Piezoelectric Materials and Actuators Group, The State Key Lab. of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing, P.R.China Zip: 100084 Tel: +86-10-62784038 (O) Fax: +86-10-62771160 E-mail: email@example.com
Ph.D. (1996～2000): Department of Electromechanical Control and Automation, Faculty of Mechatronic Engineering, Harbin Institute of Technology, China M.S. (1994～1996): Depart. of Electromechanical Control and Automation, Faculty of Mechatronic Engineering, Harbin Institute of Technology, China B.S. (1990～1994): Depart. of Precision Instrumentation, Faculty of Mechatronic Engineering, Harbin Institute of Technology, China
Associate Professor (2003～now): School of Materials Science and Engineering, Tsinghua University, China Assistant Professor (2002～2003): Depart. of Materials Science and Engineering, Tsinghua University, ChinaPostdoctoral fellow (2000～2002): Depart. of Materials Science and Engineering, Tsinghua University, China
IEEE member, 《IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control》Permanent Reviewer, Senior member of the Chinese Mechanical Engineering Society, Senior member of the Chinese Acoustic Society, Senior member of the Chinese Institute of Electronics Reviewer of Journals,《Small & Special Electrical Machines》、《Piezoelectrics & Acoustooptics》、《Journal of Harbin Engineering University》、《Nanotechnology and Precision Engineering》、《Acta Mechanica Sinica》、《Journal of Xi′an Jiaotong University》、《JMST》、《Chinese Journal of Acoustics》
1、Piezoelectric Material and Multilayer Piezoelectric Ceramic（MPC） Co-fired Monolithic MPC and Applications Tape Casting Techniques of Piezoelectric Material Fatigue and Fracture of MPC Structures and Devices Theoretical Research and it’s Application of MPC and PVDF
2、Piezoelectric Devices and Applications Linear or Rotational Motion Piezoelectric Actuators and Ultrasonic Motors Slim Multilayer Piezoelectric Speaker High performance Multilayer Piezoelectric Transformer Micro Piezoelectric Manipulator with a Probe and Nanometer Resolution Monolithic Multilayer Piezoelectric Actuator for the Car Ejector MEMS-based Piezoelectric Micro Pump Piezoelectric Unimorph, Bimorph, Multimorph and Applications Piezoelectric Techniques for Zoom/Focus Mechanism of Cellular Phone Ultra-Small Piezoelectric Precision Positioning System Piezoelectric Micro Motor using MPC and Utra-low Driving Voltage Piezoelectric Active Control Technology of Liquid Deformation and Flow Piezoelectric Sensor and Touch-Screen Techniques
3、Simulation, Optimization and Measurement of Piezoelectric Structures and Devices FEM Analysis Measurement of Vibration and Temperature Acoustic Measurement (SPL,THD,etc) Piezoelectric Speaker Laser Doppler Scanning Technique for Vibration Modal Shapes
1. A Fundamental Research on Some Key Techniques of Ultrasonic Motors
The traveling wave type and standing wave type of ultrasonic motors driven by the frictional mechanism are researched as major objects in this project. The project includes as follows: considering the dynamic models of the ultrasonic motors as electromechanical couple systems, studying some optimal design methods of the structures and optimizing control techniques using multivariable, miniaturizing and integrating of the drivers, as well as developing some new types of ultrasonic motors with the patent rights. The investigative contents of the project comprise also other key techniques: improving efficiency, increasing lifetime, enhancing control accuracy and reducing noise level of the ultrasonic motors. The implementation of the project will provide theoretical and technical foundation for industrialization of the ultrasonic motors in China.
2. Optimization design technology of novel piezoelectric micro motor
As to application and industrialization, we come up against the same problems about the development of the novel micro piezoelectric motor with an outer diameter smaller than 3mm. In this item, a new type of piezoelectric micro motor with a rod-shaped ceramic stator and higher output torque, superior to conventional piezoelectric motors with a film or cylinder stator, has been fabricated. According to the vibration theory and piezoelectricity, vibration model of the prototype motor was measured using scanning laser vibrometer PSV300 and miniature driving circuit with excellent impedance matching was designed. Through laser Doppler technology and FEM, its structure was also optimized. The maximum output torque can reach to 0.4mNm for stainless steel stator and 0.35mNm for copper stator. The preload is about 270mN and the resonant frequency 57 to 62 kHz. This kind of motor may be applied in the fields of military industry, mobile telephone, robots, medical appliances, and aerospace, etc.
