音叉振动式微机械陀螺结构拓扑自组织设计方法的研究
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摘要
微结构拓扑设计是结构设计中的难点和热点问题,也是结构设计领域的前沿研究方向。微结构拓扑设计是制约MEMS实用化的关键技术之一,设计和制作出高性能、高灵敏度的微器件结构是MEMS实用化的重要保证。从微结构拓扑出发,同时考虑其内部连接和工作环境,建立微器件高精度行为模型和结构拓扑优化设计方法,是MEMS性能设计和系统设计中的关键性难题。即在MEMS的微小尺度效应和复杂动力学机制下,存在微结构弹性变形同其输出性能(电信号)的高精度映射关系(微器件高精度行为模型)的难题,以及在追求高性能MEMS的评价下,其设计过程中结构拓扑的大自由变量度表征和大计算量(微器件结构拓扑优化设计方法)的难题。
从解决此类高性能、高灵敏度微结构拓扑设计的关键性难题出发,本论文以一种体微机械加工技术制备的音叉振动式微机械陀螺为研究对象,提出基于元胞自动机的结构拓扑自组织设计方法。将灵活地表征具有大自由度、复杂动力学机制特征的、自下而上的自组织理论引入微机械陀螺结构拓扑设计中,以提高微机械陀螺的灵敏度和带宽等性能参数为出发点,对微机械陀螺的结构拓扑设计方法进行了系统而深入的研究:
(1)基于微机械陀螺的简化模型,分析了音叉振动式微机械陀螺的基本工作原理、空气阻尼特性、驱动与检测方法以及弹性梁的设计。总结了微机械陀螺简化模型在其原理性概念设计中的优点和问题,提出了基于弹性理论的高性能、高灵敏度的微器件结构拓扑设计模型的必要性。
(2)为提高设计和解析过程中微机械陀螺检测电容的计算精度,解决高精度微机械陀螺结构解析和优化过程中的计算时间问题,利用弹性理论和多自由度动态有限元解析理论,首次提出了微机械陀螺检测电容的子结构化解析模型,建立了微陀螺结构的弹性变形同其输出性能(电信号)的高精度映射关系,确立了微器件的高精度行为模型,在实现微机械陀螺的高精度解析和分析的基础上,完成了面向微机械陀螺最终输出性能/检测电容的动力学特性与检测特性分析;考虑到工作环境对微机械陀螺的影响不可忽视,采用热-力耦合分析的非线性有限元方法,分析了环境温度对微机械陀螺的固有频率、检测电容输出和带宽等性能参数的影响。
(3)为提高微机械陀螺的灵敏度(输出性能)和带宽等性能参数,提出适用于表征大自由度微结构设计的自组织拓扑设计流程,将元胞自动机应用于具有大自由度、非线性、复杂性的微结构拓扑的自组织设计模型表达中。从微机械陀螺的实际结构和动态特性出发,构建微机械陀螺拓扑演化的间接规则,用于驱动结构的自组织演化过程;基于最终输出性能,提出微机械陀螺的性能评价方法。基于微机械陀螺的子结构模型,建立高灵敏度的子结构化的微器件结构拓扑设计模型,解决了拓扑优化中的时间和效率问题。以弹性梁的拓扑优化为算例,将微机械陀螺的自组织拓扑演化规则应用于弹性梁的拓扑演化过程中,实现了微机械陀螺的自组织拓扑优化,优化后的数值计算表明微机械陀螺的整体性能有了大幅度提高,同时保持了很高的品质因子。
(4)为实际验证优化后微机械陀螺的性能,根据优化后的结果,进行了改进后微机械陀螺器件的制作、封装和测试。测试结果表明,改进后的微机械陀螺在灵敏度和带宽等性能方面均有了大幅提高,证明了本文提出的自组织设计方法的有效性。微机械陀螺的自组织拓扑设计方法提供了一种缩短实际微机械陀螺研制周期、实现微机械陀螺高效设计的有效途径。
Topology design of microstructure is a hot research topic as well as the most challenging and difficult problem in structural design. Topology design of microstructure is also one of the key technologies that limit the practical application of micro-electro-mechanical system (MEMS). Design and fabrication of MEMS device with high performance and high sensitivity is an important assurance of the practical application of MEMS. However, it is very difficult to set out from the topology of microstructure and consider microstructure topology, internal connection and working environment synthetically to build the behavioral model of MEMS device. That is, in the mechanism of the scale effects and complex dynamics, it is difficult to build the high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance (electrical signal). In seeking of high-performance MEMS, it is necessary to describe the high degree of freedom and solve the problem of large calculation amount in structural topology design.
For the solving of the key problem in topology design of high-performance and high-sensitivity microstructure, this paper focuses on a tuning fork vibratory micromachined gyroscope fabricated by the bulk silicon micromachining procedures. The self-organizing structural topology design methodology using Cellular Automata (CA) is presented for the design and optimization of the micromachined gyroscope. The down-top self-organizing theory with the features of complex dynamics mechanism is applied in the design and optimization of the structural topology of the micromachined gyroscope. To increase the sensitivity and bandwidth of the micromachined gyroscope, the structural topology design methodology for the micromachined gyroscope is researched systemically and in depth. The contents of this paper are as follows:
(1) Several issues about the basic working principle, the air damping characteristics, the driving and sensing method, the design of elastic beam are discussed based on the rigid body model of micronmachined gyroscope. And then, the merits and some defects of rigid body model in the concept design are profoundly discussed. The necessity of the high-performance and high-sensitivity structural topology model for MEMS device based on elastic theory is presented.
(2) To improve the analytical and design precision of the detection capacitance and solve the problem of long computation time in structural analysis and optimization of the micromachined gyroscope, the detection capacitance analysis method based on the substructuring model is first proposed by employing the dynamic finite element theory of multi-degree of freedom. The high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance is therefore built. The performance-oriented analysis and calculation of the dynamics and detecting characteristics for the micromachined gyroscope is realized. Since the working environment cannot be ignored, the nonlinear finite element method for mechanical-thermal coupled field is employed to analysis the influence of environmental temperature on the natural frequencies, the output of detection capacitance and bandwidth of the micromachined gyroscope.
(3) To increase the sensitivity (output performance) and bandwidth of the micromachined gyroscope, a procedure for design of microstructure with high degree of freedom is presented. The Cellular Automata is applied in the expression of self-organizing design model of the high degree of freedom, nonlinear and complex microstructure topology. Considering the practical structure and dynamic characteristics of the micromachined gyroscope, the indirect local rule for topology evolution is built to drive the self-organizing evolution process. A performance evaluation function is derived based on the output performance. The high-sensitivity substructuring model for the topology design of the micromachined gyroscope is established to conduct analysis and optimization with a reasonable accuracy and a reduced computational cost. The optimization of the spring beams is processed as a numerical example, and the proposed method is applied in the topology optimization of the spring beams. The self-organizing topology optimization of the micromachined gyroscope is achieved. The optimization result shows that the performance of micromachined gyroscope is promoted greatly without change in the high Q-factors.
(4) To test the performance of the optimized structure in practice, the improved micromachined gyroscope is fabricated and tested according to the optimization results. The testing results show that the improved micromachined gyroscope has much promotion on sensitivity and bandwidth, which proves the validity of the self-organizing topology design methodology. The self-organizing topology design provides an effective method to shorten the design period for micromachined gyroscope.
从解决此类高性能、高灵敏度微结构拓扑设计的关键性难题出发,本论文以一种体微机械加工技术制备的音叉振动式微机械陀螺为研究对象,提出基于元胞自动机的结构拓扑自组织设计方法。将灵活地表征具有大自由度、复杂动力学机制特征的、自下而上的自组织理论引入微机械陀螺结构拓扑设计中,以提高微机械陀螺的灵敏度和带宽等性能参数为出发点,对微机械陀螺的结构拓扑设计方法进行了系统而深入的研究:
(1)基于微机械陀螺的简化模型,分析了音叉振动式微机械陀螺的基本工作原理、空气阻尼特性、驱动与检测方法以及弹性梁的设计。总结了微机械陀螺简化模型在其原理性概念设计中的优点和问题,提出了基于弹性理论的高性能、高灵敏度的微器件结构拓扑设计模型的必要性。
(2)为提高设计和解析过程中微机械陀螺检测电容的计算精度,解决高精度微机械陀螺结构解析和优化过程中的计算时间问题,利用弹性理论和多自由度动态有限元解析理论,首次提出了微机械陀螺检测电容的子结构化解析模型,建立了微陀螺结构的弹性变形同其输出性能(电信号)的高精度映射关系,确立了微器件的高精度行为模型,在实现微机械陀螺的高精度解析和分析的基础上,完成了面向微机械陀螺最终输出性能/检测电容的动力学特性与检测特性分析;考虑到工作环境对微机械陀螺的影响不可忽视,采用热-力耦合分析的非线性有限元方法,分析了环境温度对微机械陀螺的固有频率、检测电容输出和带宽等性能参数的影响。
(3)为提高微机械陀螺的灵敏度(输出性能)和带宽等性能参数,提出适用于表征大自由度微结构设计的自组织拓扑设计流程,将元胞自动机应用于具有大自由度、非线性、复杂性的微结构拓扑的自组织设计模型表达中。从微机械陀螺的实际结构和动态特性出发,构建微机械陀螺拓扑演化的间接规则,用于驱动结构的自组织演化过程;基于最终输出性能,提出微机械陀螺的性能评价方法。基于微机械陀螺的子结构模型,建立高灵敏度的子结构化的微器件结构拓扑设计模型,解决了拓扑优化中的时间和效率问题。以弹性梁的拓扑优化为算例,将微机械陀螺的自组织拓扑演化规则应用于弹性梁的拓扑演化过程中,实现了微机械陀螺的自组织拓扑优化,优化后的数值计算表明微机械陀螺的整体性能有了大幅度提高,同时保持了很高的品质因子。
(4)为实际验证优化后微机械陀螺的性能,根据优化后的结果,进行了改进后微机械陀螺器件的制作、封装和测试。测试结果表明,改进后的微机械陀螺在灵敏度和带宽等性能方面均有了大幅提高,证明了本文提出的自组织设计方法的有效性。微机械陀螺的自组织拓扑设计方法提供了一种缩短实际微机械陀螺研制周期、实现微机械陀螺高效设计的有效途径。
Topology design of microstructure is a hot research topic as well as the most challenging and difficult problem in structural design. Topology design of microstructure is also one of the key technologies that limit the practical application of micro-electro-mechanical system (MEMS). Design and fabrication of MEMS device with high performance and high sensitivity is an important assurance of the practical application of MEMS. However, it is very difficult to set out from the topology of microstructure and consider microstructure topology, internal connection and working environment synthetically to build the behavioral model of MEMS device. That is, in the mechanism of the scale effects and complex dynamics, it is difficult to build the high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance (electrical signal). In seeking of high-performance MEMS, it is necessary to describe the high degree of freedom and solve the problem of large calculation amount in structural topology design.
