微机电系统的多域耦合分析与多学科设计优化
|
摘要
随着微机电系统(MEMS)技术的逐渐成熟,越来越多的MEMS器件或相关产品投入市场,为降低制作成本、缩短研制周期、提高产品可靠性,迫切需要引入有效的设计方法。另一方面伴随着MEMS加工工艺的标准化,使得MEMS设计在一定程度上可与具体工艺相分离,从而大大地促进了MEMS建模与仿真技术的迅速发展,与以前相比MEMS CAD更具实际应用价值。
微机电系统融合了力、电、流体、光、磁、热等多个物理域,这些物理域之间的复杂耦合效应对MEMS的建模与仿真提出了巨大挑战。为准确预测在这些物理域共同作用下系统的行为特性,需要深入研究物理域之间的耦合机理,探讨快速分析与模拟系统行为的有效方法。此外在MEMS的设计过程中,需要从整体的角度出发综合考虑微传感器、微致动器、电子接口电路、控制电路、工艺等多学科或子系统,并权衡它们对系统特性的影响,因而研究有效的系统设计与优化方法非常必要。本文针对静电致动微梁和微机械振动陀螺的多域耦合问题展开深入研究,并在对多个子系统分析的基础上对微机械陀螺进行多学科设计优化。
本文的主要研究内容包括:
1)应用降阶宏建模技术快速求解MEMS多能域耦合问题。论文详细论述了面向多域耦合分析的MEMS宏建模方法,如基于节点分析法的参数化宏建模方法、基于Churn过程的非线性宏建模方法以及基于Amoldi算法的自动宏建模方法,并讨论了这些方法各自的优缺点及应用场合。
2)采用基于Churn过程和基于Arnoldi算法的宏建模方法求解静电致动微梁的多能域耦合问题。当器件工作于无阻尼、非线性情况时,利用基于Churn过程的宏建模方法对其进行静电—结构耦合分析;当器件工作于有阻尼、线性条件时,采用基于Krylov子空间的Amoldi算法对原始状态空间模型实行降阶,由降阶模型实现微梁的静电—结构—阻尼等多域耦合分析,仿真结果表明宏建模方法能快速、准确地实现多域耦合MEMS器件的瞬态分析。
3)将基于物理级数值模拟的集总参数宏建模技术应用于微机械陀螺的多域耦合分析中。通过适当的方式将结构域、静电域、空气阻尼域进行分离,提取每一物理域的集总参数宏模型,然后在系统级仿真器中利用集总参数模型建立微机械陀螺的多域耦合模型,快速地实现了陀螺的瞬态分析。
4)由静电场的数值模拟准确地捕捉电容的边缘效应,准确地提取静电驱动梳齿和检测平板中电容与位移关系;根据热—流体控制方程类似原理,在数值模拟的
With the rapid progress in microelectromechanical systems (MEMS) technology, MEMS-specific modeling and simulation environments are increasingly needed to improve performance of MEMS device before costly and time-consuming prototyping. In addition, more and more MEMS fabrication processes are standardized to meet the requirement of commercialization of MEMS products which accelerate the development of modeling and simulation.Generally speaking, MEMS couple multiple physical domains such as mechanical, electrical, fluidic, optical, magnetic and thermal to implement their functions. The inherent coupled property poses difficult challenges for modeling and simulation of MEMS. It is necessary to require an effective method to predict the behavior of MEMS device through researching on these tightly coupling effects. On the other hand, most of MEMS integrate micro-transducers with readout and control circuit on a common board, design and optimization of MEMS require comprehensive consideration for the coupling effects of fabrication process, structure physical parameters, operational environments, and electronics.In the thesis, electrostatically-actuated microbeam and micromachined gyroscope are taken as examples to demonstrate the procedure of multi-domain coupling analysis and system design optimization of MEMS. The main contents in this thesis are described as follows:1) Model order reduction (MOR) techniques are proposed to quickly solve the coupling problems existing in MEMS. Parameterized macromodeling method based on nodal analysis technique, nonlinear macromodeling method based on Churn process, and automatically macromodeling method based on Arnoldi algorithm are detailedly discussed. Their appropriate applications are identified through comparison among these macromodeling methods.2) In the case of non-damping and nonlinear condition, electrostatic-structural coupling analysis is performed for the flexible electrostatic fixed-fixed microbeam using Churn process. When damping and nonlinear conditions are concerned, discretized ordinary differential equations (ODEs) are firstly derived from the original partial differential equations using finite differential method (FDM), and then Arnoldi process based on
Krylov subspace is applied to generate reduced order model (ROM). Electrical-structural-fluidic multi-domain coupling analysis is implemented using the generated ROM. The results prove that macromodeling methods can quickly solve the coupling problem with little compromising accuracy.3) The multiple domains can be decomposed into elastic field, electrostatic field and air-damping field. The lumped parameter macromodeling method for every domain, therefore, is utilized to analyze coupling effects in micromachined gyroscope based on physically numerical simulation. The obtained lumped models can be described using hardware description language (HDL) and then inserted into system level model to do transient analysis of micromachined gyroscope.4) The electrostatic numerical analysis is performed to capture fringing effect in micro structural capacitance so that the relationship of capacitance with displacement can be accurately extracted. The principle of thermal-fluidic analogy is used to extract lumped parameters (damping coefficient and squeeze stiffness) of squeeze film damping in perforation plate structure. Modal analysis technology is used to extract the effective stiffness and mass in driving and sensing modes of gyroscope.5) Multidisciplinary design optimization idea is introduced for the overall preliminary design of micromachined gyroscope. To optimize the whole performance of microgyroscope such as sensitivity a multidisciplinary design model is proposed with consideration of the coupling effects of fabrication process, structure physical parameters, environmental quality factor, and electronics.6) Genetic algorithm is applied to optimize the proposed MDO problem and obtain the global trade-off optimum. The prototype of microgyroscope is fabricated with optimal parameters, and test results for the gyroscope show that MDO methodology is a promising approach to effectively explore system trade-off and design space for complex MEMS.
