Research ArticleOpen AccessGoogle Scholar indexed
Vibration of Nano Beam Induced by Ramp Type Heating
- 1
- 2
World Journal of Nano Science and Engineering·Volume 01 (2011)·Pages 37–44·Published 29 June 2011·DOI10.4236/wjnse.2011.12006
Copy link · social · email
Abstract
The non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, became the most significant effects in the nano-scale beam. In the present study, a generalized solution for the generalized thermoelastic vibration of a bounded nano-beam resonator induced by ramp type of heating is developed and the solutions take into account the above two effects. The Laplace transforms and direct method are used to determine the lateral vibration, the temperature, the displacement, the stress and the energy of the beam. The effects of the relaxation time and the ramping time parameters have been studied with some comparisons.
KeywordsThermoelasticityNano-BeamRamp-Type HeatingNon-Fourier Heat Conduction
- M. Biot, “Thermoelasticity and irreversible thermo-dynamics,” Journal of Applied Physics, Vol. 27, 1956, pp. 240-253.
- H. Lord, and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” Journal of Mechanics and Physics of Solids, Vol. 15, 1967, pp. 299-309.
- J. K. Diao, K. Gall and M. L. Dunn, “Atomistic simulation of the structure and elastic properties of gold nanowires,” Journal of Mechanics and Physics of Solids, Vol. 52, 2004, pp.1935-1962.
- J. Kidawa-Kukla, “Application of the Green functions to the problem of the thermally induced vibration of a beam,” Journal of Sound and Vibration, Vol. 262, 2003, pp. 865-876.
- B.A. Boley, “Approximate analyses of thermally induced vibrations of beams and plates,” Journal of Applied Mechanics, Vol. 39, 1972, pp. 212-216.
- G.D. Manolis and D.E. Beskos, “Thermally induced vibrations of beam structures,” Computer Methods in Applied Mechanics and Engineering, Vol. 21, 1980, pp. 337-355.
- N.S. Al-Huniti, M.A. Al-Nimr and M. Naij, “Dynamic response of a rod due to a moving heat source under the hyperbolic heat conduction model,” Journal of Sound and Vibration, Vol. 242, 2001, pp. 629-640.
- Ai Kah Soh, Yuxin Sun and Daining Fang, “Vibration of microscale beam induced by laser pulse,” Journal of Sound and Vibration, Vol. 311, 2008, pp. 243-253.
- Yuxin Sun, Daining Fang, Masumi Saka and Ai Kah Soh, “Laser-induced vibrations of micro-beams under different boundary conditions,” International Journal of Solids and Structures, Vol. 45, 2008, pp.1993-2013.
- J.S. Rao, “Nonlinear Vibration and One Dimensional Structures, “Wiley, Advanced theory of vibration, New York, Chichester, Brisbane, Toronto, Singapore, 1992.
- Y.X. Sun, D.N. Fang, A.K. Soh, “Thermoelastic damping in micro-beam resonators,” International Journal of Solids and Structures, Vol. 43, 2006, pp. 3213-3229.
- D.N. Fang, Y.X. Sun and A.K. Soh, “Analysis of frequency spectrum of laser-induced vibration of microbeam resonators,” Chinese Physics Letters, Vol. 23, No (6), 2006, pp. 1554-1557.
- A. Duwel, J. Gorman, M. Weinstein, J. Borenstein and P. Ward, “Experimental study of thermoelastic damping in MEMS gyros,” Sensors and Actuators A, Vol. 103, 2003, pp. 70-75.
- J.C. Misra,, S.C. Samanta, A.K. Chakrabarti and S.C. Misra, “Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating”, International Journal of Engineering Science, Vol. 29, 1991, pp. 1505-1514.