For the solving of the key problem in topology design of high-performance and high-sensitivity microstructure, this paper focuses on a tuning fork vibratory micromachined gyroscope fabricated by the bulk silicon micromachining procedures. The self-organizing structural topology design methodology using Cellular Automata (CA) is presented for the design and optimization of the micromachined gyroscope. The down-top self-organizing theory with the features of complex dynamics mechanism is applied in the design and optimization of the structural topology of the micromachined gyroscope. To increase the sensitivity and bandwidth of the micromachined gyroscope, the structural topology design methodology for the micromachined gyroscope is researched systemically and in depth. The contents of this paper are as follows:
(1) Several issues about the basic working principle, the air damping characteristics, the driving and sensing method, the design of elastic beam are discussed based on the rigid body model of micronmachined gyroscope. And then, the merits and some defects of rigid body model in the concept design are profoundly discussed. The necessity of the high-performance and high-sensitivity structural topology model for MEMS device based on elastic theory is presented.
(2) To improve the analytical and design precision of the detection capacitance and solve the problem of long computation time in structural analysis and optimization of the micromachined gyroscope, the detection capacitance analysis method based on the substructuring model is first proposed by employing the dynamic finite element theory of multi-degree of freedom. The high-precision mapping relationship (high-precision behavior model of MEMS device) between elastic deformation and the output performance is therefore built. The performance-oriented analysis and calculation of the dynamics and detecting characteristics for the micromachined gyroscope is realized. Since the working environment cannot be ignored, the nonlinear finite element method for mechanical-thermal coupled field is employed to analysis the influence of environmental temperature on the natural frequencies, the output of detection capacitance and bandwidth of the micromachined gyroscope.
(3) To increase the sensitivity (output performance) and bandwidth of the micromachined gyroscope, a procedure for design of microstructure with high degree of freedom is presented. The Cellular Automata is applied in the expression of self-organizing design model of the high degree of freedom, nonlinear and complex microstructure topology. Considering the practical structure and dynamic characteristics of the micromachined gyroscope, the indirect local rule for topology evolution is built to drive the self-organizing evolution process. A performance evaluation function is derived based on the output performance. The high-sensitivity substructuring model for the topology design of the micromachined gyroscope is established to conduct analysis and optimization with a reasonable accuracy and a reduced computational cost. The optimization of the spring beams is processed as a numerical example, and the proposed method is applied in the topology optimization of the spring beams. The self-organizing topology optimization of the micromachined gyroscope is achieved. The optimization result shows that the performance of micromachined gyroscope is promoted greatly without change in the high Q-factors.
(4) To test the performance of the optimized structure in practice, the improved micromachined gyroscope is fabricated and tested according to the optimization results. The testing results show that the improved micromachined gyroscope has much promotion on sensitivity and bandwidth, which proves the validity of the self-organizing topology design methodology. The self-organizing topology design provides an effective method to shorten the design period for micromachined gyroscope.
引文
[1] 王安麟, 王炬香, 刘传国, 等. 基于 CA 的结构拓扑设计的研究—平面薄板加强筋拓扑形态创成的仿真, 机械强度, 2001, 23(2): 181-186
[2] 王安麟, 姜涛. 基于进化元胞自动机的结构拓扑优化, 机械工程学报, 2005, 41(2): 1-5
[3] 王安麟. 复杂系统的分析与建模, 上海交通大学出版社, 2004 年 2 月
[4] 李旭辉. MEMS 发展应用现状, 传感器与微系统, 2006, 25(5): 7-9
[5] 闫冬. 基于加速度计的无陀螺惯性导航系统的研究, 硕士学位论文, 吉林大学, 2003
[6] R.T. M'Closkey, S. Gibson, J. Hui. Modal parameter identification of a MEMS gyroscope, Proceedings of the 2000 American Control Conference, 2000, 3: 1699-1704
[7] V. Chtchekatourov, L. Vietzorreck, W. Fisch, P. Russer. Time-domain system identification modeling for microwave structures, International Conference on Mathematical Methods in Electromagnetic Theory 2000: 137-139
[8] 李昊, 胡云昌, 曹宏铎. 桁架结构布局优化现状与主要问题, 青岛大学学报(工程技术版), 2002, 17(3): 49-52
[9] Atsushi Kawamoto, Martin P. Bendsoe, Ole Sigmund. Articulated mechanism by an enumeration approach, 15th Nordic Seminar on Computational Mechanics, Denmark, 2002: 59-62,
[10] M. P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Volume 71, 197-224, 1988
[11] M.P. Bendsoe. Optimal shape design as a material distribution problem, Structural and Multidisciplinary Optimization, 1989, 1(1): 193-202
[12] B. Hassani, E. Hinton. A review of homogenization and topology optimization I - homogenization theory for media with periodic structure, Computers and Structures, 1998, 69(6): 707-718
[13] B. Hassani, E. Hinton. A review of homogenization and topology opimization II - analytical and numerical solution of homogenization equations, Computers and Structures, 1998, 69(6): 719-738
[14] B. Hassani, E. Hinton. A review of homogenization and topology optimization III - topology optimization using optimality criteria, Computers and Structures, 1998, 69(6): 739-756
[15] L. Ambrosio, G.. Buttazzo, An optimal design problem with perimeter penalization, Calculus of Variations and Partial Differential Equations, 1993, 1(1): 55-69
[16] C.S. Jog, R.B. Haber. Stability of finite element models for distributed-parameter optimization and topology design, Computer Methods in Applied Mechanics and Engineering, 1996, 130 (3-4): 203-226
[17] J. Petersson, O. Sigmund. Slope constrained topology optimization, International Journal For Numerical Methods In Engineering, 1998, 41 (8): 1417-1434,
[18] M. Zhou, Y. K. Shyy, H. L. Thomas. Checkerboard and minimum member size control in topologyoptimization, Structural and Multidisciplinary Optimization, 2001, 21(2): 152-158
[19] Gang-Won Jang, Sangkeun Lee, Yoon-Young Kim, Dongwoo Sheen. Topology optimization using non-conforming finite elements: three-dimensional case, International Journal for Numerical Methods in Engineering, 2005, 63(6): 859 - 875
[20] 刘震宇, 王晓明, 郭东明. 利用窗函数解决连续体结构拓扑优化中的棋盘格式问题, 中国机械工程, 2000, 11(6): 704-707
[21] O. Sigmund, J. Petersson. Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization, 1998, 16(1): 68-75
[22] G.L.N. Rozvany. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics, Structural and Multidisciplinary Optimization, 2001, 21(2): 90-108
[23] 樊学军. 均匀化理论及其在生物力学中的应用, 力学进展, 1996, 26(2): 187-197
[24] C.C. Swan, I. Kosaka. Homogenization-based analysis and design of composites, Computers and Structures, 1997, 64(1-4): 603-621
[25] S. Nishiwaki, M.I. Frecker, S. Min, N. Kikuchi, Topology optimization of compliant mechanisms using the homogenization method, International Journal for Numerical Methods In Engineering, 1998, 42(3): 535-559