3. Two-DOF Precision Piezoelectric Positioning System for Optical Adjustments
A two degree-of-freedom precision positioner driven by two ？15 mm ultrasonic motors, which use wobble vibration modes and four ring-shaped piezoelectric wafers for each one. The ultrasonic motors are mounted on the one side and driven by two AC input voltages with a 90 degree phase shift and around 40 kHz resonant frequency. The other side of the positioner will be tilted by a thrust force of the screws, which are connected to the output axis of the ultrasonic motors. The positioner is capable to produce a small tilting angle resolution, 0.002°, displacement resolution 20 nm and driving force ～1 Kg. This two degree-of-freedom precision positioner can be applied in the fields of optical communication, laser modulation, etc.
4. Special Piezoelectric Actuators with a Mechanical Position Feedback Ultrasonic motors with multi-points mechanical position feedback will be developed in this project. Among them, ？15 mm wobble ultrasonic motors and ？30 mm traveling wave ultrasonic motors are used to drive the fabricated MPF system, which has a fan-shaped movable element, disk-shaped mounted insulation plate with eight metallic points. Ultrasonic motors will stop at each contact point and restart by a high level from control system. The rotation time between two points is about 100 ms for ？15 mm ultrasonic motors and 150 ms for ？30 mm traveling wave ultrasonic motors. The outline of the circuit is about 70 mm ？50 mm and each circuit has two output terminals for two ultrasonic motors. Standard input voltage of the driver is 10～15VDC and input voltage of the motors is about 400Vp-p.
5. High Performance Multilayer Piezoelectric Transformer
Low-firing multiplayer piezoelectric transformer (MPT) was studied in Beijing Tsinghua University in the 1980’s. This kind of MPT has high voltage step-up ratio, low driving voltage and small size. Its voltage step-up ratio is ten times higher than that of conventional Rosen type single layer transformer. Recently, with the increasing requirement of backlight inverters of portable computers and other electronic instruments, the MPT has attracted significant interests. The low-firing MPT and its inverter have many advantages, such as a thin shape, small size, high transfer efficiency, non electromagnetic interference. A new type inverter used for the backlight driving of liquid crystal display in portable computer are being developed and commercialized.
6. Improve Aerodynamic Character of Aerofoil Using Micro-Oscillating Generator
Presently, applications of the piezoelectric microjet can be found in many fields of scientific instruments, industrial control, biomedicine, etc. Based on different injecting medium, there are two kinds of jet systems: piezoelectric liquid-jet and piezoelectric airflow-jet systems. The piezoelectric liquid-jet system has already been applied to the atomizing drug delivery system, biology mass spectrum analysis, jet printer, etc. while piezoelectric airflow jet system has many potential applications in the fields of electronic refrigeration, military industry, gesture rectification of micro/silicon planet, aerodynamic improvement of aerofoil, etc. A piezoelectric jet element with single nozzle is fabricated and measured in our group. Theoretical model of vibrating piezoelectric-metal composite shell used inside the piezoelectric micro airflow jet is established, and resonant frequency equations and vibrating displacement equations with axisymmetric vibration behavior can be obtained. Using energy method the resonant frequency of the vibrating composite structure is resolved. The detailed emulation calculation and experimental test are developed for the practical piezoelectric micro airflow jet. The experimental results of vibration modes, distribution of displacement and velocity are measured by Laser Doppler Vibrometer. The relationship between the vibrating amplitude and driving voltage is established. The geometrical parameter of the piezoelectric ceramic layer is optimized by FEM.
7. Research on diffuser/nozzle-based valve less piezoelectric pump
A simple structured micropump actuated by a piezoelectric ceramic actuator and fabricated with the silicon-based microelectromechanical system (MEMS) process is presented. The piezoelectric actuation has been employed for the deflection of the membranes because of its benefits, such as small size and no EMI in comparison with the other types, especially electromagnetic counterpart and so on. The micropump consists of silicon and glass by means of anodic bonding. The diffusers are used instead of passive check valves. To analyze the principle of the diffuser/nozzle-based valve less piezoelectric pump, and calculated the cone angle and diffusion ratio which have key influences on the pump performance using fluent software. The diffuser/nozzle-based valve less piezoelectric pump using conventional process has been fabricated by a master Miss. Li EZ in my group, see follows. And silicon-based micropump has been investigating by another doctoral candidate Mr. Wang BW in my group.
