Microsystem Technologies

, Volume 24, Issue 7, pp 3149–3160 | Cite as

Theoretical modal analysis and parameter study of Z-shaped electrothermal microactuators

  • Zhuo Zhang
  • Yueqing Yu
  • Xuping Zhang
Technical Paper


This paper presents a comprehensive modal analysis of Z-shaped beam electrothermal microactuators for the first time. Both longitudinal and lateral vibrations are taken into account to obtain the vibration equations of the unique geometric feature: a Z-shaped beam with a shuttle in the middle. The natural frequencies and the associated mode shapes of the Z-shaped beams are calculated based on the vibration equations subjected to both boundary and continuity conditions. Finite element simulations are performed using ANSYS software to verify the analytically calculated natural frequencies and mode shapes of the Z-shaped beams. Based on the modal analysis, this paper also investigates the relationship between the natural frequencies and volume scale of the Z-shaped beam electrothermal microactuators. In addition, comprehensive parameter analysis is conducted to provide insights and guidance on designing and optimization of the Z-shaped beam electrothermal microactuators.



This work was supported by National Natural Science Foundation of China (No. 51575006).


  1. Ali A, Azim RA, Khan US, Syed AA, lzhar U (2012) Design, simulation and optimization of electrothermal micro actuator. Appl Mech Mater 229–231:1939–1943CrossRefGoogle Scholar
  2. Baracu A, Voicu R, Muller R, Avram A, Pustan M, Chiorean R, Birleanu C, Dudescu C (2014) Design and fabrication of a MEMS chevron-type thermal actuator. In: International conferences and exhibition on nanotechnologies and organic electronics, Thessaloniki, GreeceGoogle Scholar
  3. Burnie M (2010) Modal analysis of MEMS gyroscopic sensors. Master, Queen’s University, Kingston, Ontario, CanadaGoogle Scholar
  4. Chen W, Huang S (2009) Design and fabrication of topologically optimal miniature microgripper integrated with an electro-thermal microactuator. J Eng Tech Edu 6(2):166–181Google Scholar
  5. Chen W, Yeh P, Hu C, Fang W (2008) Design and characterization of single-layer step-bridge structure for out-of-plane thermal actuator. Microelectromech Syst 17:70–77CrossRefGoogle Scholar
  6. Chu J, Zhang R, Chen Z (2011) A novel SU-8 electrothermal microgripper based on the type synthesis of the kinematic chain method and the stiffness matrix method. J Micromech Microeng 21:054030CrossRefGoogle Scholar
  7. Enikov ET, Kedar SS, Lazarov KV (2005) Analytical model for analysis and design of V-shaped thermal microactuator. J Microelectromech Syst 14(4):788–798CrossRefGoogle Scholar
  8. Fowler A, Rakotondrabe M, Moheimani S (2013) Closed-loop control of a novel 2-DOF MEMS nanopositioner with electrothermal actuation. In: The sixth IFAC symposium on mechatronic systems, Hangzhou, ChinaGoogle Scholar
  9. Guan C, Zhu Y (2010) An electrothermal microactuator with Z-shaped beams. J Micromech Microeng 20:085014CrossRefGoogle Scholar
  10. Gupta S, Pahwa T, Narwal R, Prasad B, Kumar D (2012) Optimizing the performance of MEMS electrostatic comb drive actuator with different flexure springs. In: Proceedings of the 2012 COMSOL conference, Bangalore, IndiaGoogle Scholar
  11. Hussein H, Tahhan A, Moal PL, Bourbon G, Haddab Y, Lutz P (2016) Dynamic electro-thermo-mechanical modelling of a U-shaped electro-thermal actuator. J. Micromech. Microeng. 26:025010CrossRefGoogle Scholar
  12. Kim Y-S, Dagalakis NG, Gupta SK (2014) Design of MEMS based three-axis motion stage by incorporating a nested structure. J Micromech Microeng 24:075009CrossRefGoogle Scholar
  13. Kumar V, Sharma NN (2014) Design and validation of silicon-on-insulator based U shaped thermal microactuator. Int J Mater Mech Manuf 2(1):86–91MathSciNetGoogle Scholar
  14. Kwan AMH, Song S, Lu X, Lu L, Teh Y, Teh Y, Chong EWC, Gao Y, Hau W, Zeng F, Wong M, Huang C, Taniyama A, Makino Y, Nishino S, Tsuchiya T, Tabata O (2012) Improved designs for an electrothermal in-plane microactuator. J Microelectromech Syst 21(3):586–595CrossRefGoogle Scholar
  15. Li L, Uttamchandani D (2009) Dynamic response modelling and characterization of a vertical electrothermal actuator. J Micromech Microeng 19:075014CrossRefGoogle Scholar