[26] 王晓明, 刘震宇, 郭东明. 基于均匀化理论的微小型柔性结构拓扑优化的敏度分析, 中国机械工程, 1999, 10(11): 1264-1267
[27] 张荭蔚, 顾力强. 基于有限元分析技术的大客车车门结构拓扑优化设计研究, 机械设计与研究, 2002,18(5): 46-48
[28] 夏利娟, 吴嘉蒙, 金咸定. 工程结构的拓扑优化设计研究, 船舶力学, 2002, 6(6): 107-113
[29] M.P. Bendsoe, O. Sigmund, Material interpolations in topology optimization, Archive of Applied Mechanics, 1999, 69(9-10): 635-654
[30] 袁振, 吴长春, 庄守兵. 基于杂交元和变密度法的连续体结构拓扑优化设计, 中国科学技术大学学报, 2001, 31(6): 695-699
[31] 左孔天, 陈立平, 王书亭, 等. 用拓扑优化方法进行微型柔性机构的设计研究, 中国机械工程, 2004, 15(21): 1886-1890
[32] Y.M. Xie, G.P. Steven. Simple evolutionary procedure for structural optimization, Computers and Structures, 1993, 49(5): 885-896
[33] O.M. Querin, G.P. Steven, Y.M. Xie. Evolutionary structural optimization (ESO) using a bi-directional algorithm, Engineering Computation, 1998, 15(8): 1031-1048
[34] O.M. Querin, G.P. Steven, Y.M. Xie. Evolutionary structural optimization using an additive algorithm, Finite Elements in Analysis and Design, 2000, 34(3-4): 291-308
[35] Pasi Tanskanen. The evolutionary structural optimization method: theoretical aspects, Computer Methods in Applied Mechanics and Engineering, 2002, 191(47-48): 5485-5498
[36] M. Zhou, G.L.N. Rozvany. On the validity of ESO type methods in topology optimization, Structural andMultidisciplinary Optimization, 2001, 21 (1): 80-83
[37] G.L.N. Rozvany. Stress ratio and compliance based methods in topology optimization - a critical review, Structural and Multidisciplinary Optimization, 2001, 21 (1): 109-119
[38] C.D. Nha, Y. M. Xie, G. P. Steven. An evolutionary structural optimization method for sizing problems with discrete design variables, Computers and Structures, 1998, 68(4): 419-431
[39] G.P. Steven, O.M. Querin, Y.M. Xie. Evolutionary structural optimisation (ESO) for combined topology and size optimisation of discrete structures, Computer Methods in Applied Mechanics and Engineering, 2000, 188(4): 743-754
[40] Q. Li, G.P. Steven, O.M. Querin, Y. M. Xie. Shape and topology design for heat conduction by Evolutionary Structural Optimization, International Journal of Heat and Mass Transfer, 1999, 42(17): 3361-3371
[41] Y.M. Xie, G.P. Steven. Evolutionary structural optimization for dynamic problems, Computers and Structures, 1996, 58(6): 1067-1073
[42] H. Kim, O.M. Querin, G.P. Steven, Y.M. Xie. Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh, Structural and Multidisciplinary Optimization, 2003, 24(6): 441-448
[43] 王小平, 曹立明. 遗传算法-理论、应用与软件实现, 西安交通大学出版社, 2002 年 1 月第 1 版
[44] 唐文艳, 顾元宪. 遗传算法在结构优化中的研究进展, 力学进展, 2002, 32(1): 26-40
[45] 张思才, 张方晓. 自适应遗传算法在桁架结构优化设计中的应用, 湘潭大学自然科学学报, 2002, 24(4): 37-41
[46] 朱峰. 遗传算法在离散变量结构优化中的应用及其改进方案综述, 世界地震工程, 2002, 18(4): 131-135
[47] 罗志凡, 荣见华, 杜海珍. 基于遗传算法和梯度算法的一种结构优化混合方法, 计算机工程与应用, 2003, (8): 71-73
[48] N.D. Lagaros, M. Papadrakakis, G. Kokossalakis. Structural optimization using evolutionary algorithms, Computers and Structures, 2002, 80(7-8): 571-589
[49] 张明辉, 王尚锦. 遗传算法在结构形状优化中的应用, 机械科学与技术, 2001, 20(6): 824-827
[50] 佟维. 利用遗传算法的结构优化设计, 大连铁道学院学报, 2000, 21(2): 7-12
[51] H. Kawamura, H. Ohmori, N. Kito. Truss topology optimization by a modified genetic algorithm, Structural and Multidisciplinary Optimization, 2002, 23(6): 467-472
[52] F. Cappello, A. Mancuso. A genetic algorithm for combined topology and shape optimizations, Computer-Aided Design, 2003, 35(8): 761-769
[53] C.D. Chapman, K. Saitou, M.J. Jakiela. Genetic algorithms as an approach to configuration and topology design, American Society of Mechanical Engineers - Design Engineering Division (Publication) DE, 1993, 65(pt 1): 485-498
[54] M.J. Jakiela, C. Chapman, J. Duda, et al. Continuum structural topology design with genetic algorithms, Computer Methods in Applied Mechanics and Engineering, 2000, 186(2-4): 339-356
[55] Roman Gatzi, Marion Uebersax, Oliver Konig, Strucctural optimization tool using genetic algorithms and ANSYS, CAD-FEM User’s Meeting, Schweiz, 2000:1-9
[56] Ting-Yu Chen, Chia-Yang Lin. Determination of optimum design spaces for topology optimization, Finite Elements in Analysis and Design, 2000, 36(1): 1-16
[57] 夏利民, 谷士文, 沈新权. 基于水平集的 3D 动画, 计算机研究与发展, 2002,39(2): 236-241
[58] 夏利民, 谷士文, 沈新权, 孙星明. 基于水平集模型的 3D 表面重建, 小型计算机系统, 2002, 22(12): 1445-1448
[59] 王峥, 杨新, 李俊, 施鹏飞. 提高水平集方法初始化计算速度的研究, 信号处理, 2002, 18(2): 97-101
[60] 王峥, 杨新, 李俊, 施鹏飞. 水平集方法中曲线跟踪算法的改进, 上海交通大学学报, 2002, 36(12): 1833-1836
[61] 高鑫, 刘来福. 基于水平集曲率的图像滤噪与增强, 北京师范大学学报(自然科学版), 2001, 37(1): 5-9
[62] M.Y. Wang, X. Wang, D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2): 227-246
[63] M.Y. Wang, X. Wang, D. Guo. Structural shape and topology optimization in a level set based implicit moving boundary framework, Structural and Multidisciplinary Optimization, 2004, 27(1-2): 1-19
[64] J.A. Sethian, A. Wiegmann. Structural boundary design via level set and immersed interface methods, Journal of Computational Physics, 2000, 163(2): 489-528
[65] Gregoire Allaire, Francois Jouve, Anca-Maria Toader. A level-set method for shape optimization (Une méthode de lignes de niveaux pour l'optimisation de forme), Comptes Rendus Mathematique, 2002, 334(12): 1125-1130
[66] J.A. Sethian. Evolution, implementation and application of level set and fast marching methods for advancing fronts, Journal of Computational Physics, 2001, 169(2): 503-555
[67] Stanley Osher, Ronald P. Fedkiw. Level set methods: an overview and some recent results, Journal of Computational Physics, 2001, 169(2): 463-502
[68] D. Adalsteinsson, J.A. Sethian. A level set approach to a unified model for etching, deposition, and lithography I: Algorithms and two-dimensional simulations, Journal of Computational Physics, 1995, 120(1): 128-144
[69] D. Adalsteinsson, J.A. Sethian, A level set approach to a unified model for etching, deposition, and lithography II: Three-dimensional simulations, Journal of Computational Physics, 1995, 122(2): 348-366
[70] D. Adalsteinsson, J.A. Sethian, A level set approach to a unified model for etching, deposition and lithography III: Redeposition, remission, surface diffusion and complex simulations, Journal of Computational Physics, 1997, 138(1): 193-223
[71] S. Wolfram. Universality and Complexity in Cellular Automata, Physica D: Nonlinear Phenomena, 1983, 10(1-2): 1-35
[72] Brian Tatting, Zafer G?rdal. Cellular Automata for design of two-dimensional continuum structures, Proceedings of 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis andOptimization, 2000: AIAA-2000-4832
[73] Zafer G?rdal, Tatting Brian. Cellular automata for design of truss structures with linear and nonlinear response, 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference and Exhibit, 2000: AIAA 2000-1580
[74] R. Zakhama, M.M. Abdalla, H. Smaoui, Z. G?rdal. Topology design of geometrically nonlinear 2D elastic continua using CA and an equivalent truss model, Collection of Technical Papers - 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2006: 804-813
[75] Douglas J. Slotta. Structural design using cellular automata, Master Degree Thesis, Virginia Polytechnic Institute and State University, 2001
[76] E. Kita, T. Toyoda. Structural design using cellular Automata. Structural and Multidisciplinary Optimization, 2000, 19(1): 64-73