8. Various piezoelectric actuating elements and structures
Piezoelectric micro-structure (PMS) with a 5×5mm reflected face for a laser beam scanning has been fabricated using a conventional linear cutting process. This device consists of CuSn4-3 substrate, PZT5A piezoelectric bimorph, micro mechanical hinges, and reflected face. It can generate one-dimensional bending vibration modal shapes with various nodal lines, i.e. the 1st, 2nd and 3rd harmonic motion, which has been measured using Laser Scanning Vibrometer (LSV). The reflected face inside the device can be rotated with the dilatation of the piezoelectric bimorph. By means of analysis on slope coefficient of the reflected area, some factors that affect the scanning angle of the reflected face are investigated. The collected experimental data reveal that the maximum scanning angle of this piezoelectric micro structure ranges from -0.25° to +0.25° under an alternating current 5V. Such piezoelectric micro-structure can be optimized and, in the future, applied as an actuating element inside micro systems, laser modulation system, communication system. And the silicon based PMS and its application will be studied in the future.
9. Piezoelectric transducer for distance measurement
For the application of airborne distance sensing, a bimorph flexural structure is usually used. The maximum operation frequency is limited by the attenuation of sound waves in the air, which increases as the operation frequency increases, and is usually below 100 kHz for sensing distances up to 3 m. The operation frequencies also depend on the physical properties of the materials and transducer structure parameters. The ultrasonic performance of such a transducer, such a directivity of their beam and sound pressure at axial direction strongly depends on the vibration profiles of the transducer. A bimorph flexural PUT based on low-sintering piezoelectric ceramics PMN-PNN-PZT, which have high piezoelectric constant (d33>680pC/N), high electromechanical coupling factor (Kp=0.70～0.73), was fabricated.
10. Disk-Pivot Micro Piezoelectric Actuator Using Vibration Mode B11
Micro piezoelectric actuator using vibration mode B11 (Bmn, where m is the number of nodal circles, n is the nodal diameters) is designed. Different from conventional wobble-type ultrasonic motor using piezoelectric rod or cylinder, piezoelectric disc is used to excite wobble modes and metal cylinder stator is used to amplify the transverse displacement, metal rod rotor is actuated to rotate. The outer diameter of the actuator is 14 mm. There are features such as low drive voltage, micromation, and convenient control of wobble state by modifying the structure of stator, etc. Finite Element Analysis (FEA) of the stator has been made. It is found that the resonant frequency of vibration mode B11 is 49.03 kHz, which is measured at 45.7 kHz by the laser vibrometer and impedance analyzer. The rotation speed has been measured, which could be as high as 10071 rpm under an alternating current 100 V. Such piezoelectric actuator can be optimized and adjusted to fit practical conditions. It can be applied in the fields of precise instrument, bioengineering and other micro actuate system. Besides the above, 3 to 4 new types of micro motors with an outer diameter smaller 8mm and co-fired monolithic multilayer piezoelectric ceramic have been designed and studied by one postdoctor and two masters in my group.
11. Ultrasonic Motor with Slots on the Piezoelectric Vibration Converter
A vibration conversion type ultrasonic motor based on semiwave combined rod type piezoelectric vibrator is composed of rotor, stator, pre stretching mechanism and mechanical torque output mechanism. Said stator consists of the upper stator, piezoelectric plate, electrode plate and lower stator. Said rotor consists of friction disk in contact with the top end face of upper stator and a metallic disk adhered onto top surface of said friction disk. Said pre stretching mechanism is composed of rubber washer, spring washer and circular clip. Said mechanical torque output mechanism comprises shaft and upper and lower bearings.
The dynamic behavior of a vibration converter of an ultrasonic motor is described using finite element method. Tetrahedral finite elements with three dimensions are formulated with the effects of piezoelectric coupling. And the solution of the coupled electroelastic equations of dynamic motion is presented. The simulated response of the vibration converter is calculated, and shows excellent consistency with experimental results, which proved that finite element modeling is a good approach to optimize piezoelectric apparatus design. A gradual optimized method is employed to ascertain the most compatible structure.
