Damping Ratio in Micro-Beam Resonators Based on Magneto-Thermo-Elasticity

Subject Areas : Engineering

A Khanchehgardan ¹ , G Rezazadeh ² , A Amiri ³

1 - Mechanical Engineering Department, Urmia University, Urmia, Iran
2 - Mechanical Engineering Department, Urmia University, Urmia, Iran
3 - Mechanical Engineering Department, Urmia University, Urmia, Iran

Received: 2017-02-03 Accepted : 2017-03-27 Published : 2017-06-30

Keywords: magnetic field, MEMS, Thermo-elasticity, Maxwell stress tensor, Lorentz force,

Abstract :

This paper investigates damping ratio in micro-beam resonators based on magneto-thermo-elasticity. A unique aspect of the present study is the effect of permanent magnetic field on the stiffness and thermo-elastic damping of the micro resonators. In our modeling the theory of thermo-elasticity with interacting of an externally applied permanent magnetic field is taken into account. Combined theoretical and numerical studies investigate the permanent magnetic field effect on the damping ratio in clamped-clamped and cantilever micro-beams. Furthermore, the influence of the magnetic field intensity on the frequency of the micro-beams with thermo-elastic damping effect is evaluated. Such evaluations are used to determine the influence of magnetic field on the vibration amplitude of the resonators. The meaningful conclusion is that the magnetic field increases the equivalent stiffness and thermo-elastic damping and consequently the energy consumption of the resonators.

References:

[1] Ghaffari S., Ahn C.H., Ng E.J., Wang S., Kenny T.W., 2013, Crystallographic effects in modeling fundamental behavior of MEMS silicon resonators, Microelectronics Journal 44: 586-591‎‎.
[2] Kim B., Candler R.N., Hopcroft M.A., Agarwal M., Park W.T., Kenny T.W., 2007, Frequency stability of wafer-scale film encapsulated silicon based MEMS resonators, Sensors and Actuators A‎ 136: 125-131‎‎.
[3] Saeedi-Vahdat A., Rezazadeh G., 2011, Effects of axial and residual stresses on thermo-elastic damping in capacitive micro-beam resonators, Journal of The Franklin Institute 348: 622-639.
[4] Khanchehgardan A., Rezazadeh G., Shabani R., 2014, Effect of mass diffusion on the damping ratio in micro-beam resonators, International Journal of Solids and Structures 51: 3147-3155.
[5] Zener C., 1937, Internal friction in solids. I. Theory of internal friction in reeds, Search Results Physical Review 52: 230-235.
[6] Nowacki W., 1974, Dynamical problems of thermos diffusion in solids I, Bulletin of the Polish Academy of Sciences Technical Sciences 22: 55-64.
[7] Sherief H., Hamza F., Saleh H., 2004, The theory of generalized thermo-elastic diffusion, International Journal of Engineering Science 42: 591-608.
[8] Ezzat M.A., Awad E.S., 2009, Micropolar generalized magneto-thermoelasticity with modified Ohm’s and Fourier’s laws, Journal of Mathematical Analysis and Applications 353: 99-113.
[9] Abd-Alla A.N., Yahia A.A., Abo-Dahab S.M., 2003, On the reflection of the generalized magneto-thermoviscoelastic plane waves, Chaos Solitons & Fractals 16: 211-231.
[10] Othman M.I.A., 2004, Generalized electro magneto-thermo viscoelastic in case of 2-D thermal shock problem in a finite conducting half-space with one relaxation time, Acta Mechanica 169: 37-51.
[11] Singh B., Kumar R., 1998, Reflection and refraction of micropolar elastic waves at a loosely bonded interface between viscoelastic solid and micropolar elastic solid, International Journal of Engineering Science 36: 101-117.
[12] Aouadi M., 2007, A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 44: 5711-5722.
[13] Sharma J.N., Sharma Y.D., Sharma P.K., 2008, On the propagation of elasto-thermo diffusive surface waves in heat-conducting materials, Journal of Sound and Vibration 351(4): 927-938.
[14] Kumar R., Deswal S., 2002, Surface wave propagation in a micropolar thermo-elastic medium without energy dissipation, Journal of Sound and Vibration 256: 173-178.
[15] Moon F.C., Pao Y.H., 1968, Magneto-elastic buckling of a thin plate, Journal of Applied Mechanics 37: 53-58.
[16] Shih Y.S., Wu G.Y., Chen E.J.S., 1998, Transient vibrations of a simply-supported beam with axial loads and transverse magnetic fields, Mechanics of Structures and Machines 26(2): 115-130.
[17] Sharma K., 2010, Boundary value problems in generalized thermodiffusive elastic medium, Journal of Solid Mechanics 2(4): 348-362.
[18] Liu M.F., Chang T.P., 2005, Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force, Journal of Sound and Vibration 288(1-2): 399-411.
[19] Kong S., Zhou S., Nie Z., Wang K., 2008, The size-dependent natural frequency of Bernoulli–Euler micro-beams, International Journal of Engineering Science 46: 427-437.
[20] Sun Y., Fang D., Soh A.K., 2006, Thermo-elastic damping in micro-beam resonators, International Journal of Solids and Structures 43: 3213-3229.
[21] Alizada A.N., Sofiyev A.H., Kuruoglu N., 2012, Stress analysis of a substrate coated by nanomaterials with vacancies subjected to uniform extension load, Acta Mechanica 223: 1371-1383.
[22] Alizada A.N., Sofiyev A.H., 2011, On the mechanics of deformation and stability of the beam with a nanocoating, Journal of Reinforced Plastics and Composites 30(18): 1583-1595.