微机电系统融合了力、电、流体、光、磁、热等多个物理域,这些物理域之间的复杂耦合效应对MEMS的建模与仿真提出了巨大挑战。为准确预测在这些物理域共同作用下系统的行为特性,需要深入研究物理域之间的耦合机理,探讨快速分析与模拟系统行为的有效方法。此外在MEMS的设计过程中,需要从整体的角度出发综合考虑微传感器、微致动器、电子接口电路、控制电路、工艺等多学科或子系统,并权衡它们对系统特性的影响,因而研究有效的系统设计与优化方法非常必要。本文针对静电致动微梁和微机械振动陀螺的多域耦合问题展开深入研究,并在对多个子系统分析的基础上对微机械陀螺进行多学科设计优化。
本文的主要研究内容包括:
1)应用降阶宏建模技术快速求解MEMS多能域耦合问题。论文详细论述了面向多域耦合分析的MEMS宏建模方法,如基于节点分析法的参数化宏建模方法、基于Churn过程的非线性宏建模方法以及基于Amoldi算法的自动宏建模方法,并讨论了这些方法各自的优缺点及应用场合。
2)采用基于Churn过程和基于Arnoldi算法的宏建模方法求解静电致动微梁的多能域耦合问题。当器件工作于无阻尼、非线性情况时,利用基于Churn过程的宏建模方法对其进行静电—结构耦合分析;当器件工作于有阻尼、线性条件时,采用基于Krylov子空间的Amoldi算法对原始状态空间模型实行降阶,由降阶模型实现微梁的静电—结构—阻尼等多域耦合分析,仿真结果表明宏建模方法能快速、准确地实现多域耦合MEMS器件的瞬态分析。
3)将基于物理级数值模拟的集总参数宏建模技术应用于微机械陀螺的多域耦合分析中。通过适当的方式将结构域、静电域、空气阻尼域进行分离,提取每一物理域的集总参数宏模型,然后在系统级仿真器中利用集总参数模型建立微机械陀螺的多域耦合模型,快速地实现了陀螺的瞬态分析。
4)由静电场的数值模拟准确地捕捉电容的边缘效应,准确地提取静电驱动梳齿和检测平板中电容与位移关系;根据热—流体控制方程类似原理,在数值模拟的
With the rapid progress in microelectromechanical systems (MEMS) technology, MEMS-specific modeling and simulation environments are increasingly needed to improve performance of MEMS device before costly and time-consuming prototyping. In addition, more and more MEMS fabrication processes are standardized to meet the requirement of commercialization of MEMS products which accelerate the development of modeling and simulation.Generally speaking, MEMS couple multiple physical domains such as mechanical, electrical, fluidic, optical, magnetic and thermal to implement their functions. The inherent coupled property poses difficult challenges for modeling and simulation of MEMS. It is necessary to require an effective method to predict the behavior of MEMS device through researching on these tightly coupling effects. On the other hand, most of MEMS integrate micro-transducers with readout and control circuit on a common board, design and optimization of MEMS require comprehensive consideration for the coupling effects of fabrication process, structure physical parameters, operational environments, and electronics.In the thesis, electrostatically-actuated microbeam and micromachined gyroscope are taken as examples to demonstrate the procedure of multi-domain coupling analysis and system design optimization of MEMS. The main contents in this thesis are described as follows:1) Model order reduction (MOR) techniques are proposed to quickly solve the coupling problems existing in MEMS. Parameterized macromodeling method based on nodal analysis technique, nonlinear macromodeling method based on Churn process, and automatically macromodeling method based on Arnoldi algorithm are detailedly discussed. Their appropriate applications are identified through comparison among these macromodeling methods.2) In the case of non-damping and nonlinear condition, electrostatic-structural coupling analysis is performed for the flexible electrostatic fixed-fixed microbeam using Churn process. When damping and nonlinear conditions are concerned, discretized ordinary differential equations (ODEs) are firstly derived from the original partial differential equations using finite differential method (FDM), and then Arnoldi process based on
Krylov subspace is applied to generate reduced order model (ROM). Electrical-structural-fluidic multi-domain coupling analysis is implemented using the generated ROM. The results prove that macromodeling methods can quickly solve the coupling problem with little compromising accuracy.3) The multiple domains can be decomposed into elastic field, electrostatic field and air-damping field. The lumped parameter macromodeling method for every domain, therefore, is utilized to analyze coupling effects in micromachined gyroscope based on physically numerical simulation. The obtained lumped models can be described using hardware description language (HDL) and then inserted into system level model to do transient analysis of micromachined gyroscope.4) The electrostatic numerical analysis is performed to capture fringing effect in micro structural capacitance so that the relationship of capacitance with displacement can be accurately extracted. The principle of thermal-fluidic analogy is used to extract lumped parameters (damping coefficient and squeeze stiffness) of squeeze film damping in perforation plate structure. Modal analysis technology is used to extract the effective stiffness and mass in driving and sensing modes of gyroscope.5) Multidisciplinary design optimization idea is introduced for the overall preliminary design of micromachined gyroscope. To optimize the whole performance of microgyroscope such as sensitivity a multidisciplinary design model is proposed with consideration of the coupling effects of fabrication process, structure physical parameters, environmental quality factor, and electronics.6) Genetic algorithm is applied to optimize the proposed MDO problem and obtain the global trade-off optimum. The prototype of microgyroscope is fabricated with optimal parameters, and test results for the gyroscope show that MDO methodology is a promising approach to effectively explore system trade-off and design space for complex MEMS.
引文
1.范伟政,马炳和编.微机械与微细加工技术.西安:西北工业大学出版社,2000
2.刘广玉,樊尚春,周浩敏.微机械电子系统及其应用.北京:航空航天大学出版社,2003
3.石庚辰.微机电系统技术.北京:国防工业出版社,2002
4. Gregory T. A. Kovacs. Micromachined Transducers. New York: McGraw-Hill, 1999
5. Stout, Phillip, Yang, H. Q, Dionne, et al. CFD-ACE+MEMS: A CAD system for simulation and modeling of MEMS. Proceedings of SPIE-The International Society for Optical Engineering, 1999(3680): 328-339
6. Liateni K L, Hee Jung, Maher M A, et al. Moving from analysis to design: A MEMS CAD tool evolution. Proceedings of SPIE-The International Society for Optical Engineering, 2000(4019): 188-192
7. Maseeh, Fariborz. IntelliCAD: the CAD for MEMS. Wescon Conference Record, 1995: 320-324
8. Liu, Jie, Wu Bicheng, Liu Xiaojun, et al. nteroperation of heterogeneous CAD tools in Ptolemy Ⅱ. Proceedings of SPIE-The International Society for Optical Engineering, 1999(3680): 249-258
9. Romanowicz B F, Bart S F, Gilbert, J R. Integrated CAD tools for top-down design of MEMS/MOEMS systems Proceedings of SPIE-The International Society for Optical Engineering, 1999 (3680): 171-178
10. S. D. Senturia, et al. A computer-aided design system for microelectromechanical systems (MEMCAD). Journal of MEMS. 1992, 1 (1): 3-13
11. S. D. Senturia. CAD for microelectromechanical systems. Pro. Transducer 1995, Stockholm, Sweden, June 25-29, 1995: 5-8
12. S. D. Senturia. The future of microsensor and microactuator design. Sensors and Actuators A. 1996, A (56): 125-127
13. S. D. Senturia, CAD Challenges for Microsensor, Microactuators, and Microsystem, Pro. IEEE, 1998, 86(8): 1611-1626.
14. S. D. Senturia. Microsystem design. Boston: Kluwer Academic Publishers. 2002
15. N. Zhou. J. V. Clark. K. S. J. Pister. Nodal Analysis for MEMS Design Using SUGARy0.5. Santa Clara, CA, April 6-8. 1998
16. G. K. Fedder. Simulation of Microelectromechanical Systems. Ph. D Thesis. U. C. Berkeley, EECS, 1994
17.张海霞,郭辉.MEMS CAD系统IMEE的研究和开发.微纳电子技术.2003.40(7/8):92-95
18.陈兢,刘理天,李志坚.纹膜结构微麦克风的动态特性:使用EDA/CAD工具进行Top-down设计.半导体学报.2001,22(7):951-956
19.孟为民,李伟华,黄庆安.MEMS的设计方法与系统模拟.传感器技术 2001,20(10):57-60
20.孙道恒.MEMS耦合场分析与系统级仿真.中国机械工程.2002,13(9):765-768
21.康建初,尹宝林,高鹏.支持MEMS的CAD/CAE系统结构研究.北京航空航天大学学报.1998,24(4):475-478
22.卢桂章,赵新.基于部件库的MEMS设计方法.微纳电了技术.2003.40(7/8):36-39
23.霍鹏飞,马炳和,苑伟政.基于组件网络方法的微加速度计的建模与仿真.航空学报.2003,24(5):466-470
24. Petersen, K. E. Dynamic Micromechanics on Silicon: Techniques and Devices, IEEE Trans. Electr. Dev., Vol. ED-25, 1978: 1242-1249
25. X. Cai, et al. Self-consistent electromechanical analysis of complex 3D Microelectromechanical Structures using relaxation/multiple accelerated method. Sensors and Materials. 1994, 6(2): 85-99
26. U. Beerschwinger, et al. Coupled electrostatic and mechanical FEA of a micromotor. Journal of Microelectromechanical Systems. 1994, 3(4): 162-171
27. J. R. Gilbert, G. K. Ananthasuresh, and S. D. Senturia. 3D modeling of contact problems and hysteresis in coupled electromechnics. Proc. IEEE Workshop Microelectromechanical Systems. 1996, 11(15): 127-132
28. H. Yie, X. Cai, and J. White. Convergence properties of relaxation versus the surface Newton generalized conjugate residual algorithm for self-consistent electromechancial analysis of 3D microlelctromechanical structures. Proc. NUOAD V, 1994: 137-140
29. N. R. Aluru, J. White, A Multilevel Newton Method for Mixed-energy domain simulation of MEMS. Journal of MEMS, 1999, 8(3): 299-301
30. R. Mullen, S. K. Hsu. Boundary element methods in coupled electromechanical systems. Boundary Elements XU. Stress Analysis. Comp. Mech. pub. 1993(2): 517-525
31. R. Mullen, et al. Theoretical modeling of boundary conditions in microfabircation beams. Proc. IEEE. Microelectromechanical Systems. Nara Japan. 1987: 70-77
32. F. Shi, P. Ramesh and S. Mukherjee. Simulation Methods for Microelectromechanical Structures (MEMS) with Application to A Microtweeze. Computers&Structures. 1995, 56(5): 769-783
33. S. G. Adams, C. Y. Hui, and N. C. Macdonald. Simulation of microelectromechanical systems using a hybrid BEM/FEM code with the application to the stability analysis of a tunable oscillator. Proc. ASME. Dynamic Systems Control Division. 1995, 57(2): 931-939
34. J. R. Gilbert, R. Legtenberg, and S. D. Senturia. 3D coupled electromechanical for MEMS: Application of Cosolve-EM. Proc. IEEE. Microelectromechcainical Systems. 1995, 2: 122-127
35.王从舜,张为斌等.微电子机械系统中典型构件的力电耦合分析及其应用研究.机械强度.2001,23(4):503-506
36. Olivier Francais, Isabelle Dufour. Dynamics simulation of an electrostatic micropump with pull-in and hysteresis phenomena. Sensors and Actuators. 1998, A(70): 56-60
37. Marc Dequesnes, S. V. Rotkin, N. RAluru. Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches. Nanotechnology. 2002(13): 120-131
38. Yael Nemirovsky, Ofir Bochobza-Degani. A Methodology and Model for the Pull-in Parameters of Electrostatic Actuators. Journal of microelectromechanical systems, 2001, 10(4): 601-614.