12. Three-DOF multilayer piezoelectric micromanipulator with a probe
To satisfy the need for semiconductor, biomedicine, nanodevices, etc, micromanipulators have been considered as a key technique, which can manipulate objects in nana-scale. What’s more, they are small in size and can move smartly. The piezoelectric ceramics (PZT) is usually used as materials for micro-actuator, considering its simple structure, small size, lightweight and high resolution. We promote a novel model of 3-DOF multilayer PZT micromanipulator and simulate it with FEA (finite element analysis). States under different applied voltages were discussed, including the motion along axis Z and the rotation along axis X and the bisector between X-Y. After analyzing the distribution of stress, we propose some method, which helps to improve the capability of the micromanipulator. We also do some quantificational analysis about the micromanipulator, discovering that the relationship between the displacements of the probe and applied voltages is perfecting linear. Comparing the constant D defining the relationship of the displacements of the probe and applied voltages, it proves that the simulation is correct. We compare the capability between the single-layer and multi-layer PZT just only to show that the multi-layer PZT can reduce applied voltages producing the same displacement.
13. Vibration mechanism and multilayer structure of piezoelectric devices
The program focuses on the monolithic multilayer piezoelectric actuators and their applications, such as ultrasonic motors, automobile ejectors, etc. The outline of the prototype for automobile ejectors is 10x10x30 mm and ones of other ultrasonic motors are 2x2x3 mm to 5x5x4 mm. The monolithic multilayer structures are manufactured using tape casting technique. The vibration mechanism including vibration modes will be studied using scanning laser vibrometer and Finite Element Method. And the fatigue and other characters will also investigated using experimental and theoretical methods. Because of multilayer piezoelectric ceramic, the working voltage may be reduced from 200V inside previous prototypes to 20V. Only in this way, could transformer inside the circuit power be omitted and circuit outline scaled down. So the applications of piezoelectric actuators and motors could be expanded to more fields.
14. Ultra Slim Speaker (USS) based on Multilayer Piezoelectric Actuator
The thinner structure and lower power consumption are benefit for the customers. The ultra slim speakers studied in my group have such features as follows: ultra slim < 0.5 mm, small number of components, simple design, no magnetic field, lower power consumption. but now there are still challenges, for example, “spiky” frequency response, different application, high capacity load, processing technique, etc. i am supervising a master to overcome these problems and cooperating with some famous companies.
1998 1st Prize of China Instrument and Control Society Scholarship 2004 3rd Grade Awards of Science and Technology in Shaanxi Province of China 2006 New Star in Science and Technology by Beijing Municipal Science and Technology Commission （BEIJING NOVA PROGRAM ） 2006 New Century Excellent Talents in University (NCET) by Ministry of Education of China 2007 3rd Grade Awards of Science and Technology of Chinese Institute of Electronics