[77] O.E. Canyurt, P. Hajela. A cellular framework for structural analysis and optimization, Computer Methods in Applied Mechanics and Engineering, 2005, 194(30-33): 3516-3534
[78] S. Setoodeh, Z. G?rdal, L.T. Watson. Design of variable-stiffness composite layers using cellular automata, Computer Methods in Applied Mechanics and Engineering, 2006,195 (9-12): 836-851
[79] S. Missoum, Z. Gürdal, S. Setoodeh. Study of a new local update scheme for cellular automata in structural design, Structural and Multidisciplinary Optimization, 2004, 29 (2): 103-112
[80] S. Setoodeh,; M.M. Abdalla, Z. G?rdal. Combined Topology and fiber path design of composite layers using cellular automata, Structural and Multidisciplinary Optimization, 2005, 30 (6): 413-421
[81] M.M. Abdalla, Z. G?rdal. Structural design using Cellular Automata for eigenvalue problems, Structural and Multidisciplinary Optimization, 2004, 26 (3-4): 200-208
[82] N.M. Patel, J.E. Renaud, H. Agarwal, A. Tovar. Reliability based topology optimization using the hybrid cellular automaton method. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2005: 4125-4137
[83] N.M. Patel, J.E.Renaud, A.Tovar. Compliant mechanism design using the hybrid cellular automaton method, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2005: 5893-5904
[84] A. Tovar, W.I. Quevedo, N.M. Patel, J.E. Renaud. Hybrid cellular automata with local control rules: a new approach to topology optimization inspired by bone functional adaptation, 6th World Congresses of Structural and Multidisciplinary Optimization, 2005: 1-11
[85] A. Tovar, G.L. Niebur, M. Sen, et al. Bone structure adaptation as a cellular automaton optimization process, Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2004: 4242-4255
[86] A. Tovar. Bone remodeling as a hybrid cellular automaton optimization process, Ph.D. Degree Thesis, University of Notre Dame, 2004
[87] A. Tovar, N.M. Patel, G.L. Niebur, et al. Topology optimization using a Hybrid Cellular Automatonmethod with local control rules, Journal of Mechanical Design, 2006, 128(6): 1205-1216
[88] Thomas R. Hartka. Cellular automata for structural optimization on recongfigurable computers, Master Degree Thesis, Virginia Polytechnic Institute, 2004
[89] 沈成武, 戴诗亮, 杨吉新, 唐小兵. 平面弹性力学中的细胞自动机方法, 清华大学学报(自然科学版), 2001, 41(11): 35-38
[90] 沈成武, 唐小兵, 杨吉新. 平面桁架力学分析的细胞自动机方法初探, 武汉交通科技大学学报, 2000, 24(2): 105-108
[91] 杨吉新, 沈成武, 唐小兵. 细胞自动机方法解最小挠度薄板弯曲问题, 力学季刊, 2002, 23(2): 260-264
[92] 郑波尽, 李元香, 吴漫川. 细胞自动机函数优化算法, 计算机工程, 2003, 29(19): 66-67
[93] P. Hajela, B. Kim, On the use of energy minimization for CA based analysis in elasticity, Structural and Multidisciplinary Optimization, 2001, 23(1): 24-33
[94] 薛文胜. 浅析几种新型陀螺的发展动态, 电子科技大学学报, 1995, 24(5): 485-489
[95] C. Song, B. Ha, S. Lee. Micromachined inertial sensors, IEEE International Conference on Intelligent Robots and Systems, Korea, 1999: 1049-1056
[96] 茅盘松. 硅微型振动陀螺的设计, 传感器技术, 1995, (5): 29-31
[97] N. Yazdi, F. Ayazi, K. Najafi. Micromachined inertial sensors, Proceedings of the IEEE, 1998, 86, 1640-1659
[98] 李新刚, 袁建平. 微机械陀螺的发展现状, 力学进展, 2003, 33(3): 289-301
[99] 谷庆红. 微机械陀螺仪的研制现状, 中国惯性技术学报, 2003, 11(5): 67-72
[100] B. Boxenhorn, P. Greiff. A vibratory micromechanical gyroscope, AIAA Guidance and Control Conference, USA, 1988: 1033-1040
[101] J. Bernstein, S. Cho, A. T. King, A. Kourepenis, et al. A micromachined comb-drive tuning fork rate gyroscope, IEEE Micro Electro Mechanical Systems Workshop (MEMS’93), Fort Lauderdale, 1993: 143-148
[102] M. Weinberg, J. Bernstein, S. Cho, et al. A micromachined comb-drive tuning fork gyroscope for commercial applications, Proceedings of Sensor Exposition, USA, 1994: 187-193
[103] Y. Mochida, M. Tamura, K. Ohwada. A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes, Sensors and Actuators A, 2000, 80(2): 170-178
[104] W. Geiger, W. U. Butt, A. Gaiber, et al. Decoupled microgyros and the design principle DAVED, Sensors and Actuators, 2002, 95(2-3): 239-249
[105] 姜涛. 考虑加工误差的微机械陀螺随机性能分析及健壮性设计, 博士学位论文, 上海交通大学, 2006
[106] http://www.analog.com/zh/prod/0,2877,ADXRS150,00.html
[107] 禹奇才, 张亚芳, 刘锋. 工程力学(理论力学部分), 华南理工大学出版社, 2002
[108] 陈雪萌. 一种压阻式微机械陀螺的研究, 博士学位论文, 中国科学院上海微系统与信息技术研究所, 2005
[109] 李伟剑. 微机电系统的多域耦合分析与多学科设计优化, 博士学位论文, 西北工业大学, 2004
[110] 陈永, 基于滑膜阻尼效应的音叉式微机械陀螺研究, 博士学位论文, 中国科学院上海微系统与信息技术研究所, 2004
[111] M. Yachi, H. Ishikawa, Y. Satoh. Support structure for LiTaO3 crystal tuning fork vibratory gyroscope, 1997 IEEE Ultrasonics Symposium, 1997: 811-814
[112] Z.C. Feng, Kapil Gore. Dynamic characteristics of vibratory gyroscopes, IEEE Sensors Journal, 2004, 4(1): 80-84
[113] Aiwu Ruan, Man Siu Tse, Gang Yih Chong. Simulation and optimization of a micromachined gyroscope using high-aspect-ratio micromachining fabrication process, Proceedings of SPIE, 2001, 4593: 176-185
[114] Cenk Acar, Andrei M. Shkel. An approach for increasing drive-mode bandwidth of mems vibratory gyroscopes, Journal of Microelectromechanical Systems, 2005, 14 (3): 520-528
[115] A. Kugi, D. Thull, H. Seidel. Modelling and optimization of a silicon tuning fork gyroscope. Proceedings in Applied Mathematics and Mechanics, 2004: 59-62
[116] Y. Chen, J. Jiao, B. Xiong. A novel tuning fork gyroscope with high Q-factors working at atmospheric pressure, Microsystem Technologies, 2005, 11 (2-3): 111-116
[117] 陈永, 焦继伟, 熊斌, 等. 一种基于滑膜阻尼效应的新型微机械陀螺, 中国机械工程, 2004, 15(2): 103-106
[118] 陈永, 焦继伟, 王惠泉, 等. 大气下工作的微机械陀螺的设计及其噪声特性, 半导体学报, 2005, 26(1): 148-151
[119] Tao Jiang, Anlin Wang, Jiwei Jiao, Guangjun Liu. Detection capacitance analysis method for tuning fork micromachined gyroscope based on elastic body model, Sensors and Actuators A, 2006, 128(1): 52-59
[120] 姜涛, 王安麟, 刘广军, 等. 基于摄动法的微机械陀螺随机性能的统计分析, 上海交通大学学报, 2006, 40(11): 1918-1923
[121] 清华大学工程力学系. 机械振动(上册), 机械工业出版社, 1978
[122] 姜涛, 王安麟, 刘广军, 等. 音叉振动式微机械陀螺输出电容的统计特性分析, 机械工程学报, 2007, 43(8): 114-118
[123] 傅志方. 振动模态分析与参数识辨, 机械工业出版社, 1990
[124] 殷学纲, 陈淮, 蹇开林. 结构振动分析的子结构方法, 中国铁道出版社, 1991
[125] K. Sadek, W. Moussa. Application of adaptive multilevel substructuring technique to model CMOS micromachined thermistor gas sensor, Part (I): a feasibility study, Proceedings of the International Conference on MEMS, NANO and Smart Systems (ICMENS’03), 2003: 382-389
[126] D. Ostergaard, M.Gyimesi, Finite element based reduced order modeling of micro electro mechanical systems (MEMS). International Conference on Modeling and Simulation of Microsystems, 2000: 684-687
[127] G. Wachutka. Coupled-field modeling of microdevices and microsystems, International Conference on Simulation of Semiconductor Processes and Devices, 2002: 9-14
[128] S.F. Bart, S. Zhang, V.L. Rabinovich, et al. Coupled package-device modeling for microelectromechanicalsystems, Microelectronics Reliability 1999, 40 (7): 1235-1241
[129] L. Yin, G.K. Ananthasuresh. A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisms. Sensors and Actuators A, 2002, 97-98: 599-609
[130] 苑伟政, 李伟剑. 基于遗传算法的微机械陀螺的多学科设计优化, 机械强度, 2004, 26(2): 170-174
[131] 苑伟政, 吕湘连, 李伟剑. 基于集总参数宏模型的微机械陀螺多域耦合分析, 中国机械工程, 2006, 17(4): 401-405
[132] D. DeVoe. Thermal issues in MEMS and microscale systems, IEEE Transactions on Components and Packaging Technologies, 2003, 25(4): 576-583