39. Ofir Bochobza-Degani, David Elata, Yael Nemirovsky. An efficient relaxation based DIPIE algorithm tbr computer aided design of electrostatic actuators. 2002 IEEE: 200-204
40. Eva-Renate Konig, Peter Groth, Gerhard Wachutka. New Coupled-field simulation tool for MEMS based on the TP2000 CAD platform. Sensors and Actuators 1999 (76): 9-18
41. Gang Li, N. R. Aluru. Linear, nonlinear and mixed-regime analysis of electrostatic MEMS. Sensors and Actuators 2001A (91): 278-291
42. Robert M. Kirby, George Em Karniadakis, et al. An Integrated Simulator for Coupled Domain Problems in MEMS. Journal of Microelectromechanical Systems. 2001, 10(3): 379-391
43.余雄庆.飞机设计新技术——多学科设计优化.航空科学技术,1999(1):19-21
44. Jan Blachut, Hans A. Eschenauer, Emerging Methods for Multidisciplinary Optimization. NewYork: Springer Press, 2001
45. Tappeta R V, Nagendra S, Renaud J E. A Multidisciplinary design optimization approach for high temperature aircraft engine components. Structural Optimization, 1999, 18(2-3): 134-145
46. Sobieszczanski, Emiley M S, et al. Advancement of Bi-level integrated system synthesis (BLISS). AIAA: 2000-0421
47. Jason Bostjancic, Gabriel Torres, Beau Massenburg. Multidisciplinary Optimization Report for U. F. O: University of Florida Observer Aircraft Design and Optimization, Second annual, ISSMO Micro Aerial Vehicle Competition May 9, 1998
48. Masoud Rais-Rohani, George R. Hicks. Multidisciplinary Design and Prototype Development of a Micro Air Vehicle. Journal of Aircraft, Vol 36, NO. 1, January-February 1999: 227-234
49. X Liu, D. W. Begg. On simultaneous optimization of smart structures-Part Ⅰ: Theory. Computer methods in applied mechanics and engineering. 2000 (184): 15-24
50. X Liu, D. W. Begg. On simultaneous optimization of smart structures-Part Ⅰ: Algorithm and examples. Computer methods in applied mechanics and engineering. 2000 (184): 25-37
51.余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中应用.航空学报.2000(21):1-6
52.王爱俊,余雄庆,陈大融.复杂微机电系统的多学科设计方法研究.机械设计.2000(11):7-9
53. R. K. Gupta, S. D. Senturia. Pull-in time dynamics as a measure of absolute pressure. The Tenth Annual International Workshop on MEMS, New York, 1997: 290-294
54. Y.J.Yang, S.D.Senturia. Effect of air damping on the dynamics of nonuniform deformations of microstmctures. IEEE International Conference on Solid-State Sensors and Actuators. New York, 1997: 1093-1096
55. E.S.Hung, S.D.Senturia. Generating efficient dynamical models for microelectromechanical systems from a few finite-element simultion runs. Journal of MEMS.1999,8(3): 280-289
56. P.Greiff, B.Boxenhorm, T.King, L.Niles. Silicon monolithic micromechanical gyroscope. Transders'91. San Francisco, CA, USA, 24-27 June 1991:966-968
57. J.Bernstein, S.Cho, A.T.King, A.Kourepins, P.Maciel, M.Weinberg. A micromachined comb-drive tunging fork gyroscope. Proc. IEEE Micro Electromechanical Systems Conference, FL, USA, February. 1993: 143-148
58. O.Paul, H.Baltes. Novel fully CMOS compatible vacuum sensor. Sensors and Actuators A. Vol.46/47, 1995: 428-431
59. K.Tanaka, Y.Mochida, M.Sugimoto, et al. A micromachined vibrating gyroscope. Sensors and Actuators 1995 A (50): 111-115
60. W.A.Clark, R.T.Howe, R.Horowitz. Surface micromachined Z-axis vibratory rate gyroscope. Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, USA, 3-6 June 1996: 283-287
61. Kyu-Yeon Park, Chong-Won Lee, Yong-su Oh, et al. Laterally oscillated and force-balance micro vibratory rate gyroscope supported by fish -hook-shape springs. Sensors and Actuators 1998 A (64): 69-76
62. W.Geiger, J.Merz, T.Fischer, et al. The Silicon Angular Rate Sensor System MAR-RR. Tvansducers'99. Sendai, Japan, June 7-10, 1999: 1578-1581
63. J.A.Geen, S.J.Sherman, J.F.Chang and S.R.Lewis. Single-chip surface-micromacining integrated gyroscope with 50 deg/hour root Allan variance. IEEE International Solid-State Circuits Conference, San Francisco. CA. Feb. 3-7, 2002: 426-427.
64. W.Geiger, W.U.Butt, A.GaiBer, et al. Decoupled microgyros and the design principle DAVED, Sensors and Actuators 2002,A (95): 239-249
65. W.Gerger, B.Folkmer, U.Sobe, et al. New designs of micromachined vibrating rate gyroscopes with decoupled oscillation modes. Sensors and Actuators 1998,A(56): 118-124
66. Yoichi Mochida, Masaya Tamura, Kuniki Ohwada. A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes. Sensors and Actuators 80 (2000): 170-178
67. Said Emre Alper, Tayfun Akin. A symmetric surface micromachined gyroscope with decoupled oscillation modes. Sensors and Actuators 2002,A (97-98): 347-358
68. Tianhao Zhang, K.Chakrabarty, R.B.Fair. Integrated hierarchical design of microelectrofluidic systems using SystemC. Microelectronics Journal, Volume 33, Issues 5-6,6 May 2002: 459-470
69. T. Mukherjee, G K. Fedder, D. Ramaswamy and J. White. Emerging Simulation Approaches for Micromachined Devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.2000.19 (12): 1572-1589
70. G K. Fedder. Issues in MEMS macromodeling. Proceedings of the 2003 IEEE/ACM Int. Workshop on Behavioral Modeling and Simulation (BMAS '03), October 7-8, San Jose, California, 2003
71. Elmer S. Hung, Yao-Joe Yang, and Stephen D.Senturia. Low-Order Models for fast Dynamical Simulation of MEMS Microstructures. Transducer'97.1997: 1101-1104
72. Sven Reitz, Jens Bastian, Joachim Haase, Peter Schneider, Peter Schwarz, System level modeling of microsystems using order reduction methods. Symp. "Design, Test, Integration and Packaging of MEMS/MOEMS", Cannes, May 2002:365-373
73. Sanjay Lall, Jerrold E.Marsden, Sonja Glavaski. A subspace approach to balanced truncation for model reduction of nonlinear control systems. International Journal of Robust and Nonlinear Control. 2002(12): 519-535
74. A.C.Cangellaris, L.Zhao. Model order reduction techniques for electromagnetic macromodeling based on finite methods. International Journal of Numerical Modelling: Electronic Networks, Device and Fields. 2000 (3): 181-197
75. Zhaojun Bai. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Applied Numerical Mathematics. 2002(43): 9-44
76. S. Orieux, C. Rossi, D. Esteve. Compact model based on a lumped parameter approach for the prediction of solid propellant micro-rocket performance. Sensor and Actuators 2002 A (101): 383-391
77. Mirko Jakovljevic, Peter A. Fotiu, Zeljko Mrcarica, Vanco Litovski, Helmut Detter, Electro-thermal simulation of Microsystems with mixed abstraction modeling. Microelectronics Reliability 2001 (41): 823-835