Representative Publications (Optional) 1.Xiangcheng Chu, Zuojin Zhong, Cong Zhu, Yanqiang Zhao, and Longtu Li, A novel low-voltage non-resonant piezoelectric linear actuator based on two alternative principles, FERROELECTRICS, 2016, VOL. 505, 147–158 2.Cong Zhu, Xiangcheng Chu, Songmei Yuan, Zuojin Zhong, Yanqiang Zhao, Shuning Gao. Development of an ultrasonic linear motor with ultra-positioning capability and four driving feet, Ultrasonics 72 (2016) 66–72 3.Yanqiang Zhao, Songmei Yuan, Xiangcheng Chu, Shuning Gao, Zuojin Zhong, and Cong Zhu, Ultrasonic micro-motor with multilayer piezoelectric ceramic and chamfered driving tips, REVIEW OF SCIENTIFIC INSTRUMENTS 87, 095108 (2016) 4.Gao, Renlong; Chu, Xiangcheng; Huan, Yu; Zhong, Zuojin; Wang, Xiaohui; Li, Longtu, Ceramic-electrode inter-diffusion of (K, Na)NbO3-based multilayer ceramics with Ag0.7Pd0.3 electrode, Journal of the European Ceramic Society, v 35, n 1, p 389-392, January 1, 2015 5.Gao, Renlong; Chu, Xiangcheng; Huan, Yu; Sun, Yiming; Liu, Jiayi; Wang, Xiaohui; Li, Longtu, A study on (K, Na) NbO3 based multilayer piezoelectric ceramics micro speaker, Smart Materials and Structures, v 23, n 10, October 1, 2014 6.Gao, Ren-Long; Chu, Xiang-Cheng; Huan, Yu; Wang, Xiao-Hui; Li, Long-Tu, Investigation on co-fired multilayer KNN-based lead-free piezoceramics, Physica Status Solidi (A) Applications and Materials Science, v 211, n 10, p 2378-2383, October 2014, EI, SCI 7.Gao, Ren-Long; Chu, Xiang-Cheng; Huan, Yu; Wang, Xiao-Hui; Li, Long-Tu, (K, Na) NbO3 based piezoceramics prepared by a two-step calcining and ball milling route, Materials Letters, v 123, p 242-245, May 15, 2014 8.Chu, Xiangcheng; Wang, Jiawei; Yuan, Songmei; Li, Longtu; Cui, Hongchao, A screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator, Review of Scientific Instruments, v 85, n 6, June 2014 9.Chu, Xiang-Cheng; Xu, Ya-Nan; Li, Long-Tu, Hydrothermal synthesis and effects of pH values on properties of CdWO4 powders, Journal of Materials Science: Materials in Electronics, v 25, n 6, p 2601-2604, June 2014 10.Chu, Xiang-Cheng; Gao, Ren-Long; Huan, Yu; Wang, Xiao-hui; Li, Long-Tu, Effects of the co-addition of Li, Sb, Ta on the phase structure and piezoelectric properties of (Na, K)NbO3 lead free piezoceramics, RARE METAL MATERIALS AND ENGINEERING, v 42 n 1A, p130-134, 2013 11.Chu, Xiang-Cheng; Liu, Jia-Yi; Gao, Ren-Long; Chang, Jie; Li, Long-Tu, Design and analysis of a piezoelectric material based touch screen with additional pressure and its acceleration measurement functions, Smart Materials and Structures, v 22, n 12, December 2013 12.Chu, Xiang-Cheng; Xu, Ya-Nan; Yuan, Song-Mei; Wang, Ling; Liu, Ming; Li, Long-Tu, A novel WIM sensor for highway based on PVDF piezoelectric material, Journal of Vibration, Measurement and Diagnosis, v 33, n 3, p 351-356, June 2013 13.Wang, Lin; Chu, Xiang-Cheng; Liu, Jia-Yi; Li, Long-Tu, Research of the piezoelectric touch panel based on PVDF, RARE METAL MATERIALS AND ENGINEERING, v 42 n 1A, p139-141, 2013 14.Xu, Ya-Nan; Chu, Xiang-Cheng, Piezoceramic stack actuators for micropositioning stage, Key Engineering Materials, v 512-515, p 1337-1341, 2012 15.Chu, Xiangcheng; Ding, Li-Dan; Meng, Xiang-Yu; Li, Long-Tu, Vibration and temperature measuring experiments on multilayer piezoelectric actuator, Advanced Materials Research, v 177, p 306-309, 2011 16.Ding, Li-Dan; Chu, Xiang-Cheng; Li, Long-Tu, Environmental stability of the step-down multilayer piezoelectric transformer, RARE METAL MATERIALS AND ENGINEERING, v 40 n 1, p455-458, 2011 17.Chu, Xiang-Cheng; Chen, Xiang-Yu; Ma, Long; Li, Long-Tu, A miniature high-speed piezoelectric motor with a disk-pivot structure, INTERNATIONAL JOURNAL OF MODERN PHYSICS B, v 24, n 15-16, p2404-2409, JUN 2010 18.Chu, Xiangcheng; Bi, Xiaopeng; Li, Longtu, Relevant basic scientific issues in multi-layer piezoelectric ceramics, Journal of the Chinese Ceramic Society, v 37, n 6, p 1055-1062, June 2009 19.Bi, Xiao-Peng; Chu, Xiang-Cheng; Ji, Ye; Li, Long-Tu, Structural design and experimental research of a novel piezoelectric actuator, Journal of Synthetic Crystals, v 38, n SUPPL. 