[133] K. Shcheglov, C. Evans, R. Gutierrez, T.K. Tang. Temperature dependent characteristics of the JPL silicon MEMS gyroscope. IEEE, Aerospace Conference Proceedings, 2000: 403-411
[134] R.P. Leland. Mechanical-Thermal Noise in MEMS Gyroscopes, IEEE Sensors Journal, 2005, 5(3): 793-500
[135] C.C. Painter, A.M. Shkel. Structural and thermal modeling of a z-axis rate integrating gyroscope, Journal of Micromechanics and Microengineering 2003, 13(2): 229-237
[136] Y.J. Yang, K.Y. Shen. Nonlinear heat-transfer macromodeling for MEMS thermal devices, Journal of Micromechanics and Microengineering, 2005, 15 (2): 408-418
[137] M. Allen, M. Raulli, K. Maute, D.M. Frangopol. Reliability-based analysis and design optimization of electrostatically actuated MEMS, Computers and Structures, 2004, 82(13-14): 1007-1020
[138] 裘安萍, 苏岩, 王寿荣, 周百令. 残余应力对 z 轴硅微机械振动陀螺仪性能的影响, 机械工程学报, 2005, 41(6): 228-232
[139] Jeong Sam Han, Byung Man Kwak. Robust optimal design of a vibratory microgyroscope considering fabrication errors, Journal of Micromechanics And Microengineering, 2001, 11 (6): 662-671
[140] Andojo Ongkodjojo, Francis E H Tay. Global optimization and design for microelectromechanical systems devices based on simulated annealing, Journal of Micromechanics and Microengineering, 2002, 12 (6): 878-897
[141] Noboru Wakatuki, Subaru Kudo, Yutaka Satoh, Hiroshi Tanaka. A new approach to piezoelectric crystal gyroscopes for higher sensitivity, 1998 IEEE Ultrasonics Symposium, 1998: 477-480
[142] Junhua Wei, Anlin Wang, Nianci Du. Study of self-organizing control of traffic signals in an urban network based on Cellular Automata. IEEE Transactions on Vehicular Technology, 2005, 54 (2): 744-748
[143] S. Takesue. Boltzmann-type equations for elementary reversible cellular automata, Physica D: Nonlinear Phenomena, 1997, 103(1-4): 190-200
[144] 祝玉学, 赵学龙. 物理系统的元胞自动机模拟, 清华大学出版社, 2003
[145] 魏俊华. 城市交通信号自组织控制方法的研究, 博士学位论文, 上海交通大学, 2005
[146] S. Wolfram. Theory and applications of Cellular Automata, World Scientific, Singapore, 1996
[147] David Alonso. Ricard V. Solé, The DivGame simulator: a stochastic cellular automata model of rainforest dynamics, Ecological Modelling, 2000, 133(1-2): 131-141
[148] D. D'Ambrosio, Gregorio S. Di, S. Gabriele, et al. A Cellular Automata model for soil erosion by water,Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, 2001, 26(1):33-39
[149] Karafyllidis Ioannis, Thanailakis Adonios. A model for predicting forest fire spreading using cellular automata, Ecological Modelling, 1997, 99(1): 87-97
[150] Gregorio S. Di, R. Serra, M. Villani. Applying Cellular Automata to complex environmental problems: The simulation of the bioremediation of contaminated soils, Theoretical Computer Science, 1999, 217(1): 131-156
[151] X. Tong, C. Beckermann, A. Karma, et al. Phase field simulation of dendritic crystal growth in a forced flow, Physical Review E, 2001, 63(1): 1-16
[152] Jr. Spillman, B. William. Evolutionary computational techniques for complex adaptive structures, Proceedings of SPIE, 2001, 4512: 163-171
[153] 贾海朋. 结构与柔性机构拓扑优化, 博士学位论文, 大连理工大学, 2004
[154] O. Sigmund. Design of multiphysics actuators using topology optimization - Part I: One-material structures, Computer Methods in Applied Mechanics and Engineering, 2001, 190 (49-50): 6577-6604
[155] O. Sigmund. Design of multiphysics actuators using topology optimization - Part I: Two-material structures, Computer Methods in Applied Mechanics and Engineering, 2001, 190 (49-50): 6605-6627
[156] M.M. Neves, O. Sigmund, M.P. Bends?e. Topology optimization of periodic microstructures with a penalization of highly localized buckling modes, International Journal for Numerical Methods in Engineering, 2002, 54 (6): 809-834
[157] 姜涛, 朱灯林, 王安麟, 王石刚. 整合规则下的结构拓扑自组织进化设计, 机械科学与技术, 2005, 24(8): 943-946
[158] JongBok Jang, Anlin Wang, Guangjun Liu, Analysis for performance of a vibratory micromachined gyroscope based on mode-acceleration method, International Technology and Innovation Conference, China, 2006: 634-639
[159] 张美艳, 王丽炜, 陈力奋. 非亏损对称系统的子结构灵敏度综合方法, 振动与冲击, 2004, 23(1): 65-69
[160] Y. Mochida, M. Tamura, K. Ohwada. Micromachined vibrating rate gyroscope with independent beams for the drive and detection modes, Sensors and Actuators A, 2000, 80 (2): 170-178
[161] H. Yang, M. Bao, H. Yin, S. Shen. A novel bulk micromachined gyroscope based on a rectangular beam-mass structure, Sensors and Actuators A, 2002, 96 (2-3): 145-151
[162] 张正福, 音叉振动式微机械陀螺结构动态性能解析与健壮性设计, 博士学位论文, 上海交通大学, 2007
[163] 王振宇, 成立, 祝俊. 微/纳米级微电子机械系统制造新技术, 半导体技术, 2005, 30(8): 27-33
[164] 关荣锋. MEMS 器件设计、封装工艺及应用研究, 博士学位论文, 华中科技大学, 2005
[165] 邓宏论. 微硅加速度计中静电键合封接技术的应用, 电子机械工程, 2005, 21(3): 40-41
[166] G. Wallis, D. I. Pomerantz. Field assisted glass-metal sealing. Journal of Applied Physics, 1969, 40(10): 3946-3969
[167] Huikai Xie, Gary K. Fedder. Fabrication, characterization, and analysis of a DRIE CMOS-MEMSgyroscope, IEEE Sensors Journal, 2003, 3(5): 622-631
[168] 董涛, 章维一, 侯丽雅. 微系统制造中的 3 维微成形技术, 南京理工大学学报, 2001, 25(3): 318-322
[169] Bin Xiong, Lufeng Che, Yuelin Wang. A novel bulk micromachined gyroscope with slots structure working at atmosphere, Sensors and Actuators A, 2003, 107(2): 137-145
[170] 陈一梅, 黄元庆. MEMS 封装技术, 传感器技术, 2005, 24(3): 7-9
[171] Yufeng Zhang, Xiaoyun Tan, Weiping Chen, et al. Study of MEMS packaging technology, The 6th International Conference on Electronic Packaging Technology, 2005: 643-646
[172] X. Zhang, S.B. Park, R. Navarro, M.W. Judy. Accurate assessment of packaging stress effects on MEMS devices, The Tenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems (ITHERM '06), 2006: 1336-1342
[2] 王安麟, 姜涛. 基于进化元胞自动机的结构拓扑优化, 机械工程学报, 2005, 41(2): 1-5
[3] 王安麟. 复杂系统的分析与建模, 上海交通大学出版社, 2004 年 2 月
[4] 李旭辉. MEMS 发展应用现状, 传感器与微系统, 2006, 25(5): 7-9
[5] 闫冬. 基于加速度计的无陀螺惯性导航系统的研究, 硕士学位论文, 吉林大学, 2003
[6] R.T. M'Closkey, S. Gibson, J. Hui. Modal parameter identification of a MEMS gyroscope, Proceedings of the 2000 American Control Conference, 2000, 3: 1699-1704
[7] V. Chtchekatourov, L. Vietzorreck, W. Fisch, P. Russer. Time-domain system identification modeling for microwave structures, International Conference on Mathematical Methods in Electromagnetic Theory 2000: 137-139
[8] 李昊, 胡云昌, 曹宏铎. 桁架结构布局优化现状与主要问题, 青岛大学学报(工程技术版), 2002, 17(3): 49-52
[9] Atsushi Kawamoto, Martin P. Bendsoe, Ole Sigmund. Articulated mechanism by an enumeration approach, 15th Nordic Seminar on Computational Mechanics, Denmark, 2002: 59-62,
[10] M. P. Bendsoe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, Volume 71, 197-224, 1988
[11] M.P. Bendsoe. Optimal shape design as a material distribution problem, Structural and Multidisciplinary Optimization, 1989, 1(1): 193-202
[12] B. Hassani, E. Hinton. A review of homogenization and topology optimization I - homogenization theory for media with periodic structure, Computers and Structures, 1998, 69(6): 707-718
[13] B. Hassani, E. Hinton. A review of homogenization and topology opimization II - analytical and numerical solution of homogenization equations, Computers and Structures, 1998, 69(6): 719-738
[14] B. Hassani, E. Hinton. A review of homogenization and topology optimization III - topology optimization using optimality criteria, Computers and Structures, 1998, 69(6): 739-756