78. R.Qiao, N.R.Aluru. Transient analysis of electroosmotic transport by Reduced-Order Modeling approach. International Journal for Numerical Methods in Engineering 2003 (56): 1023-1050
79. Harrie A C Tilmans. Equivalent circuit representation of electromechanical transducers: I. Lumped-parameter systems. J. Micromech.Microeng. 1996(6): 157-176
80. Harrie A C Tilmans. Equivalent circuit representation of electromechanical transducers: II. Distributed-parameter systems. J. Micromech.Microeng. 1997 (7): 285-309
81. T.Mukherjee and GK.Fedder. Hierarchical mixed-domain circuit simulation, synthesis and extraction methodology for MEMS. Journal of VLSI Signal Processing 1999 (21): 233 249
82. T. Mukherjee, G K. Fedder and R. D. Blanton. Hierarchical Design and Test of Integrated Microsystems, in IEEE Design & Test Magazine, October 1999:18-27
83. G K. Fedder and Q. Jing. A Hierarchical Circuit-Level Design Methodology Microelectromechanical Systems. IEEE Transactions on Circuits & Systems II (TCAS), Volume: 46 Issue: 10, October 1999: 1309-1315
84. J. E. Vandemeer, M. S. Kranz and G. K. Fedder. Hierarchical Representation and Simulation of Micromachined Inertial Sensors. Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM '98), Santa Clara, CA, USA. April 6-8. 1998:540-545
85. J.V.Clark, N.Zhou, K.S.J.Pister. Modified nodal analysis for MEMS with multi-energy domains. InternationalConference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators. San Diego, CA, March 27 29,2000:31 34
86. P.Voigt, GSchrag, GWachutka. Elecrofluidic full-system modeling of a flap valve micropump based on Kirchhoffian network theory. Sensors and Actuators. 1998, A (66): 9-14
87. J. E. Vandemeer. Nodal Design of Actuators and Sensors (NODAS). M.S. Thesis. 1998
88. Q.Jing and GK.Fedder. NODAS 1.3-nodal design of actuators and sensors. IEEE/VIUF International Workshop on Bahavioral Modeling and Simulation, Orlando, Fla., October 27 28, 1998
89. Qi Jing, Tamal Mukherjee and GK.Fedder. Large-Deflection Beam Model for Schematic-Based Behavioral Simulation in NODAS. Modeling and Simulation of Microsystems 2002:136-139
90. L.D.Gabbay. Computer Aided Macromdoeling for MEMS. Ph.D Thesis, MJT, MA, 1998
91. L.D.Gabbay, J.E.Mehner, S.D.Senturia. Computer-aided generation of nonlinear reduced-order dynamic macromodels: I. Non-stress-stiffness case. J.Microelectromech.Syst. 2000 (9): 262-269
92. L.D.Gabbay, J.E.Mehner, S.D.Senturia. Computer-aided generation of nonlinear reduced-order dynamic macromodels: II. Stress-stiffness case. J.Microelectromech.Syst. 2000 (9): 270-277
93. Mathew Varghese, S.D.Senturia, J.R.Gilbert, V.Rabinovich. Automatic Reduced-Order Modeling in MEMCAD using Modal Basis Functions. Transducer'01, Munich, Germany, June 10-14, 2000
94. Y.Chen, J.White. A Quadratic Method for Nonlinear Model Order Reduction. International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, 2000
95. Jinghong Chen, Sung-Mo(Steve) Kang. Dynamic Macromodeling of MEMS Mirror Devices. IEEE International Electron Device Meeting (IEDM), Washington, DC, Dec. 2001:41.5.1-41.5.4
96. Po-Ching Yen, Yao-Joe Yang. Macromodels of 3D Lateral Viscous Damping Effects for MEMS devices. The 12~th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, June 8-12, 2003: 1848-1851
97. Szu-Yuan Cheng, Che-Chia Yu, Yao-Joe Yang. Coupled-domain Nonlinear Macromodels and Pull-in Characteristics with Electro-Thermal Effect. The 12~th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, June 8-12, 2003: 1104-1107
98. D.Ramswamy, J.White. Automatic Generation of Small-Signal Dynamic Macromodels from 3-D Simuolation. Modeling and Simulation of Microsystems 2001: 27-30
99. G. K. Anathasuresh, R. K. Gupta, S. D. Senturia. An approach to macromodeling of MEMS for nonlinear dynamic simulation. DSC-Vol. 59, MEMS, ASME 1996: 401-407
100. E. B. Rudnyi, J. Lienemann, A. Greiner, et al. Mor4ansys: Generating Compact Models Directly from ANSYS Models. Technical Proceeding of the 2004 Nanotechnology Conference and Trade Show, Boston, USA. March 7-11 2004
101. J. Lienemann, D. Billger, E. B. Rudnyi, et al. MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices. Nanotechnology Conference and Trade Show, Boston, USA, March 7-11 2004
102.蔡大用,白峰彬.现代科学计算.北京:科学出版社.2001
103. M. Fischer, M. Giousouf, J. Schaepperle, et al. Electrostatically deflectable polysilicon micromirrors-dynamic behaviour and comparison with the results from FEM modeling with ANSYS. Sensors and Actuators. 1998. A(67): 89-95
104. J. R. Gilbert, P. M. Osterberg, R. M. Harris, et al. Implementation of a MEMCAD system for electrostatic and mechanical analysis of complex structures from mask description. IEEE Micro Electro Mechical System. For Lauderdale, FL, Feb. 1993
105. G. M. Kopperlman. OYSTER: a threedimensional structural simulator for micro-electro-mechanical-system design. Sensors and Actuators, Vol. 20, NO. 1/2, 1989
106. S. G. Adams, C. Y. Hui, and N. C. Macdonald. Simulation of microelectromechanical systems using a hybrid BEM/FEM code With the application to the stability analysis of a tunable oscillator. Proc. ASME. Dynamic Systems Control Division. DSC-Vol. 57-2. 1995: 931-939
107. N. R. Aluru and J. White. A coupled numerical technique for self-consistent analysis of micro-electrometrical systems. Microelectromechanical Systems (MEMS), ASME Dynamics Systems, and Control (DSC) Series. New York, 1996 (59): 275-280
108. F. Shi, P. Ramesh and S. Mukherjee. Simulation Methods for Microelectromechanical Structures (MEMS) with Application to A Microtweeze. Computers&Structures. 1995, 56(5): 769-783
109. 王从舜,张为斌等,微电子机械系统中典型构件的力电耦合分析及其应用研究.机械强度.2001.23(4):503-506
110. Gang Li and N. R. Aluru. Linear, Nonlinear and Mixed-Regime Analysis of Electrostatic MEMS. Sensors and Actuators A. 2001, 91(3): 278-291
111. Gang Li and N. R. Aluru. Efficient Mixed-Domain Analysis of Electrostatic MEMS. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 9, 2003: 1228-1242
112. M. Bachtold, J. G. Korvink, and H. Baltes. The adaptive, multipole-aeeelerated BEM for the computation of electrostatic forces. Proc. CAD for MEMS, Zurich, Germany, 1997: 14
113. D. Ramaswamy, N. Aluru, and J. White. Fast coupled-domain, mixed-regime electromechanical simulation. Proc. Int Conf. Solid-State Sensors and Actuators (Transducer'99), Sendal, Japan, June 1999: 314-317
114. K. Nabors and J. White. Fastcap: A multipole accelerated 3-D capacitance extraction program. IEEE Trans. Computer-Aided Design, Vol. 10, 1991: 1447-1459