1, p 25-27, August 2009 20.Meng, Xiang-Yu; Chu, Xiang-Cheng; Bi, Xiao-Peng; Li, Long-Tu, Process and analysis of multilayer piezoelectric ceramic for micro-motor, Journal of Synthetic Crystals, v 38, n SUPPL. 1, p 72-76, August 2009 21.Chu, Xiang-Cheng; Wu, Jun-Fei; Xu, Zhi-Han; Li, Long-Tu, Vibration and fatigue of multilayer piezoelectric transformer, RARE METAL MATERIALS AND ENGINEERING, v 38 n 2, p226-229, 2009 22.Wu, Jun-Fei; Chu, Xiang-Cheng; Ji, Ye; Zhong, Liang; Li, Long-Tu, Design and property of a square cylinder type piezoelectric ultrasonic micromotor, RARE METAL MATERIALS AND ENGINEERING, v 38 n 2, p245-248, 2009 23.Chen, Xiangyu; Chu, Xiangcheng; Li, Longtu, Design and experimental study of piezoelectric ceramics linear motor, RARE METAL MATERIALS AND ENGINEERING, v 38 n 2, p241-244, 2009 24.Chu, Xiang-Cheng; Chen, Xiang-Yu; Li, Long-Tu, Disk-pivot structure micro piezoelectric actuator with bimorph, Optics and Precision Engineering, v 16, n 12, p 2366-2370, December 2008 25.Chu, Xiangcheng; Ma, Long; Yuan, Songmei; Li, Mengkai; Li, Longtu, Two-dimensional optical scanning of a piezoelectric cantilever actuator, Journal of Electroceramics, v 21, n 1-4 SPEC. ISS., p 774-777, December 2008 26.Wang, Baowei; Chu, Xiangcheng; Li, Longtu, A piezoelectric micropump based on MEMS fabrication, Key Engineering Materials, v 368-372 PART 1, p 215-217, 2008 27.Chu, Xiangcheng; Huang, Jinding; Li, Longtu; Gui, Zhilun, Finite element analysis and design of monolithic multilayer piezoelectric micromanipulator, Key Engineering Materials, v 368-372 PART 1, p 218-220, 2008 28.Ji, Ye; Chu, Xiangcheng; Li, Longtu; Gui, Zhilun, A novel piezoelectric micro-motor using multilayer co-firing piezoelectric ceramics, Key Engineering Materials, v 368-372 PART 1, p 208-210, 2008 29.Chu, Xiangcheng; Long, Ma.; Li, Longtu; Gui, Zhilun, A micro piezoelectric motor with a disk-pivot structure, Key Engineering Materials, v 368-372 PART 1, p 202-203, 2008 30.Wang, Baowei; Chu, Xiangcheng; Li, Enzhu; Li, Longtu; Gui, Zhilun, Properties of (Na, Bi)TiO3-Ba(Zr, Ti)O3 lead-free piezoelectric ceramic, RARE METAL MATERIALS AND ENGINEERING, v 37 n 1, p493-495, JAN 2008 31.Long, Ma; Xiangcheng, Chu; Longtu, Li; Songmei, Yuan, Resonant modes of piezoelectric disc structure and their application in micro ultrasonic motors, Key Engineering Materials, v 336-338 I, p 345-347, 2007 32.Wang, Baowei; Chu, Xiangcheng; Li, Enzhu; Li, Longtu; Gui, Zhilun, Preparation and properties of K doped (Bi, Na)TiO3-Ba(Zr, Ti)O3 lead-free piezoelectric ceramic, RARE METAL MATERIALS AND ENGINEERING, v 36 n 1, p425-427, 2007 33.Chu, Xiangcheng; Huang, Jinding; Li, Sixian; Li, Lontu; Gui, Zhilun, Simulation of 3-D multilayer piezoelectric micromanipulator, RARE METAL MATERIALS AND ENGINEERING, v 36 n 1, p513-516, 2007 34.Chu, Xiangcheng; Yan, Renbo; Gong, Wen; Li, Lontu, Analysis of dynamic response for piezoelectric vibration converter by finite element simulation, Key Engineering Materials, v 336-338, p 335-337, 2007 35.Wang, Baowei; Chu, Xiangcheng; Li, Enzhu; Li, Longtu, Simulations and analysis of a piezoelectric micropump, Ultrasonics, v 44, n SUPPL., p e643-e646, December 22, 2006 36.Chu, Xiangcheng; Ma, Long; Li, Longtu, A disk-pivot structure micro piezoelectric actuator using vibration mode B11, Ultrasonics, v 44, SUPPL., p e561-e564, December 22, 2006
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