  16. Li X, Lang L, Liu J, Xia Y, Yin L, Hu J B, Fang D, Zhang H (2010) Electro-thermally actuated RF MEMS switch for wireless communication. In: Proceedings of the 2010 5th IEEE international conference on nano/micro engineered and molecular systems, Xiamen, ChinaGoogle Scholar
  17. Mayyas M (2012) Comprehensive thermal modeling of electrothermoelastic microstructures. Actuators 1:21–35CrossRefGoogle Scholar
  18. Merced E, Tan X, Sepulveda N (2014) Closed-loop tracking of large displacements in electro-thermally actuated VO2-based MEMS. J Microelectromech Syst 23(5):1073–1083CrossRefGoogle Scholar
  19. Molhave K, Hansen O (2005) Electro-thermally actuated microgrippers with integrated force-feedback. J Micromech Microeng 15:1265–1270CrossRefGoogle Scholar
  20. Moussa REK, Grossard M, Mehdi B, Arnaud H, Chaillet N (2014) Modeling and control of a piezoelectric microactuator with proprioceptive sensing capabilities. Measurement 24(6):590–604Google Scholar
  21. Ouyang J, McDonald M, Zhu Y (2013) Temperature-dependent material properties of Z-shaped MEMS thermal actuators made of single crystalline silicon. J Micromech. Microeng 23:125036CrossRefGoogle Scholar
  22. Pawinanto R E, Yunas J, Majlis B Y, Hamzah A A (2013) Finite element analysis on magnetic force generation of electromagnetic microactuator for micropump. In: 2013 IEEE regional symposium on micro and nanoelectronics, Langkawi, MalaysiaGoogle Scholar
  23. Sahu B, Taylor CR, Leang KK (2010) Emerging challenges of microactuators for nanoscale positioning, assembly, and manipulation. J Manuf Sci Eng 132:030917CrossRefGoogle Scholar
  24. Soma A, Iamoni S, Voicu R, Muller R (2014) Design and building-up of an electro-thermally actuated cell microgripper. In: Proceedings of the 2014 international conference on theoretical mechanics and applied mechanics & proceedings of the 2014 international conference on mechanical engineering, Venice, ItalyGoogle Scholar
  25. Stokey W F (2002) Vibration of systems having distributed mass and elasticity. In: Harris’ shock and vibration handbook, 5th ed. McGraw-Hill, New YorkGoogle Scholar
  26. Venditti R, Lee JSH, Sun Y, Li D (2006) An in-plane, bi-directional electrothermal MEMS actuator. J Micromech Microeng 16:2067–2070CrossRefGoogle Scholar
  27. Vij R, Singh B, Jain DK (2014) Design and analysis of electro thermally actuated microgripper. IOSR J VLSI Signal Process 4(4):46–51CrossRefGoogle Scholar
  28. Wu C, Hsu W (2006) Design and fabrication of an electrothermal microactuator for multi-level conveying. Microsyst Technol 12:293–298CrossRefGoogle Scholar
  29. Yan D, Khajepour A, Mansour R (2004) Design and modeling of a MEMS bidirectional vertical thermal actuator. J Micromech Microeng 14:841–850CrossRefGoogle Scholar
  30. Zhang Z, Yu Y, Liu X, Zhang X (2015) A Comparison model of V- and Z-shaped electrothermal microactuators. In: Proceedings of 2015 IEEE international conference on mechatronics and automation, Beijing, ChinaGoogle Scholar
  31. Zhang Z, Zhang W, Wu Q, Yu Y, Liu X, Zhang X (2015) A comprehensive analytical model and experimental validation of Z-shaped electrothermal microactuators. In: The 3rd IFToMM symposium on mechanism design for robotics, Aalborg, DenmarkGoogle Scholar
  32. Zhang Z, Yu Y, Liu X, Zhang X (2016) Dynamic electro-thermal modeling of V- and Z-shaped electrothermal microactuator. In: Proceedings of 2016 IEEE international conference on mechatronics and automation, Harbin, ChinaGoogle Scholar
  33. Zhang Z, Yu Y, Liu X, Zhang X (2017a) Dynamic modelling and analysis of V- and Z-shaped electrothermal microactuators. Microsyst Technol 23(8):3775–3789CrossRefGoogle Scholar
  34. Zhang Z, Zhang W, Wu Q, Yu Y, Liu X, Zhang X (2017b) Closed-form modelling and design analysis of V- and Z-shaped electrothermal microactuators. Micromech Microeng 27:015023CrossRefGoogle Scholar
  35. Zhu Y, Bazaei A, Moheimani SOR, Yuce MR (2011) Design, modeling and control of a micromachined nanopositioner with integrated electrothermal actuation and sensing. J Microelectromech Syst 20:711–719CrossRefGoogle Scholar
  36. Zhu Y, Moheimani SOR, Yuce MR (2012) Bidirectional electrothermal actuator with Z-shaped beams. Microelectromech Syst 12(7):2508–2509Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijingChina
  2. 2.Department of EngineeringAarhus UniversityAarhusDenmark
  3. 3.Aarhus School of EngineeringAarhus UniversityAarhusDenmark

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