115. J. R. Phillips, and J. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Computer-Aided Design, Vol. 16, Oct 1997: 1059-1072
116. Minhang Bao, Heng Yang, Yuancheng Sun. A modified Reynolds' equation for squeeze-film air damping of hole-plate. The 16th European Conference on Solid-State Transducers (EUROSENSORS ⅩⅥ) September 15-18, 2002, Prague, Czech Republic: MP04
117. T. Veijola and T. Mattila. Compact Squeezed-Film Damping Model for Perforated Surface. Transducers 2001. Munchen, June 10-14, 2001: 1506-1509
118. Yao-Joe Yang. Squeeze-Film Damping for MEMS Structures. Master Degree. MIT, 1998
119. X. Wang, M. Judy and J. White. Validating Fast Simulation of Air Damping in Micromachined Devices. Proceedings of MEMS '02, January, 2002
120. G. Schrag, G. Wachutka. Physically-Based Modeling of Squeeze Film Damping by Mixed Level System Simulation. Sensors and Actuators. 2002, A (97-98): 193-200
121. R. Saltier, G. Schrag, G. Wachutka. Mixed Level Model for Highly Perforated Torsional Actuators Coupling the Mechanical, the Electrostatic and the Fluidic Domain. Proc. of 6th International Conference on Modeling and Simulation of Microsystems, San Francisco, CA USA, 2002: 284-287
122. G. Wachutka, G. Schrag, R. Sattler. Macromodeling of Fluidic Damping Effects in Microdevices. Proc. of 4th International Conference on Advanced Semiconductor Devices and Microsystems (ASDAM-2002). Smolenice, Slovakia, Oct. 14-16, 2002: 329-332
123. G. Schrag, G. Wachutka. Accurate System Level Damping Model for Highly Perforated Micromechanical Devices. The 16th European Conference on Solid-State Transducers EUROSENSORS ⅩⅥ. Prag. Czech Republic, 15-18. 09. 2002: 80-83
124. Joseph I. S, Selden B. G Stabilization of electrostatically actuated mechanical devices. Transducer'97. Chicago, USA, June 16-29, 1997: 1133-1136
125.熊斌.栅结构微机械振动式陀螺.[博士学位论文].上海:中国科学院微系统研究所.2002
126. W. C. Tang, T. -C. H. Nguyen, M. W. Judy, et al. Electrostatic-comb drive of lateral polysilicon resonators. Sensors and Actuators. 1990, A (21-23): 328-331
127. W. C. Tang. Electrostatic comb-drive for resonant sensor and actuator applications. PhD Thesis. 1990. University of California at Berkeley
128. X Zhang and Viscous air damping in laterally driven microresonators. Proc. IEEE 1994: 199-204
129. Cho Y-H, Kwak B M, Pisano A P and Howe R T. Slide film damping in laterally driven microstructures. Sensors Actuators A 40, 1994: 31-39
130. M. G. da Silva, M. Deshpande, K. Greiner, et al. Gas damping and spring effects on MEMS devices with multiple perforations and multiple gaps. Proceedings of the 10th International Conference on Solid-State Sensors and Actuators, Sendal, Japan. Transducers '99, June 7-10 1999: 1148 1151.
131. Gad-el-Hak Mohamed. The fluid mechanics of microdevices-The Freeman Scholar Lecture. Journal of Fluids Engineering, 1999 (121): 5-33
132. J. J. Blech. On isothermal squeeze films. J. Lubr. Technol. 1983(105): 615-618
133. T. Veijola, H. Kuisma, J. Lahdenpera, et al. Equivalent-circuit model of the squeezed gas film in a silicon accelerometer. Sensors Actuators A 48, 1995: 239-48
134. http://www.ansys.com/ansys/mems/mems_downloads/thermal_analogy_damping.pdf.2003
135. F. Sharipov. Rarefied Gas Flow Through a long Rectangular Channel. J. Wac. Sci. Technol., A17(5). 1999: 3062-3066
136.车录锋,熊斌,王跃林.振子框架式微机械陀螺的有限元模拟.机械强度.2001,23(4):481-483
137. Han J S and Kwak B M Robust. Optimal design of a vibratory microgyroscope considering fabrication errors J. Micromech. Microeng., 2001(11): 662-71
138.黄小振.电容式振动微机械陀螺接口电路的设计、模拟与测试.[硕士学位论文].上海:中国科学院上海冶金研究所,2001
139. S. E. Alper, T. Akin. A plane gyroscope using a standard surface micromachining process. EUROSENSOR ⅩⅣ. 2000: 387-390.
140. Heng Yang, Minhang Bao, Hao Yin, et al. A novel bulk micromachined gyroscope based on a rectangular beam-mass structure. Sensors and Actuators 2002 A (96): 145-151
141. Farrokh Ayazi. The HARPASS process for fabrication of precision MEMS inertial sensors. Mechatronics. 2002 (12): 1185-1199
142.董景新等.微惯性仪表—微机械加速度计.清华大学出版社.北京.2003.4
143.阮爱武.梳状驱动硅微陀螺的理论及设计方法研究.[博士学位论文].西安:西北工业大学,1998
144. Andojo Ongkodjojo and Francis E H Tay. Global optimization and design for micro electro mechanical systems devices based on simulated annealing. J. Micromech. Microeng. 2002(12): 878 897
145. Blachut Jan, Eschenauer HA. Emerging methods for multidisciplinary optimization. Wien: Springer, 2001
146.王小平,曹立明.遗传算法—理论、应用与软件实现.西安:西安交通大学出版社.2002
147.邢文训,谢金星.现代优化计算方法.北京:清华大学出版社.2000
148. T. T. H. Ng, G. S. B. Leng. Application of genetic algorithm to conceptual design of a micro-air vehicle. Engineering application of artificial intelligence. 2002(15): 439-445
149. Kenneth E. M. Algorithm for global optimization of optical systems based upon genetic competition SPIE conference on optical design and analysis software. Denver, America, 1999: 40-47
150. Gregory A. K, Robert P. J and Stephen J. D. MEMS optimization incorporating genetic algorithms symposium on design, test, and microfabrication of MEMS and MOEMS. Paris, France, 1999: 84-93
151. Venkataraman P. Applied optimization with MATLAB programming. New York: Wiley Press. 2002
2.刘广玉,樊尚春,周浩敏.微机械电子系统及其应用.北京:航空航天大学出版社,2003
3.石庚辰.微机电系统技术.北京:国防工业出版社,2002
4. Gregory T. A. Kovacs. Micromachined Transducers. New York: McGraw-Hill, 1999
5. Stout, Phillip, Yang, H. Q, Dionne, et al. CFD-ACE+MEMS: A CAD system for simulation and modeling of MEMS. Proceedings of SPIE-The International Society for Optical Engineering, 1999(3680): 328-339
6. Liateni K L, Hee Jung, Maher M A, et al. Moving from analysis to design: A MEMS CAD tool evolution. Proceedings of SPIE-The International Society for Optical Engineering, 2000(4019): 188-192
7. Maseeh, Fariborz. IntelliCAD: the CAD for MEMS. Wescon Conference Record, 1995: 320-324
8. Liu, Jie, Wu Bicheng, Liu Xiaojun, et al. nteroperation of heterogeneous CAD tools in Ptolemy Ⅱ. Proceedings of SPIE-The International Society for Optical Engineering, 1999(3680): 249-258
9. Romanowicz B F, Bart S F, Gilbert, J R. Integrated CAD tools for top-down design of MEMS/MOEMS systems Proceedings of SPIE-The International Society for Optical Engineering, 1999 (3680): 171-178
10. S. D. Senturia, et al. A computer-aided design system for microelectromechanical systems (MEMCAD). Journal of MEMS. 1992, 1 (1): 3-13
11. S. D. Senturia. CAD for microelectromechanical systems. Pro. Transducer 1995, Stockholm, Sweden, June 25-29, 1995: 5-8
