On the evaluation of damping in MEMS in the slip-flow regime

International Journal for Numerical Methods in Engineering

Volumn 68, Issue 10, 2006, Pages 1031-1051

  Frangi, Attilio ^a   Spinola, G ^b   Vigna, B ^b  

^a POLITECNICO DI MILANO   (Italy)

^b STMICROELECTRONICS   (Italy)

Author keywords

BEM; Damping; Fast multipole methods; MEMS

Indexed keywords

ACCELEROMETERS; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; DAMPING; FLUID DYNAMICS; INTEGRAL EQUATIONS;

FLUID DAMPING; SLIP-FLOW; TRACTION INTEGRAL EQUATIONS;

MICROELECTROMECHANICAL DEVICES;

ACCELEROMETERS; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; DAMPING; FLUID DYNAMICS; INTEGRAL EQUATIONS; MICROELECTROMECHANICAL DEVICES;

EID: 33751570721     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1749     Document Type: Article

References (23)

1. Karniadakis GE, Beskok A. Micro Flows, Fundamentals and Simulation. Springer: New York, 2002.
2. Park JH, Bahukudumbi P, Beskok A. Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime. Physics of Fluids 2004; 16:317-330.
3. Frangi A, di Gioia A. Multipole BEM for the evaluation of damping forces on MEMS. Computational Mechanics 2005; 37:24-31.
4. Power H, Wrobel L. Boundary Integral Methods in Fluid Mechanics. Computational Mechanics Publications: Southampton, 1995.
5. Frangi A, Tausch J. A qualocation enhanced approach for the Dirichlet problem of exterior Stokes flow. Engineering Analysis with Boundary Elements 2005; 29:886-893.
6. Frangi A. A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows. Engineering Analysis with Boundary Elements 2005; 29:1039-1046.
7. Bailey CL, Barber RW, Emerson DR. Is it safe to use Navier-Stokes for gas microflows?. Proceedings of Eccomas2004, CDROM, 2004.
8. Yuhong S, Barber RW, Emerson DR. Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient. Physics of Fluids 2006; 17:047102-7.
9. Ding J, Ye W. A fast integral approach for drag force calculations to oscillatory slip Stokes flows. International Journal for Numerical Methods in Engineering 2004; 60:1535-1567.
10. Aluru NR, White J. A fast integral equation technique for analysis of microflow sensors based on drag force calculations. Proceedings of MSM, Santa Clara, CA, 1998; 283-286.
11. Ye W, Wang X, Hemmert W, Freeman D, White J. Air damping in lateral oscillating micro-resonators: a numerical and experimental study. Journal of MEMS 2003; 12:557-566.
12. Mukherjee S, Telekunta S, Mukherjee YX. BEM modeling of damping forces on MEMS with thin plates. Engineering Analysis with Boundary Elements 2005; 29:1000-1007.
13. Bonnet M. Boundary Integral Equation Methods for Solids and Fluids. Wiley: Chichester, 1999.
14. Frangi A, Novati G, Springhetti R, Rovizzi M. 3D fracture analysis by the symmetric Galerkin BEM. Computational Mechanics 2002; 28:220-232.
15. Tausch J, White J. Second kind integral formulations of the capacitance problem. Advances in Computational Mathematics 1998; 9:217-232.
16. Guiggiani M. Hypersingular formulation for boundary stress evaluation. Engineering Analysis with Boundary Elements 1994; 55:169-179.
17. Sladek V, Sladek J (eds). Singular Integrals in Boundary Element Methods, Advances in Boundary Elements. Computational Mechanics Publications: Southampton, 1998.
18. Milroy JS, Hinduja S, Davey K. The elastostatic three dimensional boundary element method: analytical integration for linear isoparametric triangular elements. Applied Mathematical Modelling 1997; 21:763-782.
19. Nishimura N. Fast multipole accelerated boundary integral equation methods. Applied Mechanical Reviews 2002; 55:299-324.
20. Greengard L, Rokhlin V. A new version of the fast multipole algorithm for the Laplace equation in three dimensions. Acta Numerica 1997; 6:229-269.
21. Nishimura N, Yoshida K, Kobayashi S. Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D. International Journal for Numerical Methods in Engineering 2001; 50:525-547.
22. Epton MA, Dembart B. Multipole translation theory for the three-dimensional Laplace and Helmholtz equations. SIAM Journal on Scientific Computing 1995; 16:865-897.
23. Frayssé V, Giraud L, Gratton S, Langou J. A set of GMRES routines for real and complex arithmetics on high performance computers. CERFACS Technical Report, TR/PA/03/3, 2003.