[15] L. Ambrosio, G.. Buttazzo, An optimal design problem with perimeter penalization, Calculus of Variations and Partial Differential Equations, 1993, 1(1): 55-69
[16] C.S. Jog, R.B. Haber. Stability of finite element models for distributed-parameter optimization and topology design, Computer Methods in Applied Mechanics and Engineering, 1996, 130 (3-4): 203-226
[17] J. Petersson, O. Sigmund. Slope constrained topology optimization, International Journal For Numerical Methods In Engineering, 1998, 41 (8): 1417-1434,
[18] M. Zhou, Y. K. Shyy, H. L. Thomas. Checkerboard and minimum member size control in topologyoptimization, Structural and Multidisciplinary Optimization, 2001, 21(2): 152-158
[19] Gang-Won Jang, Sangkeun Lee, Yoon-Young Kim, Dongwoo Sheen. Topology optimization using non-conforming finite elements: three-dimensional case, International Journal for Numerical Methods in Engineering, 2005, 63(6): 859 - 875
[20] 刘震宇, 王晓明, 郭东明. 利用窗函数解决连续体结构拓扑优化中的棋盘格式问题, 中国机械工程, 2000, 11(6): 704-707
[21] O. Sigmund, J. Petersson. Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization, 1998, 16(1): 68-75
[22] G.L.N. Rozvany. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics, Structural and Multidisciplinary Optimization, 2001, 21(2): 90-108
[23] 樊学军. 均匀化理论及其在生物力学中的应用, 力学进展, 1996, 26(2): 187-197
[24] C.C. Swan, I. Kosaka. Homogenization-based analysis and design of composites, Computers and Structures, 1997, 64(1-4): 603-621
[25] S. Nishiwaki, M.I. Frecker, S. Min, N. Kikuchi, Topology optimization of compliant mechanisms using the homogenization method, International Journal for Numerical Methods In Engineering, 1998, 42(3): 535-559
[26] 王晓明, 刘震宇, 郭东明. 基于均匀化理论的微小型柔性结构拓扑优化的敏度分析, 中国机械工程, 1999, 10(11): 1264-1267
[27] 张荭蔚, 顾力强. 基于有限元分析技术的大客车车门结构拓扑优化设计研究, 机械设计与研究, 2002,18(5): 46-48
[28] 夏利娟, 吴嘉蒙, 金咸定. 工程结构的拓扑优化设计研究, 船舶力学, 2002, 6(6): 107-113
[29] M.P. Bendsoe, O. Sigmund, Material interpolations in topology optimization, Archive of Applied Mechanics, 1999, 69(9-10): 635-654
[30] 袁振, 吴长春, 庄守兵. 基于杂交元和变密度法的连续体结构拓扑优化设计, 中国科学技术大学学报, 2001, 31(6): 695-699
[31] 左孔天, 陈立平, 王书亭, 等. 用拓扑优化方法进行微型柔性机构的设计研究, 中国机械工程, 2004, 15(21): 1886-1890
[32] Y.M. Xie, G.P. Steven. Simple evolutionary procedure for structural optimization, Computers and Structures, 1993, 49(5): 885-896
[33] O.M. Querin, G.P. Steven, Y.M. Xie. Evolutionary structural optimization (ESO) using a bi-directional algorithm, Engineering Computation, 1998, 15(8): 1031-1048
[34] O.M. Querin, G.P. Steven, Y.M. Xie. Evolutionary structural optimization using an additive algorithm, Finite Elements in Analysis and Design, 2000, 34(3-4): 291-308
[35] Pasi Tanskanen. The evolutionary structural optimization method: theoretical aspects, Computer Methods in Applied Mechanics and Engineering, 2002, 191(47-48): 5485-5498
[36] M. Zhou, G.L.N. Rozvany. On the validity of ESO type methods in topology optimization, Structural andMultidisciplinary Optimization, 2001, 21 (1): 80-83
[37] G.L.N. Rozvany. Stress ratio and compliance based methods in topology optimization - a critical review, Structural and Multidisciplinary Optimization, 2001, 21 (1): 109-119
[38] C.D. Nha, Y. M. Xie, G. P. Steven. An evolutionary structural optimization method for sizing problems with discrete design variables, Computers and Structures, 1998, 68(4): 419-431
[39] G.P. Steven, O.M. Querin, Y.M. Xie. Evolutionary structural optimisation (ESO) for combined topology and size optimisation of discrete structures, Computer Methods in Applied Mechanics and Engineering, 2000, 188(4): 743-754
[40] Q. Li, G.P. Steven, O.M. Querin, Y. M. Xie. Shape and topology design for heat conduction by Evolutionary Structural Optimization, International Journal of Heat and Mass Transfer, 1999, 42(17): 3361-3371
[41] Y.M. Xie, G.P. Steven. Evolutionary structural optimization for dynamic problems, Computers and Structures, 1996, 58(6): 1067-1073
[42] H. Kim, O.M. Querin, G.P. Steven, Y.M. Xie. Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh, Structural and Multidisciplinary Optimization, 2003, 24(6): 441-448
[43] 王小平, 曹立明. 遗传算法-理论、应用与软件实现, 西安交通大学出版社, 2002 年 1 月第 1 版
[44] 唐文艳, 顾元宪. 遗传算法在结构优化中的研究进展, 力学进展, 2002, 32(1): 26-40
[45] 张思才, 张方晓. 自适应遗传算法在桁架结构优化设计中的应用, 湘潭大学自然科学学报, 2002, 24(4): 37-41
[46] 朱峰. 遗传算法在离散变量结构优化中的应用及其改进方案综述, 世界地震工程, 2002, 18(4): 131-135
[47] 罗志凡, 荣见华, 杜海珍. 基于遗传算法和梯度算法的一种结构优化混合方法, 计算机工程与应用, 2003, (8): 71-73
[48] N.D. Lagaros, M. Papadrakakis, G. Kokossalakis. Structural optimization using evolutionary algorithms, Computers and Structures, 2002, 80(7-8): 571-589
[49] 张明辉, 王尚锦. 遗传算法在结构形状优化中的应用, 机械科学与技术, 2001, 20(6): 824-827
[50] 佟维. 利用遗传算法的结构优化设计, 大连铁道学院学报, 2000, 21(2): 7-12
[51] H. Kawamura, H. Ohmori, N. Kito. Truss topology optimization by a modified genetic algorithm, Structural and Multidisciplinary Optimization, 2002, 23(6): 467-472
[52] F. Cappello, A. Mancuso. A genetic algorithm for combined topology and shape optimizations, Computer-Aided Design, 2003, 35(8): 761-769
[53] C.D. Chapman, K. Saitou, M.J. Jakiela. Genetic algorithms as an approach to configuration and topology design, American Society of Mechanical Engineers - Design Engineering Division (Publication) DE, 1993, 65(pt 1): 485-498
[54] M.J. Jakiela, C. Chapman, J. Duda, et al. Continuum structural topology design with genetic algorithms, Computer Methods in Applied Mechanics and Engineering, 2000, 186(2-4): 339-356
[55] Roman Gatzi, Marion Uebersax, Oliver Konig, Strucctural optimization tool using genetic algorithms and ANSYS, CAD-FEM User’s Meeting, Schweiz, 2000:1-9
[56] Ting-Yu Chen, Chia-Yang Lin. Determination of optimum design spaces for topology optimization, Finite Elements in Analysis and Design, 2000, 36(1): 1-16
[57] 夏利民, 谷士文, 沈新权. 基于水平集的 3D 动画, 计算机研究与发展, 2002,39(2): 236-241
[58] 夏利民, 谷士文, 沈新权, 孙星明. 基于水平集模型的 3D 表面重建, 小型计算机系统, 2002, 22(12): 1445-1448
[59] 王峥, 杨新, 李俊, 施鹏飞. 提高水平集方法初始化计算速度的研究, 信号处理, 2002, 18(2): 97-101
[60] 王峥, 杨新, 李俊, 施鹏飞. 水平集方法中曲线跟踪算法的改进, 上海交通大学学报, 2002, 36(12): 1833-1836
[61] 高鑫, 刘来福. 基于水平集曲率的图像滤噪与增强, 北京师范大学学报(自然科学版), 2001, 37(1): 5-9
[62] M.Y. Wang, X. Wang, D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 2003, 192(1-2): 227-246
[63] M.Y. Wang, X. Wang, D. Guo. Structural shape and topology optimization in a level set based implicit moving boundary framework, Structural and Multidisciplinary Optimization, 2004, 27(1-2): 1-19
[64] J.A. Sethian, A. Wiegmann. Structural boundary design via level set and immersed interface methods, Journal of Computational Physics, 2000, 163(2): 489-528
[65] Gregoire Allaire, Francois Jouve, Anca-Maria Toader. A level-set method for shape optimization (Une méthode de lignes de niveaux pour l'optimisation de forme), Comptes Rendus Mathematique, 2002, 334(12): 1125-1130
[66] J.A. Sethian. Evolution, implementation and application of level set and fast marching methods for advancing fronts, Journal of Computational Physics, 2001, 169(2): 503-555
[67] Stanley Osher, Ronald P. Fedkiw. Level set methods: an overview and some recent results, Journal of Computational Physics, 2001, 169(2): 463-502
[68] D. Adalsteinsson, J.A. Sethian. A level set approach to a unified model for etching, deposition, and lithography I: Algorithms and two-dimensional simulations, Journal of Computational Physics, 1995, 120(1): 128-144