12. S. D. Senturia. The future of microsensor and microactuator design. Sensors and Actuators A. 1996, A (56): 125-127
13. S. D. Senturia, CAD Challenges for Microsensor, Microactuators, and Microsystem, Pro. IEEE, 1998, 86(8): 1611-1626.
14. S. D. Senturia. Microsystem design. Boston: Kluwer Academic Publishers. 2002
15. N. Zhou. J. V. Clark. K. S. J. Pister. Nodal Analysis for MEMS Design Using SUGARy0.5. Santa Clara, CA, April 6-8. 1998
16. G. K. Fedder. Simulation of Microelectromechanical Systems. Ph. D Thesis. U. C. Berkeley, EECS, 1994
17.张海霞,郭辉.MEMS CAD系统IMEE的研究和开发.微纳电子技术.2003.40(7/8):92-95
18.陈兢,刘理天,李志坚.纹膜结构微麦克风的动态特性:使用EDA/CAD工具进行Top-down设计.半导体学报.2001,22(7):951-956
19.孟为民,李伟华,黄庆安.MEMS的设计方法与系统模拟.传感器技术 2001,20(10):57-60
20.孙道恒.MEMS耦合场分析与系统级仿真.中国机械工程.2002,13(9):765-768
21.康建初,尹宝林,高鹏.支持MEMS的CAD/CAE系统结构研究.北京航空航天大学学报.1998,24(4):475-478
22.卢桂章,赵新.基于部件库的MEMS设计方法.微纳电了技术.2003.40(7/8):36-39
23.霍鹏飞,马炳和,苑伟政.基于组件网络方法的微加速度计的建模与仿真.航空学报.2003,24(5):466-470
24. Petersen, K. E. Dynamic Micromechanics on Silicon: Techniques and Devices, IEEE Trans. Electr. Dev., Vol. ED-25, 1978: 1242-1249
25. X. Cai, et al. Self-consistent electromechanical analysis of complex 3D Microelectromechanical Structures using relaxation/multiple accelerated method. Sensors and Materials. 1994, 6(2): 85-99
26. U. Beerschwinger, et al. Coupled electrostatic and mechanical FEA of a micromotor. Journal of Microelectromechanical Systems. 1994, 3(4): 162-171
27. J. R. Gilbert, G. K. Ananthasuresh, and S. D. Senturia. 3D modeling of contact problems and hysteresis in coupled electromechnics. Proc. IEEE Workshop Microelectromechanical Systems. 1996, 11(15): 127-132
28. H. Yie, X. Cai, and J. White. Convergence properties of relaxation versus the surface Newton generalized conjugate residual algorithm for self-consistent electromechancial analysis of 3D microlelctromechanical structures. Proc. NUOAD V, 1994: 137-140
29. N. R. Aluru, J. White, A Multilevel Newton Method for Mixed-energy domain simulation of MEMS. Journal of MEMS, 1999, 8(3): 299-301
30. R. Mullen, S. K. Hsu. Boundary element methods in coupled electromechanical systems. Boundary Elements XU. Stress Analysis. Comp. Mech. pub. 1993(2): 517-525
31. R. Mullen, et al. Theoretical modeling of boundary conditions in microfabircation beams. Proc. IEEE. Microelectromechanical Systems. Nara Japan. 1987: 70-77
32. F. Shi, P. Ramesh and S. Mukherjee. Simulation Methods for Microelectromechanical Structures (MEMS) with Application to A Microtweeze. Computers&Structures. 1995, 56(5): 769-783
33. S. G. Adams, C. Y. Hui, and N. C. Macdonald. Simulation of microelectromechanical systems using a hybrid BEM/FEM code with the application to the stability analysis of a tunable oscillator. Proc. ASME. Dynamic Systems Control Division. 1995, 57(2): 931-939
34. J. R. Gilbert, R. Legtenberg, and S. D. Senturia. 3D coupled electromechanical for MEMS: Application of Cosolve-EM. Proc. IEEE. Microelectromechcainical Systems. 1995, 2: 122-127
35.王从舜,张为斌等.微电子机械系统中典型构件的力电耦合分析及其应用研究.机械强度.2001,23(4):503-506
36. Olivier Francais, Isabelle Dufour. Dynamics simulation of an electrostatic micropump with pull-in and hysteresis phenomena. Sensors and Actuators. 1998, A(70): 56-60
37. Marc Dequesnes, S. V. Rotkin, N. RAluru. Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches. Nanotechnology. 2002(13): 120-131
38. Yael Nemirovsky, Ofir Bochobza-Degani. A Methodology and Model for the Pull-in Parameters of Electrostatic Actuators. Journal of microelectromechanical systems, 2001, 10(4): 601-614.
39. Ofir Bochobza-Degani, David Elata, Yael Nemirovsky. An efficient relaxation based DIPIE algorithm tbr computer aided design of electrostatic actuators. 2002 IEEE: 200-204
40. Eva-Renate Konig, Peter Groth, Gerhard Wachutka. New Coupled-field simulation tool for MEMS based on the TP2000 CAD platform. Sensors and Actuators 1999 (76): 9-18
41. Gang Li, N. R. Aluru. Linear, nonlinear and mixed-regime analysis of electrostatic MEMS. Sensors and Actuators 2001A (91): 278-291
42. Robert M. Kirby, George Em Karniadakis, et al. An Integrated Simulator for Coupled Domain Problems in MEMS. Journal of Microelectromechanical Systems. 2001, 10(3): 379-391
43.余雄庆.飞机设计新技术——多学科设计优化.航空科学技术,1999(1):19-21
44. Jan Blachut, Hans A. Eschenauer, Emerging Methods for Multidisciplinary Optimization. NewYork: Springer Press, 2001
45. Tappeta R V, Nagendra S, Renaud J E. A Multidisciplinary design optimization approach for high temperature aircraft engine components. Structural Optimization, 1999, 18(2-3): 134-145
46. Sobieszczanski, Emiley M S, et al. Advancement of Bi-level integrated system synthesis (BLISS). AIAA: 2000-0421
47. Jason Bostjancic, Gabriel Torres, Beau Massenburg. Multidisciplinary Optimization Report for U. F. O: University of Florida Observer Aircraft Design and Optimization, Second annual, ISSMO Micro Aerial Vehicle Competition May 9, 1998
48. Masoud Rais-Rohani, George R. Hicks. Multidisciplinary Design and Prototype Development of a Micro Air Vehicle. Journal of Aircraft, Vol 36, NO. 1, January-February 1999: 227-234
49. X Liu, D. W. Begg. On simultaneous optimization of smart structures-Part Ⅰ: Theory. Computer methods in applied mechanics and engineering. 2000 (184): 15-24
50. X Liu, D. W. Begg. On simultaneous optimization of smart structures-Part Ⅰ: Algorithm and examples. Computer methods in applied mechanics and engineering. 2000 (184): 25-37
51.余雄庆,丁运亮.多学科设计优化算法及其在飞行器设计中应用.航空学报.2000(21):1-6
52.王爱俊,余雄庆,陈大融.复杂微机电系统的多学科设计方法研究.机械设计.2000(11):7-9
53. R. K. Gupta, S. D. Senturia. Pull-in time dynamics as a measure of absolute pressure. The Tenth Annual International Workshop on MEMS, New York, 1997: 290-294
54. Y.J.Yang, S.D.Senturia. Effect of air damping on the dynamics of nonuniform deformations of microstmctures. IEEE International Conference on Solid-State Sensors and Actuators. New York, 1997: 1093-1096
55. E.S.Hung, S.D.Senturia. Generating efficient dynamical models for microelectromechanical systems from a few finite-element simultion runs. Journal of MEMS.1999,8(3): 280-289
56. P.Greiff, B.Boxenhorm, T.King, L.Niles. Silicon monolithic micromechanical gyroscope. Transders'91. San Francisco, CA, USA, 24-27 June 1991:966-968
57. J.Bernstein, S.Cho, A.T.King, A.Kourepins, P.Maciel, M.Weinberg. A micromachined comb-drive tunging fork gyroscope. Proc. IEEE Micro Electromechanical Systems Conference, FL, USA, February. 1993: 143-148
58. O.Paul, H.Baltes. Novel fully CMOS compatible vacuum sensor. Sensors and Actuators A. Vol.46/47, 1995: 428-431
59. K.Tanaka, Y.Mochida, M.Sugimoto, et al. A micromachined vibrating gyroscope. Sensors and Actuators 1995 A (50): 111-115
60. W.A.Clark, R.T.Howe, R.Horowitz. Surface micromachined Z-axis vibratory rate gyroscope. Solid-State Sensor and Actuator Workshop, Hilton Head Island, SC, USA, 3-6 June 1996: 283-287
61. Kyu-Yeon Park, Chong-Won Lee, Yong-su Oh, et al. Laterally oscillated and force-balance micro vibratory rate gyroscope supported by fish -hook-shape springs. Sensors and Actuators 1998 A (64): 69-76
62. W.Geiger, J.Merz, T.Fischer, et al. The Silicon Angular Rate Sensor System MAR-RR. Tvansducers'99. Sendai, Japan, June 7-10, 1999: 1578-1581
63. J.A.Geen, S.J.Sherman, J.F.Chang and S.R.Lewis. Single-chip surface-micromacining integrated gyroscope with 50 deg/hour root Allan variance. IEEE International Solid-State Circuits Conference, San Francisco. CA. Feb. 3-7, 2002: 426-427.
