WJNSE  Vol.5 No.4 , December 2015
Vibration of Gold Nano-Beam with Variable Young’s Modulus Due to Thermal Shock
ABSTRACT
In this paper, we will study the most important effects in the nano-scale resonator: the coupling effect of temperature and strain rate, and the non-Fourier effect in heat conduction. A solution for the generalized thermoelastic vibration of nano-resonator induced by thermal loading has been developed. The Young’s modulus is taken as a linear function of the reference temperature. The effects of the thermal loading and the reference temperature in all the studied fields have been studied and represented in graphs with some comparisons. The Young’s modulus makes significant effects on all the studied fields where the values of the temperature, the vibration of the deflection, stress, displacement, strain, stress-strain energy increase when the Young’s modulus has taken to be variable.

Cite this paper
Al-Lehaibi, E. and Youssef, H. (2015) Vibration of Gold Nano-Beam with Variable Young’s Modulus Due to Thermal Shock. World Journal of Nano Science and Engineering, 5, 194-203. doi: 10.4236/wjnse.2015.54020.
References
[1]   Diao, J.K., Gall, K. and Dunn, M.L. (2004) Atomistic Simulation of the Structure and Elastic Properties of Gold Nanowires. Journal of the Mechanics and Physics of Solids, 52, 1935-1962.
http://dx.doi.org/10.1016/j.jmps.2004.03.009

[2]   Kidawa-Kukla, J. (2003) Application of the Green Functions to the Problem of the Thermally Induced Vibration of a Beam. Journal of Sound and Vibration, 262, 865-876.
http://dx.doi.org/10.1016/S0022-460X(02)01133-1

[3]   Boley, B.A. (1972) Approximate Analyzes of Thermally Induced Vibrations of Beams and Plates. Journal of Applied Mechanics, 39, 212-216.
http://dx.doi.org/10.1115/1.3422615

[4]   Manolis, G.D. and Beskos, D.E. (1980) Thermally Induced Vibrations of Beam Structures. Computer Methods in Applied Mechanics and Engineering, 21, 337-355.
http://dx.doi.org/10.1016/0045-7825(80)90101-2

[5]   Al-Huniti, N.S., Al-Nimr, M.A. and Naij, M. (2001) Dynamic Response of a Rod Due to a Moving Heat Source under the Hyperbolic Heat Conduction Model. Journal of Sound and Vibration, 242, 629-640.
http://dx.doi.org/10.1006/jsvi.2000.3383

[6]   Soh, A.K., Sun, Y.X. and Fang, D.N. (2008) Vibration of Microscale Beam Induced by Laser Pulse. Journal of Sound and Vibration, 311, 243-253.
http://dx.doi.org/10.1016/j.jsv.2007.09.002

[7]   Sun, Y.X., Fang, D.N., Saka, M. and Soh, A.K. (2008) Laser-Induced Vibrations of Micro-Beams under Different Boundary Conditions. International Journal of Solids and Structures, 45, 1993-2013.
http://dx.doi.org/10.1016/j.ijsolstr.2007.11.006

[8]   Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010) Scale Effects on the Longitudinal Wave Propagation in Nanoplates. Physica E, 42, 1356-1360.
http://dx.doi.org/10.1016/j.physe.2009.11.036

[9]   Bruls, R.J., Hintzen, H.T., De With, G. and Metselaar, R. (2001) The Temperature Dependence of the Young’s Modulus of MgSiN2, AlN and Si3N4. Journal of the European Ceramic Society, 21, 263-268.
http://dx.doi.org/10.1016/S0955-2219(00)00210-7

[10]   Farraro, R. and McLellan, R.B. (1977) Temperature Dependence of the Young’s Modulus and Shear Modulus of Pure Nickel, Platinum, and Molybdenum. Metallurgical Transactions A, 8, 1563-1565.
http://dx.doi.org/10.1007/BF02644859

[11]   Sun, Y.X., Fang, D.N. and Soh, A.K. (2006) Thermoelastic Damping in Micro-Beam Resonators. International Journal of Solids and Structures, 43, 3213-3229.
http://dx.doi.org/10.1016/j.ijsolstr.2005.08.011

[12]   Fang, D.N., Sun, Y.X. and Soh, A.K. (2006) Analysis of Frequency Spectrum of Laser-Induced Vibration of Microbeam Resonators. Chinese Physics Letters, 23, 1554-1557.
http://dx.doi.org/10.1088/0256-307X/23/6/055

[13]   Duwel, A., Gorman, J., Weinstein, M., Borenstein, J. and Ward, P. (2003) Experimental Study of Thermoelastic Damping in MEMS Gyros. Sensors and Actuators A, 103, 70-75.
http://dx.doi.org/10.1016/S0924-4247(02)00318-7

[14]   Lord, H. and Shulman, Y. (1967) A Generalized Dynamical Theory of Thermoelasticity. Journal of the Mechanics and Physics of Solids, 15, 299-309.
http://dx.doi.org/10.1016/0022-5096(67)90024-5

[15]   Youssef, H.M. (2013) Vibration of Gold Nano-Beam with Variable Thermal Conductivity: State-Space Approach. Applied Nanoscience, 3, 397-407.

[16]   Youssef, H.M., Elsibai, K.A. and El-Bary, A.A. (2014) Vibration of Cylindrical Gold Nano-Beam with Fractional Order Thermoelastic Waves. Jökull Journal, 64, 416-427.

[17]   Tzou, D. (1996) Macro-to-Micro Heat Transfer. Taylor & Francis, Washington DC.

[18]   Youssef, H.M., Elsibai, K.A. and El-Bary, A.A. (2014) Vibration of Gold NanoBeam in Context of Two-Temperature Generalized Thermoelasticity Subjected to Laser Pulse. Latin American Journal of Solids and Structures, 11, 2460-2482.
http://dx.doi.org/10.1590/S1679-78252014001300008

 
 
Top