Mathematical modeling and simulation of thermal effects in flexural microcantilever resonator dynamics

JVC/Journal of Vibration and Control

Volumn 12, Issue 2, 2006, Pages 139-163

  Jazar, G Nakhaie ^a  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

Mathematical modeling; Microbeam; Microelectromechanical systems dynamics; Microelectromechanical systems simulation; Microresonator; Thermal damping

Indexed keywords

COMPUTER SIMULATION; DAMPING; ELASTIC MODULI; INTERNAL FRICTION; MATHEMATICAL MODELS; MICROELECTROMECHANICAL DEVICES; NATURAL FREQUENCIES; THERMAL EFFECTS;

MICROBEAM; MICRORESONATOR SYSTEM; THERMAL DAMPING; THERMAL DEPENDENCY;

RESONATORS;

EID: 32944473775     PISSN: 10775463     EISSN: None     Source Type: Journal    
DOI: 10.1177/1077546306061555     Document Type: Article

References (36)

1. Abdolvand, R., Ho, G. K., Erbil, A., and Ayazi, F., 2003, "Thermoelastic damping in ternech-refilled polysilicon resonators," in Proceedings of the 12th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, MA, June 8-12.
2. Alblas, J. B., 1961, "On the general theory of thermoelastic friction," Applied Science Research A10, 349-362.
3. Alblas, J. B., 1981, "A note on the theory of thermoelastic damping," Journal of Thermal Stresses 4, 333-355.
4. Barmatz, M. and Chen, H. S., 1974, "Young's modulus and friction in metallic glass alloys from 1.5 to 300 K," Journal of Physical Review B 9 (10). 4073-4083.
5. De, S. K. and Aluru, N. R., 2004, "Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS," Journal of Microelectromechanical Systems 11 (5). 737-758.
6. Fejer, M. M., Rowan, S., Cagnoli, G., Crooks, D. R. M., Gretarsson, A., Harry, G.M., Hough, J., Penn, S.D., Sneddon, P. H., and Vyatchanin, S. P., 2004, "Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors," Physical Review D 70, 082003.
7. Gough, W., 1968, "The graphical analysis of a Lorentzian function and a differentiated Lorentzian function," Journal of Physical Review A 2 (1). 704-709.
8. Gysin, U., Rast, S., Meyer, E., Lee, D. W., Vettiger, P., and Gerber, C., 2004, "Temperature dependence of the force sensitivity of silicon cantilevers," Physical Review B 69, 045403, 1-6.
9. Hsu, T. R., 2002, MEMS and Microsystems Design and Manufacture, MGraw Hill, New York.
10. Hsu, W. T., Clark, J. R., and Nguyen, C. T, 2001, "Q-optimized lateral free-free beam micromechanical resonators," in Proceedings of the 11th International Conference on Solid-State Sensors and Actuators (Transducers '01), Munich, Germany, pp. 1110-1113.
11. Husman, M. E., Hough, J., and Robertson, N. A., 2004, "Thermal noise in a pendulum suspended by multiple wires," Classical Quantum Gravity 21, 1371-1381.
12. Jeong, J., Chung, S., Lee, S. H., and Kwon, D., 2003, "Evaluation of elastic properties and temperature effects in Si thin film using an electrostatic microresonator," Journal of Microelectromechanical Systems 12 (4). 524-530.
13. Kaajakari, V., Mattila, T., Oja, A., and Seppä, H., 2004, "Nonlinear limits for single-crystal silicon microresonators," IEEE Journal of Microelectromechanical Systems 13 (5). 715-724.
14. Kanda, T., Morita, T., Kurosawa, M. K., and Higuchi, T., 2000, "A flat type touch probe sensor using PZT thin film vibrator," Sensors and Actuators 83, 67-75.
15. Karami, G. and Garnich, M., 2005, "Micromechanical study of thermoelastic behavior of composites with periodic fiber wariness," Journal of Composites B 36, 241-248.