64. W.Geiger, W.U.Butt, A.GaiBer, et al. Decoupled microgyros and the design principle DAVED, Sensors and Actuators 2002,A (95): 239-249
65. W.Gerger, B.Folkmer, U.Sobe, et al. New designs of micromachined vibrating rate gyroscopes with decoupled oscillation modes. Sensors and Actuators 1998,A(56): 118-124
66. Yoichi Mochida, Masaya Tamura, Kuniki Ohwada. A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes. Sensors and Actuators 80 (2000): 170-178
67. Said Emre Alper, Tayfun Akin. A symmetric surface micromachined gyroscope with decoupled oscillation modes. Sensors and Actuators 2002,A (97-98): 347-358
68. Tianhao Zhang, K.Chakrabarty, R.B.Fair. Integrated hierarchical design of microelectrofluidic systems using SystemC. Microelectronics Journal, Volume 33, Issues 5-6,6 May 2002: 459-470
69. T. Mukherjee, G K. Fedder, D. Ramaswamy and J. White. Emerging Simulation Approaches for Micromachined Devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.2000.19 (12): 1572-1589
70. G K. Fedder. Issues in MEMS macromodeling. Proceedings of the 2003 IEEE/ACM Int. Workshop on Behavioral Modeling and Simulation (BMAS '03), October 7-8, San Jose, California, 2003
71. Elmer S. Hung, Yao-Joe Yang, and Stephen D.Senturia. Low-Order Models for fast Dynamical Simulation of MEMS Microstructures. Transducer'97.1997: 1101-1104
72. Sven Reitz, Jens Bastian, Joachim Haase, Peter Schneider, Peter Schwarz, System level modeling of microsystems using order reduction methods. Symp. "Design, Test, Integration and Packaging of MEMS/MOEMS", Cannes, May 2002:365-373
73. Sanjay Lall, Jerrold E.Marsden, Sonja Glavaski. A subspace approach to balanced truncation for model reduction of nonlinear control systems. International Journal of Robust and Nonlinear Control. 2002(12): 519-535
74. A.C.Cangellaris, L.Zhao. Model order reduction techniques for electromagnetic macromodeling based on finite methods. International Journal of Numerical Modelling: Electronic Networks, Device and Fields. 2000 (3): 181-197
75. Zhaojun Bai. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Applied Numerical Mathematics. 2002(43): 9-44
76. S. Orieux, C. Rossi, D. Esteve. Compact model based on a lumped parameter approach for the prediction of solid propellant micro-rocket performance. Sensor and Actuators 2002 A (101): 383-391
77. Mirko Jakovljevic, Peter A. Fotiu, Zeljko Mrcarica, Vanco Litovski, Helmut Detter, Electro-thermal simulation of Microsystems with mixed abstraction modeling. Microelectronics Reliability 2001 (41): 823-835
78. R.Qiao, N.R.Aluru. Transient analysis of electroosmotic transport by Reduced-Order Modeling approach. International Journal for Numerical Methods in Engineering 2003 (56): 1023-1050
79. Harrie A C Tilmans. Equivalent circuit representation of electromechanical transducers: I. Lumped-parameter systems. J. Micromech.Microeng. 1996(6): 157-176
80. Harrie A C Tilmans. Equivalent circuit representation of electromechanical transducers: II. Distributed-parameter systems. J. Micromech.Microeng. 1997 (7): 285-309
81. T.Mukherjee and GK.Fedder. Hierarchical mixed-domain circuit simulation, synthesis and extraction methodology for MEMS. Journal of VLSI Signal Processing 1999 (21): 233 249
82. T. Mukherjee, G K. Fedder and R. D. Blanton. Hierarchical Design and Test of Integrated Microsystems, in IEEE Design & Test Magazine, October 1999:18-27
83. G K. Fedder and Q. Jing. A Hierarchical Circuit-Level Design Methodology Microelectromechanical Systems. IEEE Transactions on Circuits & Systems II (TCAS), Volume: 46 Issue: 10, October 1999: 1309-1315
84. J. E. Vandemeer, M. S. Kranz and G. K. Fedder. Hierarchical Representation and Simulation of Micromachined Inertial Sensors. Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators (MSM '98), Santa Clara, CA, USA. April 6-8. 1998:540-545
85. J.V.Clark, N.Zhou, K.S.J.Pister. Modified nodal analysis for MEMS with multi-energy domains. InternationalConference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators. San Diego, CA, March 27 29,2000:31 34
86. P.Voigt, GSchrag, GWachutka. Elecrofluidic full-system modeling of a flap valve micropump based on Kirchhoffian network theory. Sensors and Actuators. 1998, A (66): 9-14
87. J. E. Vandemeer. Nodal Design of Actuators and Sensors (NODAS). M.S. Thesis. 1998
88. Q.Jing and GK.Fedder. NODAS 1.3-nodal design of actuators and sensors. IEEE/VIUF International Workshop on Bahavioral Modeling and Simulation, Orlando, Fla., October 27 28, 1998
89. Qi Jing, Tamal Mukherjee and GK.Fedder. Large-Deflection Beam Model for Schematic-Based Behavioral Simulation in NODAS. Modeling and Simulation of Microsystems 2002:136-139
90. L.D.Gabbay. Computer Aided Macromdoeling for MEMS. Ph.D Thesis, MJT, MA, 1998
91. L.D.Gabbay, J.E.Mehner, S.D.Senturia. Computer-aided generation of nonlinear reduced-order dynamic macromodels: I. Non-stress-stiffness case. J.Microelectromech.Syst. 2000 (9): 262-269
92. L.D.Gabbay, J.E.Mehner, S.D.Senturia. Computer-aided generation of nonlinear reduced-order dynamic macromodels: II. Stress-stiffness case. J.Microelectromech.Syst. 2000 (9): 270-277
93. Mathew Varghese, S.D.Senturia, J.R.Gilbert, V.Rabinovich. Automatic Reduced-Order Modeling in MEMCAD using Modal Basis Functions. Transducer'01, Munich, Germany, June 10-14, 2000
94. Y.Chen, J.White. A Quadratic Method for Nonlinear Model Order Reduction. International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, 2000
95. Jinghong Chen, Sung-Mo(Steve) Kang. Dynamic Macromodeling of MEMS Mirror Devices. IEEE International Electron Device Meeting (IEDM), Washington, DC, Dec. 2001:41.5.1-41.5.4
96. Po-Ching Yen, Yao-Joe Yang. Macromodels of 3D Lateral Viscous Damping Effects for MEMS devices. The 12~th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, June 8-12, 2003: 1848-1851
97. Szu-Yuan Cheng, Che-Chia Yu, Yao-Joe Yang. Coupled-domain Nonlinear Macromodels and Pull-in Characteristics with Electro-Thermal Effect. The 12~th International Conference on Solid State Sensors, Actuators and Microsystems, Boston, June 8-12, 2003: 1104-1107
98. D.Ramswamy, J.White. Automatic Generation of Small-Signal Dynamic Macromodels from 3-D Simuolation. Modeling and Simulation of Microsystems 2001: 27-30
99. G. K. Anathasuresh, R. K. Gupta, S. D. Senturia. An approach to macromodeling of MEMS for nonlinear dynamic simulation. DSC-Vol. 59, MEMS, ASME 1996: 401-407
100. E. B. Rudnyi, J. Lienemann, A. Greiner, et al. Mor4ansys: Generating Compact Models Directly from ANSYS Models. Technical Proceeding of the 2004 Nanotechnology Conference and Trade Show, Boston, USA. March 7-11 2004
101. J. Lienemann, D. Billger, E. B. Rudnyi, et al. MEMS Compact Modeling Meets Model Order Reduction: Examples of the Application of Arnoldi Methods to Microsystem Devices. Nanotechnology Conference and Trade Show, Boston, USA, March 7-11 2004
102.蔡大用,白峰彬.现代科学计算.北京:科学出版社.2001
103. M. Fischer, M. Giousouf, J. Schaepperle, et al. Electrostatically deflectable polysilicon micromirrors-dynamic behaviour and comparison with the results from FEM modeling with ANSYS. Sensors and Actuators. 1998. A(67): 89-95
