An Investigation of Internal Viscous Damping Effects on the Vibration of a Microbeam Made of Functionally Graded Materials

Abstract:

In this paper, effect of the internal viscous damping on the frequency shift and damping ratios of a microbeam made of functionally graded materials is investigated for different boundary conditions. To achieve this goal the FGM microbeam is modeled by an Euler-Bernoulli beam and utilizing Hamilton principle the governing partial differential equation of motion and corresponding boundary conditions are obtained. Applying mode summation method, the governing ordinary differential Eq. is derived from the PDE. Solving the ODE analytically, frequency shift ratio of the FGM microbeam is evaluated for different boundary conditions. Results are presented in terms of material damping coefficient. The effects of design parameters such as boundary conditions, geometrical parameters, distribution function and viscous damping coefficient on the frequency shift and damping ratios are assessed.

• Periodical: Applied Mechanics and Materials (Volume 798)
• Pages: 140-147
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.798.140
• Online since: October 2015
• Authors: Erfan Maleki*, Khalil Sherafatnia, Abdoreza Pasharavesh, Abolghasem Zabihollah
• Keywords: Functionally Graded Materials, Microbeam, Vibration, Viscous Damping

References

[1] B. Kieback, A. Neubrand, H. Riedel, Processing techniques for functionally graded materials, Material Science and Engineering A, 362, 2003, 81-106.

DOI: 10.1016/s0921-5093(03)00578-1

[2] X. -F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, Journal of Sound and Vibration, Volume 318, 2008, 1210-1229.

DOI: 10.1016/j.jsv.2008.04.056

[3] S.A. Sina, H.M. Navazi, H. Haddadpour, An analytical method for free vibration analysis of functionally graded beams, Materials & Design, Volume 30, 2009, 741-747.

DOI: 10.1016/j.matdes.2008.05.015

[4] Metin Aydogdu, Vedat Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Materials & Design, Volume 28, 2007, 1651-1656.

DOI: 10.1016/j.matdes.2006.02.007

[5] H.J. Xiang, J. Yang, Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Composites Part B: Engineering, Volume 39, 2008, 292-303.

DOI: 10.1016/j.compositesb.2007.01.005

[6] Rajesh K. Bhangale, N. Ganesan, Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core, Journal of Sound and Vibration, Volume 295, 2006, 294-316.

DOI: 10.1016/j.jsv.2006.01.026

[7] X. L. Jia, J. Yang, S. Kitipornchai, C. W Lim, Forced Vibration of Electrically Actuated FGM Micro-Switches, Procedia Engineering, Volume 14, 2011, 280-287.

DOI: 10.1016/j.proeng.2011.07.034

[8] Liao-Liang Ke, Yue-Sheng Wang, Jie Yang, Sritawat Kitipornchai, Nonlinear free vibration of size-dependent functionally graded microbeams, International Journal of Engineering Science, Volume 50, 2012, 256-267.

DOI: 10.1016/j.ijengsci.2010.12.008

[9] Ting-Chiang Tsai, Jia-Hau Tsau, Chun-Sheng Chen, Vibration analysis of a beam with partially distributed internal viscous damping, International Journal of Mechanical Sciences, Volume 51, 2009, 907-914.

DOI: 10.1016/j.ijmecsci.2009.09.039

[10] Xie Z, Shepard Jr. WS, An enhanced beam model for constrained layer damping and a parameter study of damping contribution, Journal of Sound and Vibration, volume 319, 2009 , 1271–84.

DOI: 10.1016/j.jsv.2008.06.041

[11] Sorrentino S, Fasana A, Marchesiello S, Analysis of non-homogeneous Timoshenko beams with generalized damping distributions, Journal of Sound and Vibration, volume 304, 2007, 779–92.

DOI: 10.1016/j.jsv.2007.03.038

[12] Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and vibration (1999); 225(5): 935-988.

DOI: 10.1006/jsvi.1999.2257

[13] Meirovitch L. Analytical methods in vibrations. New York: MacMillan; (1967).

[14] Wakashima K, Hirano T, Niino M. Space applications of advanced structural materials (1990). ESA SP 303, 97.

[15] K. Sanjay Anandrao, R.K. Gupta, P. Ramachandran, and G. Venkateswara Rao, Free Vibration Analysis of Functionally Graded Beams, Defence Science Journal, Vol. 62, No. 3, 2012, pp.139-146.

DOI: 10.14429/dsj.62.1326