16. Khaled, A. R. A., Vafai, K., Yang, M., Zhang, X., and Ozkan, C. S., 2003, "Analysis, control and augmentation of microcantilever deflections in bio-sensing systems," Sensors and Actuators B 94, 103-115.
17. Lifshitz, R. and Roukes, M. L., 2000, "Thermoelastic damping in micro- and nanomechanical systems," Physical Review 61 (8). 5600-5609.
18. Meirovitch, L., 1997, Principles and Technologies of Vibrations, Prentice-Hall, EnglewoodCliffs, NJ.
19. Nayfeh, A. H. and Younis, M. I., 2004, "A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping," Journal of Micromechanics and Microengineering 14, 170-181.
20. Nguyen, C. T. C., 1995, "Micromechanical resonators for oscillators and filters," in Proceedings of the IEEE International Ultrasonic Symposium, Seattle, WA, November 7-10, pp. 489-499.
21. Norris, A. N. and Photiadis, D. M., 2005, "Thermoelastic relaxation in elastic structures, with applications to thin plates," Quarterly Journal of Mechanics and Applied Mathematics 58 (1). 145-163.
22. Saulson, P. R., 1990, "Thermal noise in mechanical experiments," Physical Review D 42 (8). 2437-2445.
23. Srikar, V. T. and Senturia, S. D., 2002, "Thermoelastic damping in fine-grained polysilicon flexural beam resonators," Journal of Microelectromechanical Systems 11 (5). 499-504.
24. Sudipo, K. and Aluru, N. R., 2004, "Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS," Journal of Microelectromechanical Systems 13 (5). 737-758.
25. Wang, K., Wong, A. C., and Nguyen, C. T., 2000, "VHF free-free beam high-Q micromechanical resonators," Journal of Microelectromechanical Systems 9, 347-360.
26. Yang, J. L., Ono, T., and Esashi, M., 2002, "Energy dissipation in submicrometer thick single-crystal silicon cantilevers," Journal of Microelectromechanical Systems 11, 775-783.
27. Yasymura, K. Y., Stowe, T. D., Chow, E. M., Pfafman, T., Kenny, T. M., Stipe, B. C., and Rugar, D., 2000, "Quality factors in micron- and submicron-thick cantilevers," Journal of Microelectromechanical Systems 9 (1). 117-125.
28. Younis, M. I., 2004, "Modeling and Simulation of Microelectromechanical System in Multi-Physics Fields," Ph.D. Thesis, Engineering Science and Mechanics, Virginia Polytechnic Institute and State University Blacksburg, VA.
29. Younis, M. I. and Nayfeh, A. H., 2003, "A study of the nonlinear response of a resonant microbeam to electric actuation," Nonlinear Dynamics 31, 91-117.
30. Younis, M. I., Abdel-Rahman, E. M., and Nayfeh, A. H., 2003, "A reduced-order model for electrically actuated microbeam-based MEMS," Journal of Microelectromechanical Systems 12 (5). 672-680.
31. Zalalutdinov, V., Mattila, T., Oja, A., and Seppa, H., 2004, "Nonlinear limits for single-crystal silicon microresonators," Journal of Microelectromechanical Systems 13 (5). 715-724.
32. Zener, C., 1937, "Internal friction in solids: I. Theory of internal friction in reeds," Physical Review 52, 230-235.
33. Zener, C., 1938a, "Internal friction in solids: II. General theory of thermoelastic internal friction," Physical Review 53, 90-99.
34. Zener, C., 1938b, "Internal friction in solids: IV. Relation between cold work and internal friction," Physical Review 53, 582-586.
35. Zener, C., 1948, Elasticity and Anelasticity of Metals, University of Chicago Press, Chicago, IL.
36. Zener, C., Otis, W., and Nuckolls, R., 1938, "Internal friction in solids: III. Experimental demonstration of thermoelastic internal friction," Physical Review 53, 100-101.