104. J. R. Gilbert, P. M. Osterberg, R. M. Harris, et al. Implementation of a MEMCAD system for electrostatic and mechanical analysis of complex structures from mask description. IEEE Micro Electro Mechical System. For Lauderdale, FL, Feb. 1993
105. G. M. Kopperlman. OYSTER: a threedimensional structural simulator for micro-electro-mechanical-system design. Sensors and Actuators, Vol. 20, NO. 1/2, 1989
106. S. G. Adams, C. Y. Hui, and N. C. Macdonald. Simulation of microelectromechanical systems using a hybrid BEM/FEM code With the application to the stability analysis of a tunable oscillator. Proc. ASME. Dynamic Systems Control Division. DSC-Vol. 57-2. 1995: 931-939
107. N. R. Aluru and J. White. A coupled numerical technique for self-consistent analysis of micro-electrometrical systems. Microelectromechanical Systems (MEMS), ASME Dynamics Systems, and Control (DSC) Series. New York, 1996 (59): 275-280
108. F. Shi, P. Ramesh and S. Mukherjee. Simulation Methods for Microelectromechanical Structures (MEMS) with Application to A Microtweeze. Computers&Structures. 1995, 56(5): 769-783
109. 王从舜,张为斌等,微电子机械系统中典型构件的力电耦合分析及其应用研究.机械强度.2001.23(4):503-506
110. Gang Li and N. R. Aluru. Linear, Nonlinear and Mixed-Regime Analysis of Electrostatic MEMS. Sensors and Actuators A. 2001, 91(3): 278-291
111. Gang Li and N. R. Aluru. Efficient Mixed-Domain Analysis of Electrostatic MEMS. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 22, no. 9, 2003: 1228-1242
112. M. Bachtold, J. G. Korvink, and H. Baltes. The adaptive, multipole-aeeelerated BEM for the computation of electrostatic forces. Proc. CAD for MEMS, Zurich, Germany, 1997: 14
113. D. Ramaswamy, N. Aluru, and J. White. Fast coupled-domain, mixed-regime electromechanical simulation. Proc. Int Conf. Solid-State Sensors and Actuators (Transducer'99), Sendal, Japan, June 1999: 314-317
114. K. Nabors and J. White. Fastcap: A multipole accelerated 3-D capacitance extraction program. IEEE Trans. Computer-Aided Design, Vol. 10, 1991: 1447-1459
115. J. R. Phillips, and J. White. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Trans. Computer-Aided Design, Vol. 16, Oct 1997: 1059-1072
116. Minhang Bao, Heng Yang, Yuancheng Sun. A modified Reynolds' equation for squeeze-film air damping of hole-plate. The 16th European Conference on Solid-State Transducers (EUROSENSORS ⅩⅥ) September 15-18, 2002, Prague, Czech Republic: MP04
117. T. Veijola and T. Mattila. Compact Squeezed-Film Damping Model for Perforated Surface. Transducers 2001. Munchen, June 10-14, 2001: 1506-1509
118. Yao-Joe Yang. Squeeze-Film Damping for MEMS Structures. Master Degree. MIT, 1998
119. X. Wang, M. Judy and J. White. Validating Fast Simulation of Air Damping in Micromachined Devices. Proceedings of MEMS '02, January, 2002
120. G. Schrag, G. Wachutka. Physically-Based Modeling of Squeeze Film Damping by Mixed Level System Simulation. Sensors and Actuators. 2002, A (97-98): 193-200
121. R. Saltier, G. Schrag, G. Wachutka. Mixed Level Model for Highly Perforated Torsional Actuators Coupling the Mechanical, the Electrostatic and the Fluidic Domain. Proc. of 6th International Conference on Modeling and Simulation of Microsystems, San Francisco, CA USA, 2002: 284-287
122. G. Wachutka, G. Schrag, R. Sattler. Macromodeling of Fluidic Damping Effects in Microdevices. Proc. of 4th International Conference on Advanced Semiconductor Devices and Microsystems (ASDAM-2002). Smolenice, Slovakia, Oct. 14-16, 2002: 329-332
123. G. Schrag, G. Wachutka. Accurate System Level Damping Model for Highly Perforated Micromechanical Devices. The 16th European Conference on Solid-State Transducers EUROSENSORS ⅩⅥ. Prag. Czech Republic, 15-18. 09. 2002: 80-83
124. Joseph I. S, Selden B. G Stabilization of electrostatically actuated mechanical devices. Transducer'97. Chicago, USA, June 16-29, 1997: 1133-1136
125.熊斌.栅结构微机械振动式陀螺.[博士学位论文].上海:中国科学院微系统研究所.2002
126. W. C. Tang, T. -C. H. Nguyen, M. W. Judy, et al. Electrostatic-comb drive of lateral polysilicon resonators. Sensors and Actuators. 1990, A (21-23): 328-331
127. W. C. Tang. Electrostatic comb-drive for resonant sensor and actuator applications. PhD Thesis. 1990. University of California at Berkeley
128. X Zhang and Viscous air damping in laterally driven microresonators. Proc. IEEE 1994: 199-204
129. Cho Y-H, Kwak B M, Pisano A P and Howe R T. Slide film damping in laterally driven microstructures. Sensors Actuators A 40, 1994: 31-39
130. M. G. da Silva, M. Deshpande, K. Greiner, et al. Gas damping and spring effects on MEMS devices with multiple perforations and multiple gaps. Proceedings of the 10th International Conference on Solid-State Sensors and Actuators, Sendal, Japan. Transducers '99, June 7-10 1999: 1148 1151.
131. Gad-el-Hak Mohamed. The fluid mechanics of microdevices-The Freeman Scholar Lecture. Journal of Fluids Engineering, 1999 (121): 5-33
132. J. J. Blech. On isothermal squeeze films. J. Lubr. Technol. 1983(105): 615-618
133. T. Veijola, H. Kuisma, J. Lahdenpera, et al. Equivalent-circuit model of the squeezed gas film in a silicon accelerometer. Sensors Actuators A 48, 1995: 239-48
134. http://www.ansys.com/ansys/mems/mems_downloads/thermal_analogy_damping.pdf.2003
135. F. Sharipov. Rarefied Gas Flow Through a long Rectangular Channel. J. Wac. Sci. Technol., A17(5). 1999: 3062-3066
136.车录锋,熊斌,王跃林.振子框架式微机械陀螺的有限元模拟.机械强度.2001,23(4):481-483
137. Han J S and Kwak B M Robust. Optimal design of a vibratory microgyroscope considering fabrication errors J. Micromech. Microeng., 2001(11): 662-71
138.黄小振.电容式振动微机械陀螺接口电路的设计、模拟与测试.[硕士学位论文].上海:中国科学院上海冶金研究所,2001
139. S. E. Alper, T. Akin. A plane gyroscope using a standard surface micromachining process. EUROSENSOR ⅩⅣ. 2000: 387-390.
140. Heng Yang, Minhang Bao, Hao Yin, et al. A novel bulk micromachined gyroscope based on a rectangular beam-mass structure. Sensors and Actuators 2002 A (96): 145-151
141. Farrokh Ayazi. The HARPASS process for fabrication of precision MEMS inertial sensors. Mechatronics. 2002 (12): 1185-1199
142.董景新等.微惯性仪表—微机械加速度计.清华大学出版社.北京.2003.4
143.阮爱武.梳状驱动硅微陀螺的理论及设计方法研究.[博士学位论文].西安:西北工业大学,1998
144. Andojo Ongkodjojo and Francis E H Tay. Global optimization and design for micro electro mechanical systems devices based on simulated annealing. J. Micromech. Microeng. 2002(12): 878 897
145. Blachut Jan, Eschenauer HA. Emerging methods for multidisciplinary optimization. Wien: Springer, 2001
146.王小平,曹立明.遗传算法—理论、应用与软件实现.西安:西安交通大学出版社.2002
147.邢文训,谢金星.现代优化计算方法.北京:清华大学出版社.2000
148. T. T. H. Ng, G. S. B. Leng. Application of genetic algorithm to conceptual design of a micro-air vehicle. Engineering application of artificial intelligence. 2002(15): 439-445
149. Kenneth E. M. Algorithm for global optimization of optical systems based upon genetic competition SPIE conference on optical design and analysis software. Denver, America, 1999: 40-47
150. Gregory A. K, Robert P. J and Stephen J. D. MEMS optimization incorporating genetic algorithms symposium on design, test, and microfabrication of MEMS and MOEMS. Paris, France, 1999: 84-93
151. Venkataraman P. Applied optimization with MATLAB programming. New York: Wiley Press. 2002