[69] D. Adalsteinsson, J.A. Sethian, A level set approach to a unified model for etching, deposition, and lithography II: Three-dimensional simulations, Journal of Computational Physics, 1995, 122(2): 348-366
[70] D. Adalsteinsson, J.A. Sethian, A level set approach to a unified model for etching, deposition and lithography III: Redeposition, remission, surface diffusion and complex simulations, Journal of Computational Physics, 1997, 138(1): 193-223
[71] S. Wolfram. Universality and Complexity in Cellular Automata, Physica D: Nonlinear Phenomena, 1983, 10(1-2): 1-35
[72] Brian Tatting, Zafer G?rdal. Cellular Automata for design of two-dimensional continuum structures, Proceedings of 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis andOptimization, 2000: AIAA-2000-4832
[73] Zafer G?rdal, Tatting Brian. Cellular automata for design of truss structures with linear and nonlinear response, 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference and Exhibit, 2000: AIAA 2000-1580
[74] R. Zakhama, M.M. Abdalla, H. Smaoui, Z. G?rdal. Topology design of geometrically nonlinear 2D elastic continua using CA and an equivalent truss model, Collection of Technical Papers - 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2006: 804-813
[75] Douglas J. Slotta. Structural design using cellular automata, Master Degree Thesis, Virginia Polytechnic Institute and State University, 2001
[76] E. Kita, T. Toyoda. Structural design using cellular Automata. Structural and Multidisciplinary Optimization, 2000, 19(1): 64-73
[77] O.E. Canyurt, P. Hajela. A cellular framework for structural analysis and optimization, Computer Methods in Applied Mechanics and Engineering, 2005, 194(30-33): 3516-3534
[78] S. Setoodeh, Z. G?rdal, L.T. Watson. Design of variable-stiffness composite layers using cellular automata, Computer Methods in Applied Mechanics and Engineering, 2006,195 (9-12): 836-851
[79] S. Missoum, Z. Gürdal, S. Setoodeh. Study of a new local update scheme for cellular automata in structural design, Structural and Multidisciplinary Optimization, 2004, 29 (2): 103-112
[80] S. Setoodeh,; M.M. Abdalla, Z. G?rdal. Combined Topology and fiber path design of composite layers using cellular automata, Structural and Multidisciplinary Optimization, 2005, 30 (6): 413-421
[81] M.M. Abdalla, Z. G?rdal. Structural design using Cellular Automata for eigenvalue problems, Structural and Multidisciplinary Optimization, 2004, 26 (3-4): 200-208
[82] N.M. Patel, J.E. Renaud, H. Agarwal, A. Tovar. Reliability based topology optimization using the hybrid cellular automaton method. 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2005: 4125-4137
[83] N.M. Patel, J.E.Renaud, A.Tovar. Compliant mechanism design using the hybrid cellular automaton method, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2005: 5893-5904
[84] A. Tovar, W.I. Quevedo, N.M. Patel, J.E. Renaud. Hybrid cellular automata with local control rules: a new approach to topology optimization inspired by bone functional adaptation, 6th World Congresses of Structural and Multidisciplinary Optimization, 2005: 1-11
[85] A. Tovar, G.L. Niebur, M. Sen, et al. Bone structure adaptation as a cellular automaton optimization process, Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2004: 4242-4255
[86] A. Tovar. Bone remodeling as a hybrid cellular automaton optimization process, Ph.D. Degree Thesis, University of Notre Dame, 2004
[87] A. Tovar, N.M. Patel, G.L. Niebur, et al. Topology optimization using a Hybrid Cellular Automatonmethod with local control rules, Journal of Mechanical Design, 2006, 128(6): 1205-1216
[88] Thomas R. Hartka. Cellular automata for structural optimization on recongfigurable computers, Master Degree Thesis, Virginia Polytechnic Institute, 2004
[89] 沈成武, 戴诗亮, 杨吉新, 唐小兵. 平面弹性力学中的细胞自动机方法, 清华大学学报(自然科学版), 2001, 41(11): 35-38
[90] 沈成武, 唐小兵, 杨吉新. 平面桁架力学分析的细胞自动机方法初探, 武汉交通科技大学学报, 2000, 24(2): 105-108
[91] 杨吉新, 沈成武, 唐小兵. 细胞自动机方法解最小挠度薄板弯曲问题, 力学季刊, 2002, 23(2): 260-264
[92] 郑波尽, 李元香, 吴漫川. 细胞自动机函数优化算法, 计算机工程, 2003, 29(19): 66-67
[93] P. Hajela, B. Kim, On the use of energy minimization for CA based analysis in elasticity, Structural and Multidisciplinary Optimization, 2001, 23(1): 24-33
[94] 薛文胜. 浅析几种新型陀螺的发展动态, 电子科技大学学报, 1995, 24(5): 485-489
[95] C. Song, B. Ha, S. Lee. Micromachined inertial sensors, IEEE International Conference on Intelligent Robots and Systems, Korea, 1999: 1049-1056
[96] 茅盘松. 硅微型振动陀螺的设计, 传感器技术, 1995, (5): 29-31
[97] N. Yazdi, F. Ayazi, K. Najafi. Micromachined inertial sensors, Proceedings of the IEEE, 1998, 86, 1640-1659
[98] 李新刚, 袁建平. 微机械陀螺的发展现状, 力学进展, 2003, 33(3): 289-301
[99] 谷庆红. 微机械陀螺仪的研制现状, 中国惯性技术学报, 2003, 11(5): 67-72
[100] B. Boxenhorn, P. Greiff. A vibratory micromechanical gyroscope, AIAA Guidance and Control Conference, USA, 1988: 1033-1040
[101] J. Bernstein, S. Cho, A. T. King, A. Kourepenis, et al. A micromachined comb-drive tuning fork rate gyroscope, IEEE Micro Electro Mechanical Systems Workshop (MEMS’93), Fort Lauderdale, 1993: 143-148
[102] M. Weinberg, J. Bernstein, S. Cho, et al. A micromachined comb-drive tuning fork gyroscope for commercial applications, Proceedings of Sensor Exposition, USA, 1994: 187-193
[103] Y. Mochida, M. Tamura, K. Ohwada. A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes, Sensors and Actuators A, 2000, 80(2): 170-178
[104] W. Geiger, W. U. Butt, A. Gaiber, et al. Decoupled microgyros and the design principle DAVED, Sensors and Actuators, 2002, 95(2-3): 239-249
[105] 姜涛. 考虑加工误差的微机械陀螺随机性能分析及健壮性设计, 博士学位论文, 上海交通大学, 2006
[106] http://www.analog.com/zh/prod/0,2877,ADXRS150,00.html
[107] 禹奇才, 张亚芳, 刘锋. 工程力学(理论力学部分), 华南理工大学出版社, 2002
[108] 陈雪萌. 一种压阻式微机械陀螺的研究, 博士学位论文, 中国科学院上海微系统与信息技术研究所, 2005
[109] 李伟剑. 微机电系统的多域耦合分析与多学科设计优化, 博士学位论文, 西北工业大学, 2004
[110] 陈永, 基于滑膜阻尼效应的音叉式微机械陀螺研究, 博士学位论文, 中国科学院上海微系统与信息技术研究所, 2004
[111] M. Yachi, H. Ishikawa, Y. Satoh. Support structure for LiTaO3 crystal tuning fork vibratory gyroscope, 1997 IEEE Ultrasonics Symposium, 1997: 811-814
[112] Z.C. Feng, Kapil Gore. Dynamic characteristics of vibratory gyroscopes, IEEE Sensors Journal, 2004, 4(1): 80-84
[113] Aiwu Ruan, Man Siu Tse, Gang Yih Chong. Simulation and optimization of a micromachined gyroscope using high-aspect-ratio micromachining fabrication process, Proceedings of SPIE, 2001, 4593: 176-185
[114] Cenk Acar, Andrei M. Shkel. An approach for increasing drive-mode bandwidth of mems vibratory gyroscopes, Journal of Microelectromechanical Systems, 2005, 14 (3): 520-528
[115] A. Kugi, D. Thull, H. Seidel. Modelling and optimization of a silicon tuning fork gyroscope. Proceedings in Applied Mathematics and Mechanics, 2004: 59-62
[116] Y. Chen, J. Jiao, B. Xiong. A novel tuning fork gyroscope with high Q-factors working at atmospheric pressure, Microsystem Technologies, 2005, 11 (2-3): 111-116
[117] 陈永, 焦继伟, 熊斌, 等. 一种基于滑膜阻尼效应的新型微机械陀螺, 中国机械工程, 2004, 15(2): 103-106
[118] 陈永, 焦继伟, 王惠泉, 等. 大气下工作的微机械陀螺的设计及其噪声特性, 半导体学报, 2005, 26(1): 148-151
[119] Tao Jiang, Anlin Wang, Jiwei Jiao, Guangjun Liu. Detection capacitance analysis method for tuning fork micromachined gyroscope based on elastic body model, Sensors and Actuators A, 2006, 128(1): 52-59
