional nano-actuator", Physica Scripta,  Vol. 88, No. 5, (2013), 055801.
25.   Gheshlaghi, B. and Hasheminejad, S.M., "Size dependent torsional vibration of nanotubes", Physica E: Low-dimensional Systems and Nanostructures,  Vol. 43, No. 1, (2010), 45-48.
26.   Nazemnezhad, R. and Fahimi, P., "Free torsional vibration of cracked nanobeams incorporating surface energy effects", Applied Mathematics and Mechanics,  Vol. 38, No. 2, (2017), 217-230.
27.   Mase, G.T., Smelser, R.E. and Mase, G.E., "Continuum mechanics for engineers, CRC press,  (2009).
28.   Miller, R.E. and Shenoy, V.B., "Size-dependent elastic properties of nanosized structural elements", Nanotechnology,  Vol. 11, No. 3, (2000), 139-145.
29.   Rao, S.S., "Vibration of continuous systems, John Wiley & Sons,  (2007).
30.   Nazemnezhad, R. and Hosseini-Hashemi, S., "Nonlinear free vibration analysis of timoshenko nanobeams with surface energy", Meccanica,  Vol. 50, No. 4, (2015), 1027-1044.
31.   Hosseini-Hashemi, S., Nazemnezhad, R. and Rokni, H., "Nonlocal nonlinear free vibration of nanobeams with surface effects", European Journal of Mechanics-A/Solids,  Vol. 52, (2015), 44-53.
32.   Hosseini-Hashemi, S., Fakher, M., Nazemnezhad, R. and Haghighi, M.H.S., "Dynamic behavior of thin and thick cracked nanobeams incorporating surface effects", Composites Part B: Engineering,  Vol. 61, (2014), 66-72.
33.   Assadi, A. and Farshi, B., "Vibration characteristics of circular nanoplates", Journal of Applied Physics,  Vol. 108, No. 7, (2010), 074312.
34.   Hosseini-Hashemi, S. and Nazemnezhad, R., "An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects", Composites Part B: Engineering,  Vol. 52, (2013), 199-206.
35.   Gheshlaghi, B. and Hasheminejad, S.M., "Surface effects on nonlinear free vibration of nanobeams", Composites Part B: Engineering,  Vol. 42, No. 4, (2011), 934-937.
36.   Liu, C. and Rajapakse, R., "Continuum models incorporating surface energy for static and dynamic response of nanoscale beams", IEEE Transactions on Nanotechnology,  Vol. 9, No. 4, (2010), 422-431.