[120] 姜涛, 王安麟, 刘广军, 等. 基于摄动法的微机械陀螺随机性能的统计分析, 上海交通大学学报, 2006, 40(11): 1918-1923
[121] 清华大学工程力学系. 机械振动(上册), 机械工业出版社, 1978
[122] 姜涛, 王安麟, 刘广军, 等. 音叉振动式微机械陀螺输出电容的统计特性分析, 机械工程学报, 2007, 43(8): 114-118
[123] 傅志方. 振动模态分析与参数识辨, 机械工业出版社, 1990
[124] 殷学纲, 陈淮, 蹇开林. 结构振动分析的子结构方法, 中国铁道出版社, 1991
[125] K. Sadek, W. Moussa. Application of adaptive multilevel substructuring technique to model CMOS micromachined thermistor gas sensor, Part (I): a feasibility study, Proceedings of the International Conference on MEMS, NANO and Smart Systems (ICMENS’03), 2003: 382-389
[126] D. Ostergaard, M.Gyimesi, Finite element based reduced order modeling of micro electro mechanical systems (MEMS). International Conference on Modeling and Simulation of Microsystems, 2000: 684-687
[127] G. Wachutka. Coupled-field modeling of microdevices and microsystems, International Conference on Simulation of Semiconductor Processes and Devices, 2002: 9-14
[128] S.F. Bart, S. Zhang, V.L. Rabinovich, et al. Coupled package-device modeling for microelectromechanicalsystems, Microelectronics Reliability 1999, 40 (7): 1235-1241
[129] L. Yin, G.K. Ananthasuresh. A novel topology design scheme for the multi-physics problems of electro-thermally actuated compliant micromechanisms. Sensors and Actuators A, 2002, 97-98: 599-609
[130] 苑伟政, 李伟剑. 基于遗传算法的微机械陀螺的多学科设计优化, 机械强度, 2004, 26(2): 170-174
[131] 苑伟政, 吕湘连, 李伟剑. 基于集总参数宏模型的微机械陀螺多域耦合分析, 中国机械工程, 2006, 17(4): 401-405
[132] D. DeVoe. Thermal issues in MEMS and microscale systems, IEEE Transactions on Components and Packaging Technologies, 2003, 25(4): 576-583
[133] K. Shcheglov, C. Evans, R. Gutierrez, T.K. Tang. Temperature dependent characteristics of the JPL silicon MEMS gyroscope. IEEE, Aerospace Conference Proceedings, 2000: 403-411
[134] R.P. Leland. Mechanical-Thermal Noise in MEMS Gyroscopes, IEEE Sensors Journal, 2005, 5(3): 793-500
[135] C.C. Painter, A.M. Shkel. Structural and thermal modeling of a z-axis rate integrating gyroscope, Journal of Micromechanics and Microengineering 2003, 13(2): 229-237
[136] Y.J. Yang, K.Y. Shen. Nonlinear heat-transfer macromodeling for MEMS thermal devices, Journal of Micromechanics and Microengineering, 2005, 15 (2): 408-418
[137] M. Allen, M. Raulli, K. Maute, D.M. Frangopol. Reliability-based analysis and design optimization of electrostatically actuated MEMS, Computers and Structures, 2004, 82(13-14): 1007-1020
[138] 裘安萍, 苏岩, 王寿荣, 周百令. 残余应力对 z 轴硅微机械振动陀螺仪性能的影响, 机械工程学报, 2005, 41(6): 228-232
[139] Jeong Sam Han, Byung Man Kwak. Robust optimal design of a vibratory microgyroscope considering fabrication errors, Journal of Micromechanics And Microengineering, 2001, 11 (6): 662-671
[140] Andojo Ongkodjojo, Francis E H Tay. Global optimization and design for microelectromechanical systems devices based on simulated annealing, Journal of Micromechanics and Microengineering, 2002, 12 (6): 878-897
[141] Noboru Wakatuki, Subaru Kudo, Yutaka Satoh, Hiroshi Tanaka. A new approach to piezoelectric crystal gyroscopes for higher sensitivity, 1998 IEEE Ultrasonics Symposium, 1998: 477-480
[142] Junhua Wei, Anlin Wang, Nianci Du. Study of self-organizing control of traffic signals in an urban network based on Cellular Automata. IEEE Transactions on Vehicular Technology, 2005, 54 (2): 744-748
[143] S. Takesue. Boltzmann-type equations for elementary reversible cellular automata, Physica D: Nonlinear Phenomena, 1997, 103(1-4): 190-200
[144] 祝玉学, 赵学龙. 物理系统的元胞自动机模拟, 清华大学出版社, 2003
[145] 魏俊华. 城市交通信号自组织控制方法的研究, 博士学位论文, 上海交通大学, 2005
[146] S. Wolfram. Theory and applications of Cellular Automata, World Scientific, Singapore, 1996
[147] David Alonso. Ricard V. Solé, The DivGame simulator: a stochastic cellular automata model of rainforest dynamics, Ecological Modelling, 2000, 133(1-2): 131-141
[148] D. D'Ambrosio, Gregorio S. Di, S. Gabriele, et al. A Cellular Automata model for soil erosion by water,Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere, 2001, 26(1):33-39
[149] Karafyllidis Ioannis, Thanailakis Adonios. A model for predicting forest fire spreading using cellular automata, Ecological Modelling, 1997, 99(1): 87-97
[150] Gregorio S. Di, R. Serra, M. Villani. Applying Cellular Automata to complex environmental problems: The simulation of the bioremediation of contaminated soils, Theoretical Computer Science, 1999, 217(1): 131-156
[151] X. Tong, C. Beckermann, A. Karma, et al. Phase field simulation of dendritic crystal growth in a forced flow, Physical Review E, 2001, 63(1): 1-16
[152] Jr. Spillman, B. William. Evolutionary computational techniques for complex adaptive structures, Proceedings of SPIE, 2001, 4512: 163-171
[153] 贾海朋. 结构与柔性机构拓扑优化, 博士学位论文, 大连理工大学, 2004
[154] O. Sigmund. Design of multiphysics actuators using topology optimization - Part I: One-material structures, Computer Methods in Applied Mechanics and Engineering, 2001, 190 (49-50): 6577-6604
[155] O. Sigmund. Design of multiphysics actuators using topology optimization - Part I: Two-material structures, Computer Methods in Applied Mechanics and Engineering, 2001, 190 (49-50): 6605-6627
[156] M.M. Neves, O. Sigmund, M.P. Bends?e. Topology optimization of periodic microstructures with a penalization of highly localized buckling modes, International Journal for Numerical Methods in Engineering, 2002, 54 (6): 809-834
[157] 姜涛, 朱灯林, 王安麟, 王石刚. 整合规则下的结构拓扑自组织进化设计, 机械科学与技术, 2005, 24(8): 943-946
[158] JongBok Jang, Anlin Wang, Guangjun Liu, Analysis for performance of a vibratory micromachined gyroscope based on mode-acceleration method, International Technology and Innovation Conference, China, 2006: 634-639
[159] 张美艳, 王丽炜, 陈力奋. 非亏损对称系统的子结构灵敏度综合方法, 振动与冲击, 2004, 23(1): 65-69
[160] Y. Mochida, M. Tamura, K. Ohwada. Micromachined vibrating rate gyroscope with independent beams for the drive and detection modes, Sensors and Actuators A, 2000, 80 (2): 170-178
[161] H. Yang, M. Bao, H. Yin, S. Shen. A novel bulk micromachined gyroscope based on a rectangular beam-mass structure, Sensors and Actuators A, 2002, 96 (2-3): 145-151
[162] 张正福, 音叉振动式微机械陀螺结构动态性能解析与健壮性设计, 博士学位论文, 上海交通大学, 2007
[163] 王振宇, 成立, 祝俊. 微/纳米级微电子机械系统制造新技术, 半导体技术, 2005, 30(8): 27-33
[164] 关荣锋. MEMS 器件设计、封装工艺及应用研究, 博士学位论文, 华中科技大学, 2005
[165] 邓宏论. 微硅加速度计中静电键合封接技术的应用, 电子机械工程, 2005, 21(3): 40-41
[166] G. Wallis, D. I. Pomerantz. Field assisted glass-metal sealing. Journal of Applied Physics, 1969, 40(10): 3946-3969
[167] Huikai Xie, Gary K. Fedder. Fabrication, characterization, and analysis of a DRIE CMOS-MEMSgyroscope, IEEE Sensors Journal, 2003, 3(5): 622-631
[168] 董涛, 章维一, 侯丽雅. 微系统制造中的 3 维微成形技术, 南京理工大学学报, 2001, 25(3): 318-322
[169] Bin Xiong, Lufeng Che, Yuelin Wang. A novel bulk micromachined gyroscope with slots structure working at atmosphere, Sensors and Actuators A, 2003, 107(2): 137-145
[170] 陈一梅, 黄元庆. MEMS 封装技术, 传感器技术, 2005, 24(3): 7-9
[171] Yufeng Zhang, Xiaoyun Tan, Weiping Chen, et al. Study of MEMS packaging technology, The 6th International Conference on Electronic Packaging Technology, 2005: 643-646
[172] X. Zhang, S.B. Park, R. Navarro, M.W. Judy. Accurate assessment of packaging stress effects on MEMS devices, The Tenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems (ITHERM '06), 2006: 1336-1342
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